U.S. patent application number 11/415735 was filed with the patent office on 2007-08-30 for unique space time adaptive system (uss).
Invention is credited to Thomas J. Cataldo.
Application Number | 20070200750 11/415735 |
Document ID | / |
Family ID | 38374013 |
Filed Date | 2007-08-30 |
United States Patent
Application |
20070200750 |
Kind Code |
A1 |
Cataldo; Thomas J. |
August 30, 2007 |
UNIQUE SPACE TIME ADAPTIVE SYSTEM (USS)
Abstract
A method of detecting radar returns and measuring their
parameters with or without clutter present and no clutter
cancellation employed which includes transmitting at least one
pulse; processing the returns surpassing a threshold detected in
one range azimuth bin and by processing and separating out the
returns based on their different range and azimuth. Another method
includes transmission of many pulses and has minimum of one channel
return surpassing detected threshold, which is detected in one
range Doppler bin. The method also includes processing and thereby
separating out the returns based on their different radial velocity
and or azimuth and comparing the returns to a database of expected
returns and adaptively processing returns that do not correspond to
the expected returns. The method identifies the non-corresponding
returns as indicative of at least one of clutter, land sea
interface, clutter discretes and antenna sidelobe returns each
without utilizing clutter cancellation.
Inventors: |
Cataldo; Thomas J.;
(Commack, NY) |
Correspondence
Address: |
ALFRED M. WALKER
225 OLD COUNTRY ROAD
MELVILLE
NY
11747-2712
US
|
Family ID: |
38374013 |
Appl. No.: |
11/415735 |
Filed: |
May 1, 2006 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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60677576 |
May 4, 2005 |
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Current U.S.
Class: |
342/159 ;
342/104; 342/107; 342/109; 342/113; 342/115; 342/118; 342/160;
342/162; 342/175; 342/195; 342/89; 342/90; 342/91; 342/94 |
Current CPC
Class: |
G01S 13/5246 20130101;
G01S 13/9064 20190501; G01S 2013/0254 20130101; G01S 13/22
20130101 |
Class at
Publication: |
342/159 ;
342/089; 342/090; 342/091; 342/094; 342/104; 342/107; 342/109;
342/113; 342/115; 342/118; 342/160; 342/162; 342/175; 342/195 |
International
Class: |
G01S 13/00 20060101
G01S013/00; G01S 13/52 20060101 G01S013/52 |
Claims
1. A method employing an electronic array mounted on a moving
platform and a unique space time adaptive system to detect a
plurality of radar returns in a same bin and their parameters with
or without clutter present, comprising the steps of: a)transmitting
at least one pulse; b) receiving said plurality of radar returns
from said at least one pulse over at least one channel; c)
processing said radar returns into range bins and determining
whether said radar return surpasses a threshold; d) processing said
radar returns that exceed said threshold to determine radial
velocity, range, and azimuth based upon each radar return of said
plurality of radar returns having different radial velocity and
azimuth without utilizing clutter cancellation; and e) comparing
said radar returns to a database of expected radar returns and
adaptively processing radar returns that do not correspond to the
expected radar returns, to identify said non-corresponding radar
returns as indicative of at least one of clutter, a stationary
target having moving elements, a land sea interface, clutter
discretes, and antenna sidelobe returns without utilizing clutter
cancellation.
2. The method of claim 1 wherein said at least one pulse is a
plurality of pulses, said transmission occurs at a specific
frequency, and said at least one of a channel is a plurality of
channels for synchronous reception.
3. The method of claim 1 further comprising the steps of: a)
transmitting required pulses; b) processing many said N channels
with as few as one or two pulses at a time; and, c) attaining
additional said channel data.
4. The method of claim 2 further comprising the steps of: a)
receiving data pulse in a first channel and a second channel at a
predetermined frequency; b) receiving said pulse data 1 to M
received in channel 1; c) receiving said time pulse data in channel
2 delayed, wherein said delay is equal to the number of radar
returns detected in a range Doppler bin; d) over sampling said
pulse data and said delayed pulse data in said range bin to a
desired level; e) zero filling said pulse data and said delayed
pulse data to said desired level to increase pulse data and delayed
pulse data frequency samples; f) multiplying said pulse data and
said delayed pulse data by a weighting function obtaining a
spectrum of said pulse data and said delayed pulse data; g)
thresholding, in each range Doppler bin, said pulse data and said
delayed pulse data for significant radar returns for a
determination of the parameters including radial velocity, range,
and azimuth without utilizing clutter cancellation; h) if the
number of said returns is three or less the solution is easily
obtained analytically but if there is a sum of greater than three
returns, since said solution is long and complicated an assist is
utilizable by the association of determinations of the solutions in
adjacent said range Doppler bins as being the same with said range
Doppler under processing and where there is known said clutter
return, its respective radial velocity is zero; i) determining
azimuth by processing another frequency sample; j) determining
range by processing another range sample; k) repeating steps a)
through f) to process another linear array for measuring height of
a radar return; l) delaying said pulse data and said delayed pulse
data to determine an amplitude and phase change due to frequency to
calculate horizontal velocity and vertical tangential velocity; m)
delaying said pulse data and said delayed pulse data to determine
an amplitude and phase change due to range, to calculate a radial
velocity; n) delaying a change in phase and amplitude change due to
height to calculate a vertical tangential velocity; and, o)
comparing said radar returns to a database of expected radar
returns and adaptively processing radar returns that do not
correspond to the expected radar returns to identify said
non-corresponding radar returns as indicative of clutter, a
stationary target having moving elements, a land sea interface,
clutter discretes, and antenna sidelobe returns without utilizing
clutter cancellation.
5. The method of claim 2 further comprising the steps of: a)
receiving pulse data in a first channel and a second channel at a
predetermined frequency, wherein said pulse data, 1 to M is
received in said first channel and said first channel pulse data is
delayed a rate equal to a number of expected radar returns, and
said pulse data in said second channel is delayed from said first
channel and said second channel is also delayed at said rate; b)
over sampling said pulse data and said delayed pulse data in said
range bin to a desired level; c) zero filling said pulse data and
said delayed pulse data to said desired level to increase pulse
data and delayed pulse data frequency samples; c(i) multiplying
said pulse-data and said delayed pulse data by a weighting
function, obtaining a spectrum of said pulse data and said delayed
pulse data; d) thresholding, in each range Doppler bin, said pulse
data and said delayed pulse data for significant radar returns for
a determination of the parameter including radial velocity, range,
and azimuth without utilizing clutter cancellation; e) determining
azimuth by processing another frequency sample; f) determining
range by processing another range sample; g) repeating steps a)
through f) to process another linear array for measuring height of
a radar return; h) delaying said pulse data and said delayed pulse
data to determine an amplitude and phase change due to frequency to
calculate horizontal velocity; i) delaying said pulse data and said
delayed pulse data to determine an amplitude and phase change due
to range to calculate a radial velocity; j) delaying a change in
phase and amplitude change due to height to calculate a vertical
tangential velocity; and, k) comparing said radar returns to a
database of expected radar returns and adaptively processing radar
returns that do not correspond to the expected radar returns to
identify said non-corresponding radar returns as indicative of
clutter, a stationary target having moving elements, a land sea
interface, clutter discretes, and antenna sidelobe returns without
utilizing clutter cancellation.
6. The method of claim 3 further comprising the steps of: a)
receiving channel data in a first channel 1 to M and a second
channel at a predetermined frequency, wherein said pulse 1 to pulse
2 of said first channel data is delayed a rate equal to a number of
expected radar returns, and said channel data in said second
channel is delayed D from said first channel and said second
channel is also delayed at said rate; b) over sampling said channel
data and said delayed channel data in said range bin to a desired
level; c) zero filling said channel data and said delayed channel
data to said desired level to increase channel data and delayed
channel data frequency samples; c(i) multiplying said channel data
and said delayed channel data by a weighting function obtaining a
spectrum of said channel data and said delayed channel data; d)
thresholding, in each range Doppler bin, said channel data and said
delayed channel data for significant radar returns for a
determination of the parameters including radial velocity, range,
and azimuth without utilizing clutter cancellation; e) determining
Doppler peak by processing another space frequency sample; f)
determining range by processing another range sample; g) repeating
steps a) through f) to process another linear array for measuring
height of a radar return; h) delaying said channel data and said
delayed channel data to determine an amplitude and phase change due
to space frequency to calculate horizontal velocity i) delaying
said pulse data and said delayed pulse data to determine an
amplitude and phase change due to range to calculate a radial
velocity; j) delaying a change in phase and amplitude change due to
height to calculate a vertical tangential velocity; and, k)
comparing said radar returns to a database of expected radar
returns and adaptively processing radar returns that do not
correspond to the expected radar returns to identify said
non-corresponding radar returns as indicative of clutter, a
stationary target having moving elements, a land sea interface,
clutter discretes, and antenna sidelobe returns without utilizing
clutter cancellation.
7. The method of claim 3 further comprising the steps of: a)
receiving data in a first channel and a second channel data; b)
receiving said channel data 1 to N received in channel 1; c)
receiving said time pulse data in channel 2 space delayed, wherein
said delay is equal to the number of radar returns detected in a
range azimuth bin; d) over sampling said channel data and said
delayed channel data in said range bin to a desired level; e) zero
filling said pulse data and said delayed data to said desired level
to increase channel data and delayed channel data frequency
samples; f) multiplying said channel data and said delayed channel
data by a weighting function, obtaining a spectrum of said channel
data and said delayed channel data; g) thresholding, in each range
Doppler bin, said channel data and said delayed channel data for
significant radar returns for a determination of the parameters
including radial velocity, range, and azimuth without utilizing
clutter cancellation; h) if the number of said returns is three or
less the solution is easily obtained analytically but if there is a
sum of greater than three returns, since said solution is long and
complicated an assist is utilizable by the association of
determinations of the solutions in adjacent said range Doppler bins
as being the same with said range Doppler under processing and
where there is known said clutter return, its respective radial
velocity is zero; i) determining Doppler azimuth bin by processing
another frequency sample; j) determining range by processing
another range sample; k) repeating steps a) through f) to process
another linear array for measuring height of a radar return; l)
delaying said channel data and said delayed channel data to
determine an amplitude and phase change due to frequency to
calculate horizontal velocity; m) delaying said pulse data and said
delayed pulse data to determine an amplitude and phase change due
to range to calculate an unambiguously radial velocity; n) delaying
a change in phase and amplitude change due to height to calculate a
height; and, o) comparing and radar returns to a database of
expected radar returns and adaptively processing radar returns that
do not correspond to the expected radar returns to identify and
non-corresponding radar returns as indicative of clutter, a
stationary target having elements, a land sea interface, clutter
discretes, and antenna sidelobe returns without utilizing clutter
cancellation.
8. The method of claim 2 further comprising the steps of: a)
interleaving said received data pulses synchronously with at least
one interleaved channel at a predetermined frequency wherein said
pulse data is delayed a number of times equal to an expected number
of radar returns, said delayed pulse data is processed to a number
of interleaved sets of data with a corresponding aperture change;
b) processing said interleaved sets of data independently, wherein
a transmission array is centered between an aperture 1, and an
aperture 2, said interleaved channels forming a beam width portion
on each side of said transmission array, and changes in receive
apertures corresponding to a change in receive data in the
interleaved data with aperture change; c) over sampling said pulse
data and said delayed pulse data in said range bin to a desired
level; d) zero filling said pulse data and said delayed pulse data
to said desired level to increase said pulse data and said delayed
pulse data frequency samples; e) delaying at least one interleaved
channel a number of times equal to an expected number of radar
returns, wherein said at least one interleaved pulses is multiplied
by a weighting function and spectrum is processed; f) thresholding,
in each range Doppler bin, said pulse data and said delayed pulse
data for significant radar returns, for a determination of the
parameters including radial velocity, range, and azimuth without
utilizing clutter cancellation; g) if the number of said returns is
three or less the solution is easily obtained analytically but if
there is a sum greater than three returns, since said solution is
long and complicated an assist is utilizable by the association of
determinations of the solutions in adjacent said range Doppler bins
as being the same with said range Doppler under processing and
where there is known said clutter return, its respective radial
velocity is zero; h) processing two of said data and said data
delayed, thereby determining the total phase response of all said
returns from which is also calculated said return vectors; i)
calculation of the curve return ratio as a function of azimuth is
determined, wherein the azimuth of each return may be made from
real data of relatively high said clutter only at a number of
azimuths of the receive antennas or there is determined a prior
from said measured antenna patterns; j) taking the ratio of the
respective of said relatively high said clutter only return vectors
and from a prior calculation of the curve return ratio as a
function of azimuth there is compared to the ratio calculated from
a solution of odd and even sets of data to determine the azimuth of
each said return, from which the velocity of each return is
determined; k) determining peak Doppler by processing another
frequency sample; l) determining range by processing another
frequency sample; m) repeating steps a) through f) to process
another linear array for measuring height of a radar return; n)
delaying said pulse data and said delayed pulse data to determine
an amplitude and phase change due to frequency to calculate
horizontal velocity; o) delaying said pulse data and said delayed
pulse data to determine an amplitude and phase change due to range
to calculate a radial velocity; p) delaying a change in phase and
amplitude change due to height to calculate a vertical tangential
velocity; q) comparing said radar returns to a database of expected
radar returns and adaptively processing radar returns that do not
correspond to the expected radar returns to identify said
non-corresponding radar returns as indicative of clutter, a
stationary target having moving elements, a land sea interface,
clutter discretes, and antenna sidelobe returns without utilizing
clutter cancellation; and, r) if more than a dual channel is
available, process each said dual channel and correlate.
9. The method of claim 3 further comprising the steps of: a)
interleaving said received data pulses synchronously with at least
one interleaved channel at a predetermined frequency wherein said
channel data is delayed a number of times equal to an expected
number of radar returns, and said delayed pulse data is processed
to a number of interleaved said sets of data with a corresponding
aperture change; b) processing said interleaved sets of channel
data independently, wherein a transmission array is centered
between aperture 1, and aperture 2, said interleaved channels
forming a beam width portion of each side of said transmission
array, and changes in receive apertures corresponding to a change;
in receive data in the interleaved data with aperture change; c)
over sampling said pulse data and said delayed pulse data in said
range bin to a desired level; d) zero filling said channel data and
said delayed channel data to said desired level to increase said
channel data and said delayed channel data frequency samples; e)
delaying at least one interleaved channel a number of times equal
to an expected number of radar returns, wherein said at least one
interleaved pulses is multiplied by a weighting function and
spectrum processed; f) thresholding, in each range Doppler bin,
said pulse data and said delayed pulse data for significant radar
returns for a determination of the parameters including radial
velocity, range, and azimuth without utilizing clutter
cancellation; g) if the number of said returns is three or less the
solution is easily obtained analytically but if there is a sum
greater than three returns, since said solution is long and
complicated an assist is utilizable by the association of
determinations of the solutions in adjacent said range Doppler bins
as being the same with said range Doppler under processing and
where there is known said clutter return, its respective radial
velocity is zero; h) processing two of said data and said data
delayed, thereby determining the total phase response of all said
returns from which is also calculated said return vectors; i)
calculation of the curve return ratio as a function of azimuth is
determined, wherein the azimuth of each return may be made from
real data of relatively high said clutter only at a number of
azimuths of the receive antennas or optionally there is determined
a prior from said measured antenna patterns; j) taking the ratio of
the respective of said relatively high said clutter only return
vectors and from a prior calculation of the curve return ratio as a
function of azimuth there is compared to the ratio calculated from
a solution of odd and even sets of data to determine the azimuth of
each return, from which the velocity of each said return is
determined; k) determining peak Doppler by processing another
frequency sample; l) determining range by processing another range
sample; m) repeating steps a) through f) to process another linear
array when height of a radar return is to be measured; n) delaying
said channel data and said delayed channel data to determine an
amplitude and phase change due to frequency to calculate horizontal
velocity; o) delaying said pulse data and said delayed pulse data
to determine an amplitude and phase change due to range to
calculate precise range; p) delaying a change in phase and
amplitude change to determine height; q) comparing said radar
returns to a database of expected radar returns and adaptively
processing radar returns that do not correspond to the expected
radar returns to identify said non-corresponding radar returns as
indicative of clutter, a stationary target having moving elements,
a land sea interface, clutter discretes, and antenna sidelobe
returns without utilizing clutter cancellation; and, r) if more
than dual channel is available, process each said dual channel and
correlate.
10. The method of claim 2 further comprising the steps of: a)
receiving pulse data in a first channel and a second channel at a
predetermined frequency, wherein said pulse data 1 to M is received
in said first channel and said first channel pulse data is delayed
a rate equal to a number of expected radar returns, and said pulse
data in said second channel is delayed D from said first channel
and said second channel is also delayed at said rate; b) over
sampling said pulse data and said delayed pulse data in said range
bin to a desired level; c) zero filling said pulse data and said
delayed pulse data to said desired level to increase pulse data and
delayed pulse data frequency samples; c(i) multiplying said pulse
data and said delayed pulse data by a weighting function, thereby
obtaining a spectrum of said pulse data and said delayed pulse
data; d) thresholding, in each range Doppler bin, said pulse data
and said delayed pulse data for significant radar returns for a
determination of amplitude and phase of each radar return; e)
determining by processing another frequency sample of precise peak
of frequency; f) determining range by processing another range
sample precise range; g) repeating steps a) through d) to process
another linear array when precise amplitude and phase between
linear arrays due to height of a radar return is to be measured; h)
delaying said pulse data and said delayed pulse data to determine
an amplitude and phase change due to frequency to calculate
horizontal velocity and vertical tangential velocity; i) delaying
said pulse data and said delayed pulse data to determine and
amplitude and phase change due to range to calculate an
unambiguously radial velocity; j) delaying a change in phase and
amplitude change due to height to calculate a vertical tangential
velocity; and, k) comparing said radar returns to a database of
expected radar returns and adaptively processing radar returns that
do not correspond to the expected radar returns to identify said
non-corresponding radar returns as indicative of clutter, a
stationary target having moving elements, a land sea interface,
clutter discretes, and antenna sidelobe returns without utilizing
clutter cancellation.
11. The method of claim 2 further comprising the steps of: a)
receiving pulse data in a first channel and a second channel at a
predetermined frequency, wherein said pulse data 1 to M is received
in said first channel and said first channel pulse data is delayed
a rate equal to a number of expected radar returns, and said pulse
data in said second channel is delayed D from said first channel
and said second channel is also delayed at said rate: b) over
sampling said pulse data and said delayed pulse data in said range
bin to a desired level; c) zero filling said pulse data and said
delayed pulse data to said desired level to increase pulse data and
delayed pulse data frequency samples; c(i) multiplying said pulse
data and said delayed pulse data by a weighting function obtaining
a spectrum of said pulse data and said delayed pulse data; d) said
data is delayed a number of times equal to the expected number of
said returns and each set of said delayed data is processing "M"
data points in each simultaneous apertures of data, a portion of
the beam width from the transmission array on each side; e)
determining by processing another frequency sample of precise peak
of frequency; f) determining range by processing another range
sample precise range; g) repeating steps a) through d) to process
another linear array when precise amplitude and phase between
linear arrays due to height of a radar return is to be measured; h)
delaying said pulse data and said delayed pulse data to determine
an amplitude and phase change due to frequency to calculate
horizontal velocity and vertical tangential velocity; i) delaying
said pulse data and said delayed pulse data to determine an
amplitude and phase change due to range to calculate an
unambiguously radial velocity; j) delaying a change in phase and
amplitude change due to height to calculate a vertical tangential
velocity; and, k) comparing said radar returns to a database of
expected radar returns and adaptively processing radar returns that
do not correspond to the expected radar returns to identify said
non-corresponding radar returns as indicative of clutter, a
stationary target having moving elements, a land sea interface,
clutter discretes, and antenna sidelobe returns without utilizing
clutter cancellation.
12. The method of claim 2 further comprising the steps of: a)
receiving pulse data in a first channel and a second channel at a
predetermined frequency, wherein said pulse data 1 to M is received
in said first channel and said first channel pulse data is delayed
a rate equal to a number of expected radar returns, and said pulse
data in said second channel is delayed D from said first channel
and said second channel is also delayed at said rate; b) over
sampling said pulse data and said delayed pulse data in said range
bin to a desired level; c) zero filling said pulse data and said
delayed pulse data to said desired level to increase pulse data and
delayed pulse data frequency samples; c(i) multiplying said pulse
data and said delayed pulse data by a weighting function obtaining
a spectrum of said pulse data and said delayed pulse data; d) said
data is delayed a number of times equal to the expected number of
said returns and each set of said delayed data is processing "M"
data points in each simultaneous apertures of data, a portion of
the beam width from the transmission array on each side; e)
determining by processing another frequency sample precise peak of
frequency; f) determining range by processing another range sample
precise range; g) repeating steps a) through d) to process another
linear array when precise amplitude and phase between linear arrays
due to height of a radar return is to be measured; h) delaying said
pulse data and said delayed pulse data to determine an amplitude
and phase change due to frequency to calculate horizontal velocity
and vertical tangential velocity; i) delaying said pulse data and
said delayed pulse data to determine an amplitude and phase change
due to range to calculate an unambiguously radial velocity; j)
delaying a change in phase and amplitude change due to height to
calculate a vertical tangential velocity; and, k) comparing said
radar returns to a database of expected radar returns and
adaptively processing radar returns that do not correspond to the
expected radar returns to identify said non-corresponding radar
returns as indicative of clutter, a stationary target having moving
elements, a land sea interface, clutter discretes, and antenna
sidelobe returns without utilizing clutter cancellation.
13. The method of claim 2 further comprising: employing an
electronic scanned array and as few as one linear array and few as
one pulse mounted on a moving platform in line with said platform
motion and a unique space time adaptive system to detect returns
and measure their parameters including velocity, azimuth and range
accurately with said clutter and other said returns detected in the
same range Doppler bin, where there is no said clutter cancellation
of any kind is required such as said clutter covariance matrix,
said clutter training data with or without knowledge aided said
clutter, comprising the steps of: a) receiving data transmission is
a minimum of said one pulse of a pulsatory nature; b) optionally
over sampling in said range to desired level for all said data; c)
optionally zero fill said data to desired level to attain close
frequency samples or all said data; d) said data is delayed a
number of times equal to the expected number of said returns and
each set of said delayed data is processed wherein the improvement
comprises: e) each said data is delayed a number of times equal to
the expected number of returns, each is multiplied by a weighting
function and processed with a technique such as FFT for obtaining
spectrum of said data; f) in each said range Doppler bin processed
there is thresholded to detect the presence of significant said
returns, if so, contains an addition of all said returns and
information such as range, radial velocity and azimuth, wherein
this determination constitutes sets of simultaneous equations
solved directly, with no clutter cancellation of any kind required,
for each said return to determine its said velocity, azimuth and
range; g) if the number of said returns is three or less the
solution is easily obtained analytically; h) processing said data
and said data delayed determining the total phase response of all
returns from which is also calculated the return vectors; i)
determining the total phase response of all returns from which is
also calculated the return vectors; j) processing adjacent range
azimuth bins and determining precise range; k) optionally
processing adjacent azimuth bin and Doppler bin where mover and
clutter is processed with the same results in determining a
solution's precise azimuth; l) optionally processing other linear
arrays where mover and clutter are to be processed with same
results in determining solutions and determining precise height; m)
processing a significant channel later as in steps i), j) and k)
and obtain respectively azimuth change, and height change which
determines azimuth change; n) from unambiguous azimuth change there
is determined azimuth; o) from azimuth and total velocity
determined the radial velocity is calculated; p) thereby attaining
the precise range, azimuth and height; q) optionally processing
another pulse if another pulse is obtained and obtaining another
close solution; r) optionally changing transmission frequency to
avoid jamming and correlating results, wherein the transmission
frequency is changed enough to avoid jamming, but not enough to
affect the operation of system; s) if there are significant returns
of said returns, zero velocity and said return is said clutter,
then non zero velocity of said return(s) are post processed to
determine the type of said return such as mover, sidelobes, land
sea interface, jamming, rotational motion targets, noise, jamming,
others; and, t) whereby the return identification and accurate
parameters of said returns have been determined without any clutter
cancellation at all.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the benefit, Under 35 U.S.C. .sctn.
119(e), of U.S. Provisional Application No. 60/677,576, filed May
4, 2005, which is hereby incorporated by reference.
BACKGROUND OF THE INVENTION
[0002] 1. Field of Invention
[0003] The field of the invention relates generally to radars and
more specifically to a radar mounted on a moving platform employing
an electronic scanned array with a transmission array and receive
array (channel) or arrays (channels).
[0004] 2. Description of the Related Art
[0005] In the field of this invention, detecting radar returns as
moving targets and rejecting others such as clutter and others has
been a challenge for many years. Obtaining a moving object's
velocity, azimuth, and measurement of its parameters have been an
objective of many radar systems. In relatively recent years with
the increased processing and storage of improved integrated
circuits, space time adaptive processing ("STAP") has become more
practical.
[0006] U.S. Pat. No. 5,563,601 (the "'601 patent") issued Oct. 8,
1996 and entitled TWO PORT CLUTTER SUPPRESSION INTERFEROMETRY
SYSTEM FOR RADAR DETECTION OF MOVING TARGETS is incorporated, in
it's entirety, by reference herein. The '601 discloses, in part, a
two port radar system for detecting and measuring range, azimuth
and velocity of radar returns. This patent utilizes the detection
of shadows to locate the targets azimuth and not employing any
other technique in combination with it and it is meant for land
clutter and not sea clutter.
[0007] U.S. Pat. No. 6,633,253 (the '253 patent") issued and
entitled DUAL SYNTHETIC APERTURE RADAR SYSTEM is incorporated, in
its entirety, by reference herein. The '253 patent discloses, in
part, a system which utilizes an electronic scanned array with two
receive channels (arrays) on an airborne platform. The system
employs displaced phase center antenna (DPCA) techniques to cancel
clutter and detect moving targets and measures its range, velocity
and azimuth accurately.
SUMMARY
[0008] The UNIQUE SPACE TIME ADAPTIVE SYSTEM (USS) system is unique
in a number of ways. For example, it does not require clutter
cancellation of any kind and it may employ as few as one channel or
as little as one pulse. It is as accurate or more accurate as any
known STAP system, hardware and dwell time and processing are a
minimum. It utilizes a combination of techniques, but basically
employs single or two or more equal receive arrays or pulses with
or without DPCA methodology, detects returns and measures their
velocity, azimuth and range. It also takes different looks in time
to measure differences with time, for purpose of determining radial
velocity unambiguously and tangential and vertical tangential
velocity.
[0009] In one embodiment, a system utilizes one, two, or more equal
receive channels processed with "M" pulses of time data. In another
embodiment, the system implements as few as one or two pulses of
time data and has "N" channels of data employed and processed.
[0010] Both systems will detect a return or number of returns in
the same range doppler or range azimuth bin such as clutter,
target, noise, jamming, etc and identify them out measure there
three dimensional position and velocity. This is performed without
employing any clutter cancellation of any kind.
[0011] The returns are processed to detect returns and detect
moving targets of interest and reject unwanted returns such as
clutter, sidelobes, movers, multipath returns, others.
[0012] USS does not require clutter cancellation therefore there is
no clutter covariance matrix or training data involved or knowledge
aided information. Channel matching is not required. USS has the
ability to handle more returns than clutter and target per range
doppler bin (RDB) or range azimuth bin (RAZ) and determine there
range, velocity and azimuth accurately. Thresholding and post
processing of the returns will determine if returns are clutter,
moving target, antenna sidelobes, filter sidelobes, multipath
returns, etc. It has the ability to handle ground moving targets,
high speed targets, ship detection and identification in a unique
and simplified manner.
BRIEF DESCRIPTION OF DRAWINGS
[0013] So that the manner in which the above recited features of
the present invention can be understood in detail, a more
particular description of the invention, briefly summarized above,
may be had by reference to embodiments, some of which are
illustrated in the appended drawings. It is to be noted, however,
that the appended drawings illustrate only typical embodiments of
this invention and are therefore not to be considered limiting of
its scope, for the invention may admit to other equally effective
embodiments.
[0014] FIG. 1--depicts top views of some of the positions that
ships may be as relative to the radar and the position the ship is
detected and the actual ship position;
[0015] FIG. 1A--depicts the Ship moving towards the radar;
[0016] FIG. 1B--depicts the Ship heading away from the radar;
[0017] FIG. 1C--depicts the Ship to the left of and perpendicular
to the radar;
[0018] FIG. 1D--depicts the Ship to the right of and perpendicular
to the radar;
[0019] FIG. 2--depicts a high level block diagram in accordance
with the invention;
[0020] FIG. 3--depicts an embodiment of a chart for determination
of the height of ships when detected and the solution of the height
dependent on various factors;
[0021] FIG. 4--depicts an embodiment of a Ship Parameter
Measurement Chart--in accordance with the invention;
[0022] FIG. 5--depicts an embodiment of a Chart of Proposed Systems
and Characteristics in accordance with the invention;
[0023] FIG. 6--depicts an illustrative of techniques for all
systems such as over ocean, over land, and in the air;
[0024] FIG. 7--depicts an embodiment of a Delta T technique with
additional DPCA delays in accordance with the invention;
[0025] FIG. 8--depicts an embodiment of a Delta D technique with
additional time delays in accordance with the invention;
[0026] FIG. 9--depicts an embodiment of a block diagram of a system
in accordance with the invention;
[0027] FIG. 10--depicts an exemplary illustration of a relationship
of detection phase to radial velocity phase to azimuth phase in
accordance with the invention;
[0028] FIG. 11 depicts an exemplary illustration of delta T
combined with delta I (interleaved pulses--two in example) and
aperture change synchronized with interleaved data in accordance
with the invention;
[0029] FIG. 12 depicts examples of processing returns with the
association of returns processed in adjacent range and/or doppler
bins in accordance with the invention;
[0030] FIG. 13 depicts an illustrative single aperture system with
interleaved pulses with change in aperture in accordance with the
invention; and
[0031] FIG. 14 depicts an illustrative single aperture system with
no interleaved pulses with change in aperture in accordance with
the invention.
DETAILED DESCRIPTION
I. A--Basic Concept of a Unique Space Time Adaptive Radar System
(USS)
[0032] It is to be noted that the description of this disclosure
are illustrative and cannot show all possible implementations that
may be employed from the information in the disclosure by a person
of ordinary skill in the state of the art. Therefore this
disclosure is illustrative and not limited of the scope of the
proposed invention and not limited in the scope of the role in
obtaining the objective of this disclosure.
[0033] USS processing system is applicable to all frequencies. The
system is able to utilize all radio frequencies limited on the low
end by the size of the antenna and on the high end by the practical
limitations of short waves.
Illustrated in the patent application is a one dimensional array.
The implementation may also be with two dimensional arrays as
well.
II. B Basic Operations, Equations and Methodology Fundamental to
all of the Systems Employed in this Disclosure
[0034] A--Fundamental Techniques Employed:
[0035] The mathematical fundamental equations, the radar analysis
and the computer simulation for all systems to obtain the objective
of the disclosure are presented. The techniques are as follows:
[0036] 1) Basic System is with one aperture, one PRF and one
transmission frequency. If the ambiguous range and or velocity are
to be increased another PRF and/or transmission frequency is
implemented in the second aperture. The basic techniques that are
employed are the following: [0037] a) Change in time (.DELTA.T)
[0038] b) Change in delay (.DELTA.D) [0039] c) Change in frequency
(.DELTA.F) [0040] d) Change in range (.DELTA.R) [0041] e)
Interleaved pulses (.DELTA.I) [0042] f) Groups of data (.DELTA.G)
[0043] g) Change in channel (.DELTA.C) [0044] h) Change in aperture
(.DELTA.A) [0045] i) Simultaneous beams(antennas) (.DELTA.S) [0046]
j) And/or any combinations of the techniques above and
correlated
[0047] IIC--USS Section
[0048] 1--Processing multiple returns (greater than three) employ a
number of techniques to reduce processing such as known clutter
reduces number of unknown returns by one, association of known
returns close to processed returns may reduce number of unknown
returns by one or more and analytic solution which performs well
with three or less unknown returns, and the candidate phi technique
which will correlate with the other techniques.
[0049] As the number of expected returns increases, the solution is
attainable but more difficult and complicated. To aid in this
problem any prior knowledge such as clutter is present, we know one
of the returns has "0" or near "0" velocity and/or an association
technique where adjacent RDBs processed indicates the return under
test velocity of some or more of its returns. An analytic technique
has been developed but greatly facilitated by previous
techniques.
[0050] 2--.DELTA.F processing is performed as a check on the
azimuth, it takes another sample(s) in frequency close to initial
sample and process this data the same as the initial sample and
should have the same solutions for velocity of returns but the
resulting returns amplitude and phase change gives the indication
of where the peaks of the returns resides and therefore accurate
azimuth determination. Also if addition data is processed it should
remain the same
[0051] 3--.DELTA.R processing is performed to determine the range
more accurately, it takes another sample in range close to initial
sample and process this data the same as initial sample and should
have the same solutions for velocity of returns but the resulting
returns amplitude and phase change gives the indication of where
the peaks of the returns resides and therefore the accurate range
determination Also if addition data is processed it should remain
the same
[0052] 4--.DELTA.H processing. If implementing a planar array,
processing as performed on the first linear array is done on the
other linear arrays, the same or close to same solutions for
.PHI..sub.O and .PHI..sub.1 (radial velocity of first and second
return) and .PHI..sub.AO and .PHI..sub.A1 (azimuth of first and
second returns). Also if addition data is processed it should
remain the same.
[0053] Taking next the solutions for M0 and M1 for processing each
linear array solves for the change in phase of M0 and M1, since the
amplitude changes and is proportional to the height of the
return.
[0054] If the returns are considered far field and the vertical
spacing of the arrays are .lamda./2 and .lamda.is the wavelength
and the angle the radar waves are making with the return is
.theta., the sine .theta. is proportional to the height of return
divided by the slant range. The phase differences between the
linear arrays is .lamda./2* sine .theta.*.pi./180 in radians will
give the height of the return where sine .theta.=H/R and H=R*sine
.theta. (H--height and R--range). The phase difference will give
the height of the return (illustrated in FIGS. 3 and 4). The phase
difference from linear array to linear array should be same or
close to same.
[0055] In the multi pulse technique processing a significant time
later the data is processed identically the difference in
height(phase) will give the vertical tangential velocity together
with the horizontal tangential velocity give the total tangential
velocity vector and add that to unambiguous radial velocity gives
the total three dimensional velocity vector.
[0056] 5--Applying to all systems, if we obtain multiple looks at
the return we will determine the unambiguous radial velocity and
tangential velocity and greater accuracy in determining the return
range, velocity and azimuth.
[0057] Multilooks is defined as a look with data point 1 to N and
delay the data a portion of the N point such as N/4 and adding N/4
points at the end and performing the same operations. This will
result in the increased capability as stated.
[0058] When the data is delayed and reprocessed as the first set of
data the returns radial motion will be measured by the number of
range bins or part of a bin traveled in this time
(.DELTA.R/.DELTA.T) gives the true velocity of the return and will
resolve the unambiguous velocity, if any, of the return without
resorting to another PRF and saves time. It will also be a check on
the radial velocity.
[0059] The horizontal tangential velocity will also be determined
which could not be determined before as a measure of
(.DELTA.D/.DELTA.T) doppler bins moved in the time difference and
the phase difference between linear arrays will give the height
difference, .DELTA.H/.DELTA.T, hence vertical tangential velocity.
Hence, the total velocity of the return is determined and not only
the radial velocity, the ratio of the radial velocity to the
horizontal and vertical tangential velocity will give the angle the
return is pointing in space.
[0060] Multi-looks of the return will result in better parameter
estimation of the return and estimation of the range, velocity and
azimuth.
[0061] 6--IMPLEMENTING ANOTHER PRF OR PRFs in the multipulse system
adds additional capability in determining unambiguous radial
velocity, ability to separate out the number of returns that are
detected in the same RDB and determine there velocities, reduced
clutter area competing in same RDB with other returns in both PRFs.
Also other returns that occur in same PRF in one PRF do not occur
in the same manner in the other PRF.
[0062] a. The clutter is present in one PRF is different in the
other PRF and consequently the clutter common to the two PRFs may
be reduced by as much as 50% and help significantly in determining
the nature of returns by reducing the number of returns detected in
one range bin by at least one. The returns will occur in the same
range bin or close to same range bin when one PRF is followed by
the other PRF. This occurs when the ambiguous velocity is greater
than that due to the lower PRF.
[0063] b. When the last condition exists as in previous paragraph
the clutter and returns in the first PRF occur in different doppler
bins and have the ability in one PRF a much easier ability to
process many returns than occur in the other RDB.
[0064] c. When one solution for velocity is determined in one PRF
then knowing the PRFs the other radial velocity is determinable in
the other PRF consequentially making it easier to determine the
solution for velocities when four or more returns are detected in
the same RDB.
[0065] d. When a return is detected in both PRFs the ability to
determine the unambiguous velocity is increased significantly
therefore the .DELTA.R evaluation of obtaining the unambiguous
velocity is much more accurate and effective.
[0066] e. All of the above makes the ability to determine the
identification of returns when the number per RDB is high
significantly more easily attainable. Of course more than two any
number of PRFs may be implemented.
[0067] 7--Post Detection Processing
[0068] Since as a result of processing we have to sort out the type
of returns detected. This may be movers, clutter, multipath
returns, antenna sidelobes, filter side lobes, land sea interface
and others. This presents a challenge to mathematically analyze the
returns and/or gave a data base that assist in categorizing the
returns.
[0069] Isodop correction for the velocity of the return, focusing
the array may be performed to enhance the accuracy of the
system.
Motion compensation relative to the boresight of the antenna is
assumed.
[0070] Add ISAR processing for further classification of the ship
when the parameters are processed.
[0071] 8--DPCA principles are applied in a number of techniques. To
illustrate the principles and the equations involved an example
will be presented.
[0072] Antenna length--eleven feet
[0073] TRANSMISSION ARRAY--ELEVEN FEET
[0074] Number of receive arrays--two of 5.5 feet each
[0075] PRF-1000 HZ
[0076] Velocity of platform--500 feet/second
[0077] Number of pulses--64
[0078] For DPCA compensation due to array two not traveling the
ideal distance of 2.75 feet in time equivalent of the distance is a
phase in the frequency domain. Expressing this in equation form we
have the following:
[0079] If there is no delay between array 1 and array 2 this is a
distance equal to 2.75 feet. This distance in time equivalent
equals 2.75 feet/500 feet/sec (velocity of the platform) which is
5.5 milliseconds (D/2V). .PHI. CO = 2 .times. .PI. .times. .times.
FT ##EQU1## where ##EQU1.2## T = D / 2 .times. V ##EQU1.3## and
##EQU1.4## F = F R .times. K / N ##EQU1.5## where ##EQU1.6## F R
.times. .times. is .times. .times. the .times. .times. PRF
##EQU1.7## and ##EQU1.8## N .times. .times. is .times. .times. the
.times. .times. number .times. .times. of .times. .times. PRIs = 2
.times. .PI. .times. .times. F R .times. K / ND / 2 .times. V =
.PI. .times. .times. F R .times. KD / NV ##EQU1.9## where
##EQU1.10## K .times. .times. is .times. .times. the .times.
.times. filter .times. .times. number ##EQU1.11## [0080] is the
phase compensation .PHI..sub.CO is the phase compensation for DPCA
OPERATION .PHI..sub.CE is the phase compensation error for DPCA
OPERATION .PHI..sub.CE=.pi.F.sub.RKD/2NV
[0081] The phase compensation error may now be calculated for each
delay starting with no delay where time equal 5.5 milliseconds and
substituting all parameters in the equation we get 9.8 degrees and
for next time for succeeding pulse is 7.0 degrees and the next is
4.2 degrees and the next is 1.4 degrees. It is observed that the
change in phase compensation (.DELTA.K.sub.D0) is constant.
[0082] Since this is true regardless of change in increment since
it is constant (.DELTA.x). The first phase compensation depends on
time and position in filter of return. The phase compensation term
is known (K.sub.D0) but not the position in the filter (Yo).
[0083] 9--Other Factors [0084] a. Ocean combined with overland.
capability and employing the phase corrections and phase
coefficient if necessary as explained in DSARS patent. [0085] b.
The mode of operation depends on many factors such as range,
surveillance, tracking or spot light operation, sea state, etc.
[0086] c. Surveillance mode may be combined with spot image mode.
[0087] Wake and bow wave signatures of ships signatures as a
function of their velocity and direction of the ship in help in
classification of ships. [0088] d. Surveillance mode could be a one
antenna transmit and receive system. [0089] e. High sea state
conditions create shadow conditions that could be employed for
better processing. [0090] f. In the ocean the place where the ship
actually exists there is no return have there azimuth at this
location [0091] g. Surveillance plus spot image mode may be
combined to reduce dwell time and obtain maximum information per
unit time. [0092] h. This technique may be extended to space borne
operations
[0093] Problem Areas [0094] a) High clutter sea states are a big
problem area and challenge to perform meaningful operations. [0095]
b) Long dwell time to perform accurate determinations. This is the
reason for decreased spacing of doppler bins and increased sampling
per range bin might ameliorate that condition. [0096] c) Long range
makes things very difficult. [0097] d) Performing surveillance and
tracking at the same time as classification of ships. [0098] e).
Operate without change in time operation for the surveillance
mode.
[0099] 10--Block Diagram of System
[0100] For the over ocean capability this is a simplified system as
illustrated in FIGS. 1 to 5. FIG. 1 shows different positions of
ship and effects due to these positions. FIG. 2 illustrates some
techniques employed. FIGS. 3 and 4 shows the height and shadow
determinations. FIG. 5 depicts the techniques employed as well as
different affects detected and evaluated indicating the basic data
is received from the radar in digital form and stored and processed
in any or selected techniques described in the disclosure. The data
is spectrally processed and the detection of the ship is performed
together with the detection of the shadow and black hole to
determine the ships radial velocity, azimuth and range, as well as
the measurement of the ship parameters to classify the ship with as
much accuracy as possible.
[0101] The delay data is processed to determine radial velocity
unambiguously and to determine the tangential velocities and the
ship parameters more accurately.
[0102] 11--The following analysis may be applied to all VSS systems
especially over the ocean detection of ships as follows:
[0103] 1--ONE CHANNEL-MANY PULSES-ONE RETURN SIMPLE SOLUTION
[0104] The equations are as follows: V.sub.0=M.sub.0 channel 1 time
1 V'.sub.0=M.sub.0X.sub.0 channel 2 time 1
V.sub.1=M.sub.0e.sup.j.PHI..sup.D0 channel 1 time 2
V'.sub.1=M.sub.0X.sub.0e.sup.j.PHI.'.sup.D0e.sup.j.theta..sup.0
channel 2 time 2 e.sup.j.PHI..sup.D0=V.sub.1/V.sub.0
.PHI..sub.D0=.PHI.'.sub.D0
e.sup.j.PHI.'.sup.D0e.sup.j.theta..sup.0=V'.sub.1/V'.sub.0
e.sup.j.theta..sup.0=(V'.sub.1/V'.sup.0)/(V.sub.1/V.sub.0):.theta..sub.0=-
.PHI..sub.0+.DELTA.K.sub.D0X.sub.0
[0105] M'.sub.0/M.sub.0 Where the ratio of the amplitude at
aperture 1 to aperture 2 as a function of azimuth is determined a
prior by taking antenna measurements or real measure relatively
high amplitude clutter only data. Like equations above will give
curve of ratio of outputs-vs-azimuth.
[0106] Where the definition of terms are as follows:
[0107] V.sub.0--is the return of first aperture output
[0108] V'.sub.0--is the return of second aperture output
[0109] V.sub.1--is the return of first aperture output delayed
[0110] V'.sub.1--is the return of second aperture output
delayed
[0111] .PHI..sub.D0--is the phase of the first aperture
proportional to its velocity plus azimuth
[0112] .PHI.'.sub.D0--is the phase of the second aperture
proportional to its velocity plus azimuth
[0113] The phase of M'.sub.0/M.sub.0 is .PHI..sub.D0/2 proportional
to its phase of its velocity plus azimuth. The phase
.PHI..sub.0=.PHI..sub.D0-.PHI..sub.A0 will give the phase
proportional to radial velocity.
[0114] .PHI..sub.0--phase of return proportional to radial
velocity
[0115] .PHI..sub.D0--phase of return proportional to radial
velocity plus azimuth
[0116] .PHI..sub.A0--phase of return proportional to azimuth
[0117] 12--ONE PULSE-MANY channels-ONE RETURN SIMPLE SOLUTION
[0118] The equations are as follows: V.sub.0=M.sub.0
V'.sub.0=M'.sub.0 V.sub.1=M.sub.0e.sup.j.PHI..sup.D0
V'.sub.1=M'.sub.0e.sup.j.PHI.'.sup.D0
e.sup.j.PHI..sup.D0=V.sub.1/V.sub.0
e.sup.j.PHI.'.sup.D0=V'.sub.1/V'.sub.0
.PHI..sub.D0=.PHI.'.sub.D0
[0119] Where the definition of terms are as follows:
[0120] M'.sub.0/M.sub.0 Where the ratio of the amplitude at
aperture 1 to aperture 2 as a function of azimuth is determined a
prior by taking antenna measurements or real measure relatively
high amplitude clutter only data. Like equations above will give
curve of ratio of outputs-vs-azimuth.
[0121] Where the definition of terms are as follows:
[0122] V.sub.0--is the return of first aperture output
[0123] V'.sub.0--is the return of second aperture output
[0124] V.sub.1--is the return of first aperture output delayed
[0125] V'.sub.1--is the return of second aperture output
delayed
[0126] .PHI..sub.D0--is the phase of the first aperture
proportional to its velocity plus azimuth
[0127] .PHI.'.sub.D0--is the phase of the second aperture
proportional to its velocity plus azimuth
[0128] The phase of M'.sub.0/M.sub.0 is .PHI..sub.D0 proportional
to its phase of its velocity plus azimuth. The phase
.PHI..sub.0=.PHI..sub.D0-.PHI..sub.A0 will give the phase
proportional to radial velocity.
[0129] .PHI..sub.0--phase of return proportional to radial
velocity
[0130] .PHI..sub.0--phase of return proportional to radial velocity
plus azimuth
[0131] .PHI..sub.A0--phase of return proportional to azimuth
[0132] V.sub.0--is the return of first pulse output
[0133] V.sub.1--is the return of second pulse output
[0134] .PHI..sub.A0--is the phase of the return proportional to its
velocity
[0135] 13a--TWO CHANNEL-MANY PULSES-ONE RETURN-delta D technique
where M1 return much larger than other returns for example a ship
return in the ocean or in a shadow area employing DPCA methodology.
V.sub.0=M.sub.0 channel 1 time 1-M delay 0 (1)
V.sub.1=M.sub.0X.sub.O channel 2 time 1-M delay 0 (2)
V.sub.2=M.sub.0X.sub.Oe.sup.j.theta..sup.0 channel 2 time 2-M+1
delay 1 (3)
X.sub.O=1/W.sub.M0=A.sub.M0e.sup.j(.PSI..sup.M0.sup.+K.sup.D0.sup.Y.sup.0-
.sup.)=A.sub.0 (4)
A.sub.0e.sup.j.theta..sup.0=V.sub.2/V.sub.1=A.sub.0e.sup.j(.PHI..sup.0.su-
p.-.DELTA.K.sup.D0.sup.X.sup.0.sup.) (5)
A.sub.M0=|V.sub.2/V.sub.1|:(6')e.sup.j.theta..sup.0=phase of
V.sub.2/V.sub.1 (6)
.theta..sub.0=.PHI..sub.0-.DELTA.K.sub.D0X.sub.0 (7)
[0136] Solve equation (7) for .theta..sub.0 is known and X.sub.0
are unknown and therefore from the peak of where the return is
detected which is .PHI..sub.D0 and therefore X.sub.0 and
.PHI..sub.0 has been determined and phase
.PHI..sub.A0=.PHI..sub.D0-.PHI..sub.0 will give the phase
proportional to azimuth.
M1--RETURN
[0137] With clutter only returns, it could be utilized for
producing the curve ratio between apertures-vs-azimuth.
V0--first channel output at time 1
V1--second channel output at time 1
AM0--Channel balancing amplitude factor
.PSI..sub.M0--Channel balancing phase factor
KD1--Phase coefficient to correct for detection of return not at
center of doppler bin
X0--Distance return detected from center of doppler bin
WM0--Factor that makes channel two equal to channel 1
.PHI..sub.0 phase of return proportional to radial velocity
.PHI..sub.D0--phase of return proportional to radial velocity plus
azimuth
.PHI..sub.A0--phase of return proportional to azimuth
[0138] 13b TWO CHANNEL-MANY PULSES-ONE RETURN-.PHI..sub.D0
technique
[0139] The equations are as follows: V.sub.0=M.sub.0 channel 1 time
1 V'.sub.0=M.sub.0X.sub.0 channel 2 time 1
V.sub.1=M.sub.0e.sup.j.PHI..sup.D0 channel 1 time 2
V'.sub.1=M.sub.0X.sub.0e.sup.j.PHI.'.sup.D0e.sup.j.theta..sup.0
channel 2 time 2 e.sup.j.PHI..sup.D0=V.sub.1/V.sub.0
.PHI..sub.D0=.PHI.'.sub.D0
e.sup.j.PHI.'.sup.D0e.sup.j.theta..sup.0=V'.sub.1/V'.sub.0
e.sup.j.theta..sup.0=(V'.sub.1/V'.sup.0)/(V.sub.1/V.sub.0):.theta..sub.0=-
.PHI..sub.0+.DELTA.K.sub.D0X.sub.0
[0140] Solve equation (7) for .theta..sub.0 is known and X.sub.0
are unknown and therefore from the peak of where the return is
detected which is .PHI..sub.D0 and therefore X.sub.0 and
.PHI..sub.0 has been determined and phase
.PHI..sub.A0=.PHI..sub.D0-.PHI..sub.0 will give the phase
proportional to azimuth.
The same definition of terms as in 18a.
[0141] 14a--TWO PULSE-MANY channels-ONE RETURN-delta C technique
employing DPCA methodology. V.sub.0=M.sub.0 pulse 1 channel 1-N
delay 0 (1) V.sub.1=M.sub.0X.sub.O pulse 2 channel 1-N delay 0 (2)
V.sub.2=M.sub.0X.sub.Oe.sup.j.theta..sup.0 pulse 2 time 2-N+1 delay
1 (3)
X.sub.O=1/W.sub.M0=A.sub.M0e.sup.j(.PSI..sup.M0.sup.+K.sup.D0.sup.X.-
sup.0.sup.)=A.sub.0 (4)
A.sub.0e.sup.j.gamma..sup.0=V.sub.2/V.sub.1=A.sub.0e.sup.j(.PHI..sup.A0.s-
up.-.DELTA.K.sup.D0.sup.X.sup.0.sup.) (5)
A.sub.M0=V.sub.2/V.sub.1:(6)e.sup.j.gamma..sup.0=phase of
V.sub.2/V.sub.1 (6)
.gamma..sub.0=.PHI..sub.A0-.DELTA.K.sub.D0X.sub.0 (7) Solve
equation (7) for .gamma..sub.0 is known and X.sub.0 are unknown and
therefore from the peak of where the return is detected which is
.PHI..sub.D0 and therefore .PHI..sub.A0 and .PHI..sub.0 has been
determined and phase .PHI..sub.0=.PHI..sub.D0-.PHI..sub.A0 will
give the phase proportional to radial velocity M1--return With
clutter only returns, it could be utilized for producing the curve
ratio between apertures-vs-azimuth. V0--first pulse output at
channel 1 V1--second pulse output at channel 1 AM0--Channel
balancing amplitude factor .PSI..sub.M0--Channel balancing PHASE
factor KD0--Phase coefficient to correct for detection of return
not at center of doppler bin X0--Distance return detected from
center of doppler bin WM0--Factor that makes phase channel two
equal to channel 1 .PHI..sub.0 --phase of return proportional to
radial velocity .PHI..sub.D0--phase of return proportional to
radial velocity plus azimuth .PHI..sub.A0--phase of return
proportional to azimuth
[0142] 14 b TWO CHANNEL-MANY PULSES-ONE RETURN-.PHI..sub.D0
technique
[0143] The equations are as follows: V.sub.0=M.sub.0 pulse 1
channel 1N V'.sub.0=M.sub.0X.sub.0 PULSE 2 channel 1-N
V.sub.1=M.sub.0e.sup.j.PHI..sup.D0 pulse 1 channel 2-N+1
V'.sub.1=M.sub.0X.sub.0e.sup.j.PHI.'.sup.D0e.sup.j.gamma..sup.0
PULSE 2 channel 2-N+1 e.sup.j.PHI..sup.D0=V.sub.1/V.sub.0
.PHI..sub.D0=.PHI.'.sub.D0
e.sup.j.PHI.'.sup.D0e.sup.j.gamma..sup.0=V'.sub.1/V'.sub.0
e.sup.j.gamma..sup.0=(V'.sub.1/V'.sup.0)/(V.sub.1/V.sub.0):.gamma..sub.0=-
.PHI..sub.0+.DELTA.K.sub.D0X.sub.0
[0144] Solve for .gamma..sub.0 is known and X.sub.0 are unknown and
therefore from the peak of where the return is detected which is
.PHI..sub.D0 and therefore .PHI..sub.A0 and .PHI..sub.0 has been
determined and phase .PHI..sub.0=.PHI..sub.D0-.PHI..sub.A0 will
give the phase proportional to radial velocity
The same definition of terms as in 19a.
15--Implementing Another Transmission Frequency
[0145] Against broadband jamming change the transmission frequency
to avoid jamming but not enough to change the implementation.
III--Basic Equations and Methodology
[0146] Detection of wanted returns and reject unwanted returns such
as clutter. In previous STAP approaches where a number of pulses
(M) of a particular PRF and a number channels (N-receive arrays)
are implemented.
[0147] Considering that channels returns differs in both elevation
and azimuth pattern(magnitude as well as phase), employing a
minimum number of channels reduces the channel matching problem and
reduces the storage and processing requirements significantly since
the number of channels proposed to be a few as one instead of the
usual ten or more. It proposes to perform as well or better than
any of the known STAP systems.
[0148] Also considering as in most proposed STAP implementations
some form of clutter cancellation are employed such as clutter
covariance matrix or training data or knowledge aided clutter
detection for non homogeneous data or high discretes of clutter for
better detection of returns of interest. Returns of interest have
to be thresholded above the clutter residue which may be
significant and lead to many false alarms and/or missed detections.
In the proposed USS no cancellation of clutter is required and all
the above clutter reductions are eliminated. Consequentially when
thresholding for possible meaningful returns they are not competing
with clutter and simpler to detect and measure their radial
velocity and azimuth very accurately.
[0149] This STAP methodology employs two or more channels, process
the pulse data (slow data) first into its frequency spectrum and
consequently localize clutter into its own range doppler bin (RDB)
together with any other returns that may be detected in that same
RDB such as target, thermal noise, and others.
[0150] The subsequent processing of each RDB will separate out
returns doppler wise and since clutter has zero (0) radial velocity
and other returns in the same (RDB) will have different velocities.
From determining the velocities of the returns the azimuths will be
calculated therefore no additional channels are required.
[0151] The knowledge aided STAP will be involved to determine from
the detected returns in the RDB which are clutter, targets of
interest, sidelobe returns, land sea interface, thermal noise, etc.
The knowledge aided STAP will be not be involved in canceling
clutter but in determining the returns of interest so they may be
detected and there parameters measured and determine the nature of
the return.
[0152] The following sections will be an analysis of various
techniques with their mathematical development to accomplish these
ends. It is assumed the data in time has been processed by FFT into
their individual RDBs where there exist in the cases of interest
clutter (0-velocity) and other returns (non "0" velocity).
Initially two (2) returns will be developed; it may be clutter and
moving target or two moving targets or more returns.
[0153] Two or three more returns in one RDB will be considered but
more than three returns can be processed and determine the nature
of the returns.
III-A Two channels at a time-"M"-PULSES in time data-two
returns-.PHI..sub.D technique
[0154] The analysis may be performed with a one antenna transmit
and two (channel) receive system. This system is called .DELTA.T
methodology where the data will be delayed one or more time
increments in channel 1 and 2 as required for a solution. We will
consider two returns clutter and target and the "M" pulse data
(time data) has been spectrum processed into its individual RDBs
and each will be treated as follows:
[0155] Each set of data, each time the data point is delayed it is
multiplied by a suitable weighting function and its spectrum is
obtained with such as FFT. In processing a particular RDB where we
have two returns we have the following equations:
V.sub.00=M.sub.0+M.sub.1 Channel 1 Pulse data 1-M Delay 0 (1)
V.sub.01=M.sub.0e.sup.j.PHI..sup.D0+M.sub.1e.sup.j.PHI..sup.D1
Channel 1 Pulse data 2-M+1 Delay 1 (2)
V.sub.02=M.sub.0e.sup.j2.PHI..sup.D0+M.sub.1e.sup.j2.PHI..sup.D1
Channel 1 Pulse data 3-M+2 Delay 2 (3)
V.sub.03=M.sub.0e.sup.j3.PHI..sup.D0+M.sub.1e.sup.j3.PHI..sup.D1
Channel 1 Pulse data 4-M+3 Delay 3 (4) Above equations are for two
returns where V.sub.00 --is the return in the RDB channel 1 being
processed at time 1 V.sub.01 --is the return in the RDB channel 1
being processed at time 2 V.sub.02--is the return in the RDB
channel 1 being processed at time 3 V.sub.03--is the return in the
RDB channel 1 being processed at time 4 M.sub.0--is the first
return vector M.sub.1--is the second return vector .PHI..sub.D0--is
the phase of the first return where the phase is proportional to
the phase due to radial velocity plus that due to the azimuth of
the return. .PHI..sub.D1--is the phase of the second return where
the phase is proportional to the radial velocity plus that due to
the azimuth of the return
[0156] It is noted with each delay in time of the data the vectors
of the returns phase is increased proportional to the delay which
represents the phase of the return proportional to velocity and
that due to its azimuth position in the antenna beam. Zero velocity
returns such as clutter will have phase shift equal to zero due to
its velocity but one due to its azimuth position in the antenna
beam and other returns will have phase shifts directly proportional
to their radial velocity and one due to its azimuth position in the
main beam. When returns are detected in the same RDB the sum of
their phases (.PHI..sub.D0 or .PHI..sub.D1) (frequency) are
detected in the same in RDB but are different in phase value and it
is on this basis the returns are analyzed, processed and separated
out.
[0157] Taking equations (1) and (2) and treating M.sub.0 and
M.sub.1 as the variables and solving for M.sub.0 and M.sub.1 we
have:
M.sub.0=(V.sub.00e.sup.j.PHI..sup.D1-V.sub.01)/(e.sup.j.PHI..sup.D1-e.sup-
.j.PHI..sup.D0) (1')
M.sub.1=(V.sub.00-V.sub.01e.sup.j.PHI..sup.D0)/(e.sup.J.PHI..sup.D1-e.sup-
.j.PHI..sup.D0) (2') Taking equations (2) and (3) and treating
M.sub.0e.sup.j.PHI..sup.D0 and M.sub.1e.sup.j.PHI..sup.D1 as the
variables and solving for M.sub.0e.sup.j.PHI..sup.D0 and
M.sub.1e.sup.j.PHI..sup.D1 we have:
M.sub.0e.sup.j.PHI..sup.D0=(V.sub.01e.sup.j.PHI..sup.D1-V.sub.02)/(e.sup.-
j.PHI..sup.D1-e.sup.j.PHI..sup.D0) (1'')
M.sub.1e.sup.j.PHI..sup.D1=(V.sub.01-V.sub.02e.sup.j.PHI..sup.D0)/(e.sup.-
j.PHI..sup.D1-e.sup.j.PHI..sup.D0) (2'') Equation (2'')/Equation
(2') or Equation (1'')/Equation (1') are the following:
e.sup.j.PHI..sup.D0=(V.sub.01e.sup.j.PHI..sup.D1-V.sub.02)/(V.sub.00e.sup-
.j.PHI..sup.D1-V.sub.01) (3')
e.sup.j.PHI..sup.D1=(V.sub.02-V.sub.01e.sup.j.PHI..sup.D0)/(V.sub.01-V.su-
b.00e.sup.J.PHI..sup.D0) (4') Equation (3') or Equation (4') is
easily solved for .PHI..sub.D0 and .PHI..sub.D1 which are
proportional to the total phase of return 0 and return 1
respectively. If return "Mo" is clutter then .PHI..sub.0=0
corresponding to clutter having zero (0) velocity.
[0158] Now employing equations (1) and (2) and solving for M.sub.0
and M.sub.1 knowing .PHI..sub.D0 and .PHI..sub.D1 we are now are to
find .PHI..sub.0 and .PHI..sub.1 which are proportional to velocity
of return 0 and return 1 respectively. M.sub.0 and M.sub.1 are
returns that are detected in the same RDB.
[0159] Having the second channel data and performing the same
operations as in channel 1 and the equations are as follows:
V'.sub.00=M.sub.0X.sub.01+M.sub.1X.sub.11 Channel 2 Pulse data 1-M
Delay 0 (1')
V'.sub.01=M.sub.0X.sub.01e.sup.j.PHI.'.sup.D0+M.sub.1X.sub.11e.s-
up.j.PHI.'.sup.D1 Channel 2 Pulse data 2-M+1 Delay 1 (2')
V'.sub.02=M.sub.0X.sub.01e.sup.j2.PHI.'.sup.D0+M.sub.1X.sub.11e.sup.j2.PH-
I.'.sup.D1 Channel 2 Pulse data 3-M+2 Delay 2 (3')
V'.sub.03=M.sub.0X.sub.01e.sup.j3.PHI.'.sup.D0+M.sub.1X.sub.11e.sup.j3.PH-
I.'.sup.D1 Channel 2 Pulse data 4-M+3 Delay 3 (4')
X.sub.01=e.sup.jD.PHI..sup.0e.sup.jK.sup.D0.sup.X.sup.0/W.sub.M0=|1/A.sub-
.M0|e.sup.j(K.sup.D0.sup.X.sup.0.sup.-.PSI..sup.M0.sup.) where
D=0X.sub.01=e.sup.jK.sup.D0.sup.X.sup.0/W.sub.M0=|1/A.sub.M0|e.sup.j(K.su-
p.D0.sup.X.sup.0.sup.-.PSI..sup.M0.sup.)
X.sub.11=e.sup.jD.PHI..sup.1e.sup.jK.sup.D0.sup.X.sup.1/W.sub.M1=|1/A.sub-
.M1|e.sup.j(K.sup.D0.sup.X.sup.1.sup.-.PSI..sup.M1.sup.) where
D=0X.sub.11=e.sup.jK.sup.D0.sup.X.sup.1/W.sub.M1=|1/A.sub.M1|e.sup.j(K.su-
p.D0.sup.X.sup.1.sup.-.PSI..sup.M1.sup.)
[0160] Solving equations (1') to (4') in the same manner as
equations (1) to (4) we solve for .PHI.'.sub.D0 and .PHI.'.sub.D1
and M.sub.0X.sub.01 and M.sub.1X.sub.11. .PHI.'.sub.D0 and
.PHI.'.sub.D1 solution should be the same as for .PHI..sub.D0 and
.PHI..sub.D1 since in channel 2 we have the same returns detected
in the same RDB with the same velocity components. solution for
M.sub.0X.sub.01 and M.sub.1X.sub.11 in channel 2/solving for
M.sub.0 and M.sub.1 in channel 1 yields X.sub.01 and X.sub.11
Having the second channel data delayed and performing the same
operations as in channel 1 and 2 and the equations are as follows:
V''.sub.00=M.sub.0X.sub.02+M.sub.1X.sub.12 CHANNEL 2 PULSE data
2-M+1 Delay 1 (1'')
V''.sub.01=M.sub.0X.sub.02e.sup.j.PHI.''.sup.D0+M.sub.1X.sub.12e.sup.j2.P-
HI.''.sup.D1 CHANNEL 2 PULSE data 3-M+2 Delay 2 (2'')
V''.sub.02=M.sub.0X.sub.02e.sup.j2.PHI.''.sup.D0+M.sub.1X.sub.12e.sup.j2.-
PHI.''.sup.D1 CHANNEL 2 PULSE data 4-M+3 Delay 3 (3'')
V''.sub.03=M.sub.0X.sub.02e.sup.j3.PHI.''.sup.D0+M.sub.1X.sub.12e.sup.j3.-
PHI.''.sup.D1 CHANNEL 2 PULSE data 5-M+4 Delay 4 (4'')
X.sub.02=X.sub.01e.sup.j(.PHI..sup.0.sup.+.DELTA.K.sup.D0.DELTA.X.sup.0.s-
up.).times.X.sub.01e.sup.j(.theta..sup.o.sup.):
X.sub.12=X.sub.11e.sup.j(.PHI..sup.1.sup.+.DELTA.K.sup.D0.DELTA.X.sup.0)=-
X.sub.11e.sup.j(.theta..sup.1.sup.)
V''.sub.00=M.sub.0X.sub.01e.sup.j.theta..sup.0+M.sub.1X.sub.12e.sup.j.the-
ta..sup.1 Channel 2 Pulse data 2-M+1 Delay 1 (1'')
V''.sub.01=M.sub.0X.sub.01e.sup.j2.theta..sup.0e.sup.j.PHI.''.sup.D0+M.su-
b.1X.sub.12e.sup.j2.theta..sup.1e.sup.j.PHI.''.sup.D1 Channel 2
Pulse data 3-M+2 Delay 2 (2'')
V''.sub.02=M.sub.0X.sub.01e.sup.j3.theta..sup.0e.sup.j2.PHI.''.sup.D0+M.s-
ub.1X.sub.12e.sup.j3.theta..sup.1e.sup.j2.PHI.''.sup.D1 Channel 2
Pulse data 4-M+3 Delay 3 (3'')
V''.sub.03=M.sub.0X.sub.01e.sup.j4.theta..sup.0e.sup.j3.PHI.''.sup.D0+M.s-
ub.1X.sub.12e.sup.j4.theta..sup.1e.sup.j3.PHI.''.sup.D1 Channel 2
Pulse data 5-M+4 Delay 4 (4'') Solving equations (1'') to (4'') the
same manner as equations (1) to (4) we solve for (1D0 and
.PHI..sub.D1 and M.sub.0X.sub.01 and M.sub.1X.sub.11.
.PHI.''.sub.D0 and .PHI.''.sub.D1 solution should be the same.
[0161] solution for M.sub.0X.sub.01e.sub.j.theta..sup.0 and
M.sub.1X.sub.11e.sup.j.theta..sup.1 in channel 2 delayed/solving
for M.sub.0X.sub.01 and M.sub.1X.sub.11 in channel 2 yields
e.sup.j.theta..sup.0 and e.sup.j.theta..sup.1 and
[0162] .theta..sub.0=.PHI..sub.0+.DELTA.K.sub.D0X.sub.0 where
.theta..sub.0 is known and X.sub.0 is unknown and therefore
.PHI..sub.0 has to be determined
[0163] .theta..sub.1=.PHI..sub.1+.DELTA.K.sub.D0X.sub.0 where
.theta..sub.1 is known and X.sub.1 is unknown and therefore
.PHI..sub.1 has to be determined
[0164] If the location is taken at the center of the filter the
error in determination of azimuth is plus or minus a half a RDB. If
a more accurate determination is desired a point of frequency close
to first filter is created and processed like that of first
filter.
[0165] This gives the same .PHI..sub.0 and .PHI..sub.1 and
different M.sub.0 and M.sub.1 and the ratio of the M.sub.0 and
M.sub.1 should give a good estimate of where the position
.PHI..sub.D0 and .PHI..sub.D1 is detected at in the RDB. From this
an estimate of azimuth of both returns are determined. To get a
more accurate determination another frequency may be processed or a
slight change in the range processed and results correlated for
best results.
[0166] From a second set of data a small known change in frequency
from the first set of data. We assume there will be no change in
the channel balancing terms A.sub.M0, .PSI..sub.M0 and X.sub.0 and
.PHI..sub.0 which are the amplitude and phase term but an unknown
DPCA term .DELTA.K.sub.D0 X.sub.0 where X.sub.0 is the unknown
change in position of new filter and .DELTA.K.sub.D0 DPCA known
constant therefore the term is unknown. Performing the operations
on the second set of data, the solutions are the same for
.PHI..sub.1 and .PHI..sub.0
The returns change due to frequency change from
[0167] M.sub.0 to M'.sub.0 where X.sub.F0=M'.sub.0/M.sub.0 and
M.sub.1 to M'.sub.1 where X.sub.F1=M'.sub.1/M.sub.1. Therefore we
have determined the ratio of the returns from which we estimate the
position of the peak where is the first return and from that
calculate the azimuth of the return. We can analogously perform
that for the second return.
[0168] Reference: section I J on DPCA calculations will give the
derivations of .PHI..sub.AO, .PHI..sub.D0, .PHI..sub.0 and
.PHI..sub.A1,.PHI..sub.D1,.PHI..sub.1,and .DELTA.K.sub.D0,
.DELTA.K.sub.D1, .DELTA..sub.X0, .DELTA..sub.X1, X.sub.0, X.sub.1,
.theta..sub.0, .theta..sub.1
[0169] Solving for phase proportional to azimuth in both returns we
have the following: .PHI..sub.AO=.PHI..sub.D0-.PHI..sub.0 and
.PHI..sub.A1=.PHI..sub.D1-.PHI..sub.1 Definition of terms not
defined previously: ALL "V" TERMS ARE MEASURED TERMS.--
X01--CHANNEL 2 TERM THAT makes relates channel 2 to channel 1 for
return 1 X02--CHANNEL 2 TERM THAT makes relates channel 2 to
channel 1 for return 2 .DELTA.K.sub.D0--the difference factor for
different delays for return 1 and 2 X.sub.0--the position in filter
for return 1 .theta..sub.0--the difference in angle between
different delayed data of return 1 .theta..sub.1--the difference in
angle between different delayed data of return 2
.PHI..sub.AO--phase proportional to azimuth of return 1
.PHI..sub.A1--phase proportional to azimuth of return 2
A.sub.M0--Amplitude balancing term between channel 1 and 2 for
return 1 A.sub.M1--Amplitude balancing term between channel 1 and 2
for return 2 .PSI..sub.M0--Phase balancing term between channel 1
and 2 for return 1 .PSI..sub.M1--Phase balancing term between
channel 1 and 2 for return 2
[0170] Comments and observations on technique:
1--All solutions .PHI..sub.D0, .PHI.'.sub.D0, .PHI.''.sub.D0 should
be equal and .PHI..sub.D1, .PHI.'.sub.D1, .PHI.''.sub.D1 should be
equal
2--Solving for M0 and M1 by this approach solves for the location
of their peaks therefore they have a phase shift equal to zero at
this point.
3--To solve for the channel balancing terms three sets of equations
are required but for solving for velocity and azimuth only last two
sets are required.
4--Correlate with other .DELTA.T-DPCA-technique in the following
manner:
[0171] a) same solution
[0172] b) all variables are the same value such as M0, M.sub.1,
ETC
[0173] c) .DELTA.F, .DELTA.R and .DELTA.H results should have the
same values and correlate
[0174] Analogously a small change in range bin may be taken and we
determine X.sub.R0 and X.sub.R1 which determines where the peak of
the returns in range, this does not help in the evaluation in
azimuth. If and evaluation in resolving velocity ambiguity with the
taking of a meaningful delay in time and processing again. Thus we
can determine the peak of each return in range and azimuth to
obtain the maximum amplitude for each return for further use. The
change in amplitude and phase of the range bin in conjunction with
a delay in time gives an accurate determination of velocity which
will resolve velocity ambiguity.
[0175] The change in amplitude and phase of the doppler bin in
conjunction with a delay in time gives an accurate determination of
horizontal tangential velocity.
[0176] The change in amplitude and phase in the different linear
arrays of the doppler bin in conjunction with a delay in time gives
an accurate determination of vertical tangential velocity.
[0177] Thus we have obtained the three dimensional positions and
velocities of all returns.
[0178] B. Two channel "M" pulse data in time-three
returns-.PHI..sub.D technique
[0179] The previous analysis was for two returns possible per RDB
processed; this will be for three (3) returns per RDB.
V.sub.00=M.sub.0+M1+M2 Channel 1 Pulse data 1-M Delay 0 (1)
V.sub.01=M.sub.0e.sup.j.PHI..sup.D0+M.sub.1e.sup.j.PHI..sup.D1+M.sub.1e.s-
up.j.PHI..sup.D2 Channel 1 Pulse data 2-M+1 Delay 1 (2)
V.sub.02=M.sub.0e.sup.j2.PHI..sup.D0+M.sub.1e.sup.j2.PHI..sup.D1+M.sub.2e-
.sup.j2.PHI..sup.D2 Channel 1 Pulse data 3-M+2 Delay 2 (3)
V.sub.03=M.sub.0e.sup.j3.PHI..sup.D0+M.sub.1e.sup.j3.PHI..sup.D1+M.sub.2e-
.sup.j3.PHI..sup.2 Channel 1 Pulse data 4-M+3 Delay 3 (4) All terms
previously defined except the following: M2--Third return
.PHI..sub.D2--phase proportional to radial velocity plus azimuth of
third return .PHI..sub.A2--phase proportional to azimuth of third
return .PHI..sub.2--phase proportional to radial velocity of third
return Taking equations (1) and (2) and (3) and treating M.sub.0
and M.sub.1 and M.sub.2 as the variables and solving the
determinant equation for A.sub.0 we have: .DELTA. 0 = e j.PHI. D
.times. .times. 0 1 .times. e j.PHI. D .times. .times. 1 1 .times.
e j.PHI. D .times. .times. 2 1 = 1 .times. .times. e j.PHI. D
.times. .times. 1 .times. e j.PHI. D .times. .times. 2 - 1 .times.
.times. e j.PHI. D .times. .times. 0 .times. e j.PHI. D .times.
.times. 2 + 1 .times. .times. e j.PHI. D .times. .times. 0 .times.
e j.PHI. D .times. .times. 1 .times. .times. e j2.PHI. D .times.
.times. 0 .times. e j2.PHI. D .times. .times. 1 .times. e j2.PHI. D
.times. .times. 2 .times. .times. e j2.PHI. D .times. .times. 1
.times. e j2.PHI. D .times. .times. 2 .times. .times. e j2.PHI. D
.times. .times. 0 .times. e j2.PHI. D .times. .times. 2 .times.
.times. e j2.PHI. D .times. .times. 0 .times. e j2.PHI. D .times.
.times. 1 .times. .times. .DELTA. 0 = .times. e j.PHI. D .times.
.times. 1 .times. e j2.PHI. D .times. .times. 2 - e j2.PHI. D
.times. .times. 1 .times. e j.PHI. D .times. .times. 2 - e j.PHI. D
.times. .times. 0 .times. e j2.PHI. D .times. .times. 2 + .times. e
j.PHI. D .times. .times. 2 .times. e j2.PHI. D .times. .times. 0 +
e j.PHI. D .times. .times. 0 .times. e j2.PHI. D .times. .times. 1
- e j.PHI. D .times. .times. 1 .times. e j2.PHI. D .times. .times.
0 = .times. function .times. .times. of .times. .times. .PHI. D
.times. .times. 0 , .PHI. D .times. .times. 1 .times. .times. and
.times. .times. .PHI. D .times. .times. 2 .times. .times. and
.times. .times. solving .times. .times. for .times. .times. M 0 _ =
M 0 * .DELTA. 0 M 0 _ = V 01 V 00 .times. e j.PHI. D .times.
.times. 1 1 .times. e j.PHI. D .times. .times. 2 1 = V 00 .times. e
j.PHI. D .times. .times. 1 .times. e j.PHI. D .times. .times. 2 - V
01 .times. 1 .times. .times. 1 + V 02 .times. 1 .times. .times. 1
.times. .times. V 02 .times. e j2.PHI. D .times. .times. 1 .times.
V .times. .times. e j2.PHI. D .times. .times. 2 .times. .times. e
j2.PHI. D .times. .times. 1 .times. e j2.PHI. D .times. .times. 2
.times. .times. e j2.PHI. D .times. .times. 1 .times. e j2.PHI. D
.times. .times. 1 .times. .times. e j.PHI. D .times. .times. 1
.times. e j.PHI. D .times. .times. 2 .times. .times. M 0 _ =
.times. V 00 .function. ( e j.PHI. D .times. .times. 1 .times. e
j2.PHI. D .times. .times. 2 - e j.PHI. D .times. .times. 2 .times.
e j2.PHI. D .times. .times. 1 ) - .times. V 01 ( e j2.PHI. D
.times. .times. 2 - e j2.PHI. D .times. .times. 1 ) + V 02
.function. ( e j.PHI. D .times. .times. 2 - e j.PHI. D .times.
.times. 1 ) = .times. function .times. .times. of .times. .times.
.times. .PHI. D .times. .times. 1 .times. .times. and .times.
.times. .PHI. D .times. .times. 2 .times. .times. and .times.
.times. solving .times. .times. for .times. .times. M 1 _ = M 1 *
.DELTA. 0 ( 6 ) M 1 _ = e j.PHI. D .times. .times. 0 1 .times. V 01
V 00 .times. e j.PHI. D .times. .times. 2 1 = V 00 .times. e j.PHI.
D .times. .times. 0 .times. e j.PHI. D .times. .times. 2 - V 01
.times. 1 .times. .times. 1 + V 02 .times. 1 .times. .times. 1
.times. .times. e j2.PHI. D .times. .times. 0 .times. V 02 .times.
e j2.PHI. D .times. .times. 2 .times. .times. e j2.PHI. D .times.
.times. 0 .times. e j2.PHI. D .times. .times. 2 .times. .times. e
j2.PHI. D .times. .times. 0 .times. e j2.PHI. D .times. .times. 2
.times. .times. e j.PHI. D .times. .times. 0 .times. e j.PHI. D
.times. .times. 2 .times. .times. M 1 _ = .times. V 01 .function. (
e j.PHI. D .times. .times. 0 .times. e j2.PHI. D .times. .times. 2
- e j2.PHI. D .times. .times. 0 .times. e j.PHI. D .times. .times.
2 ) - .times. V 01 ( e j2.PHI. D .times. .times. 2 - e j2.PHI. D
.times. .times. 0 ) + V 02 .function. ( e j.PHI. D .times. .times.
2 - e j.PHI. D .times. .times. 0 ) = .times. function .times.
.times. of .times. .times. .PHI. D .times. .times. 0 .times.
.times. and .times. .times. .times. .PHI. D .times. .times. 2
.times. .times. and .times. .times. solving .times. .times. for
.times. .times. M 2 _ = M 2 * .DELTA. 0 ( 7 ) M 2 _ = e j.PHI. D
.times. .times. 0 1 .times. e j.PHI. D .times. .times. 1 1 .times.
V 01 V 00 = V 00 .times. e j.PHI. D .times. .times. 0 .times. e
j.PHI. D .times. .times. 1 - V 01 .times. 1 .times. .times. 1 + V
02 .times. 1 .times. .times. 1 .times. .times. e j2.PHI. D .times.
.times. 0 .times. e j2.PHI. D .times. .times. 1 .times. V 02
.times. .times. e j2.PHI. D .times. .times. 0 .times. e j2.PHI. D
.times. .times. 1 .times. .times. e j2.PHI. D .times. .times. 0
.times. e j2.PHI. D .times. .times. 1 .times. .times. e j.PHI. D
.times. .times. 0 .times. e j.PHI. D .times. .times. 1 .times.
.times. M 2 _ = .times. V 00 .function. ( e j.PHI. D .times.
.times. 0 .times. e j2.PHI. D .times. .times. 1 - e j2.PHI. D
.times. .times. 1 .times. e j.PHI. D .times. .times. 0 ) - .times.
V 01 ( e j2.PHI. D .times. .times. 1 - e j2.PHI. D .times. .times.
0 ) + V 02 .function. ( e j.PHI. D .times. .times. 1 - e j.PHI. D
.times. .times. 0 ) = .times. function .times. .times. of .times.
.times. .PHI. D .times. .times. 0 .times. .times. and .times.
.times. .times. .PHI. D .times. .times. 1 ( 8 ) ##EQU2## Solving
for .PHI..sub.D0, .PHI..sub.D1 and .PHI..sub.D2 and substituting
these values in equations (1), (2) and (3) we determine M.sub.0,
M.sub.1 and M.sub.2
[0180] Taking equations (2), (3) and (4) and treating
M.sub.0e.sup.jD.PHI..sup.0, M.sub.1e.sup.jD.PHI..sup.1 and
M.sub.2e.sup.jD.PHI..sup.2 as the variables and solving the
determinant equation for .DELTA..sub.0 is the same and performing
the same operations as with the first set of equations we have the
following: M.sub.0e.sup.j.PHI..sup.D0=function of
(.PHI..sub.D1,.PHI..sub.D2) ( 6)
M.sub.1e.sup.j.PHI..sup.D1=function of (.PHI..sub.D0, .PHI..sub.D2)
( 7) M.sub.2e.sup.j.PHI..sup.D2=function of
(.PHI..sub.D0,.PHI..sub.D1) ( 8) Equation ( 6)/(6), ( 7)/(7) and (
8)/(8) ( 6)/(6)=e.sup.j.PHI..sup.D0=function (.PHI..sub.D1,
.PHI..sub.D2) ( 7)/(7)=e.sup.j.PHI..sup.D1=function .PHI..sub.D0,
.PHI..sub.D2) ( 8)/(8)=e.sup.j.PHI..sup.D2=function
(.PHI..sub.D0,.PHI..sub.D1) Solving for .PHI..sub.D0, .PHI..sub.D1
and .PHI..sub.D2 and substituting these values in equations (2),
(3) and (4) we determine M.sub.0e.sup.jD.PHI..sup.0,
M.sub.1e.sup.jD.PHI..sup.1 and M.sub.2e.sup.jD.PHI..sup.2.
V'.sub.00=M.sub.0X.sub.01+M.sub.1X.sub.11+M.sub.2X.sub.21 Channel 2
Pulse data 1-M Delay 0 (1')
V'.sub.01=M.sub.0X.sub.01e.sup.j.PHI.'.sup.D0+M.sub.1X.sub.11e.sup.j.PHI.-
'.sup.D1+M.sub.2X.sub.21e.sup.j2'D2 Channel 2 Pulse data 2-M+1
Delay 1 (2')
V'.sub.02=M.sub.0X.sub.01e.sup.j2.PHI.'.sup.D0+M.sub.1X.sub.11e.sup-
.j2.PHI.'.sup.D1+M.sub.2X.sub.21e.sup.j2.PHI.'.sup.D2 Channel 2
Pulse data 3-M+2 Delay 2 (3')
V'.sub.03=M.sub.0X.sub.01e.sup.j3.PHI.'.sup.D0+M.sub.1X.sub.11e.sup.j3.PH-
I.'.sup.D1.sup.+M.sub.2X.sub.21e.sup.j3.PHI.'.sup.D2 Channel 2
Pulse data 4-M+3 Delay 3 (4')
X.sub.01=e.sup.jD.PHI..sup.0e.sup.jK.sup.D0.sup.X.sup.0/W.sub.M0=|1/A.sub-
.M0|e.sup.j(K.sup.D0.sup.X.sup.0-.PSI..sup.M0.sup.) where
D=0X.sub.01=e.sup.jK.sup.D0.sup.X.sup.0/W.sub.M0|1/A.sub.M0|e.sup.j(K.sup-
.D0.sup.X.sup.0-.PSI..sup.M0.sup.)
X.sub.11=e.sup.jD.PHI..sup.1e.sup.jK.sup.D0.sup.X.sup.1/W.sub.M1=|1/A.sub-
.M1|e.sup.j(K.sup.D0.sup.X.sup.1-.PSI..sup.M1.sup.) where
D=0X.sub.01=e.sup.jK.sup.D0.sup.X.sup.1/W.sub.M1|1/A.sub.M1|e.sup.j(K.sup-
.D0.sup.X.sup.1-.PSI..sup.M1.sup.)
X.sub.21=e.sup.jD.PHI..sup.2e.sup.jK.sup.D0.sup.X.sup.2/W.sub.M2=|1/A.sub-
.M2|e.sup.j(K.sup.D0.sup.X.sup.2-.PSI..sup.M2.sup.) where
D=0X.sub.01=e.sup.jK.sup.D0.sup.X.sup.2/W.sub.M2|1/A.sub.M2|e.sup.j(K.sup-
.D0.sup.X.sup.2-.PSI..sup.M2.sup.)
[0181] Performing the same operations on equations (1'), (2') and
(3') with the variables M.sub.0X.sub.01, M.sub.1X.sub.11 and
M.sub.2X.sub.21 and .DELTA..sub.0 remains the same. The analysis is
analogous and the result is the following: and .times. .times.
solving .times. .times. for .times. .times. M 0 .times. X 01 _ = M
0 .times. X 01 * .DELTA. 0 M 0 .times. X 01 _ = .times. V 01
.function. ( e j .times. .times. .PHI. D .times. .times. 1 '
.times. e j .times. .times. .PHI. .times. D .times. .times. 2 ' - e
j .times. .times. 2 .times. .times. .PHI. D .times. .times. 1 '
.times. e j .times. .times. .PHI. D .times. .times. 2 ' ) - .times.
V 02 .function. ( e j .times. .times. 2 ' .times. .PHI. D .times.
.times. 1 - e j .times. .times. 2 .times. .PHI. D .times. .times. 2
' ) + V 03 .function. ( e j .times. .times. .PHI. D .times. .times.
1 ' - e j .times. .times. .PHI. D .times. .times. 2 ' ) = .times.
function .times. .times. of .times. .times. .PHI. D .times. .times.
1 ' .times. .times. and .times. .times. .PHI. D .times. .times. 2 '
.times. .times. and .times. .times. solving .times. .times. for
.times. .times. M 0 .times. X 11 _ = M 1 .times. X 11 * .DELTA. 0 (
6 ' ) = function .times. .times. of .times. .times. .PHI. D .times.
.times. 0 ' .times. .times. and .times. .times. .PHI. D .times.
.times. 2 ' .times. .times. and .times. .times. solving .times.
.times. for .times. .times. M 2 .times. X 21 _ = M 2 .times. X 21 *
.DELTA. 0 ( 7 ' ) = function .times. .times. of .times. .times.
.PHI. D .times. .times. 0 ' .times. .times. and .times. .times.
.PHI. D .times. .times. 1 ' ( 8 ' ) ##EQU3## Taking equation
(6')/(6) we have the following:
X.sub.01=M.sub.0X.sub.01/M.sub.0
[0182] Taking equation (7')/(7) we have the following:
X.sub.11=M.sub.1X.sub.11/M.sub.1
[0183] Taking equation (8')/(8) we have the following:
X.sub.21=M.sub.2X.sub.21/M.sub.2
V.sub.02(e.sup.j.PHI.''.sup.D0e.sup.j2.PHI.''.sup.D1-e.sup.j2.PHI.''.sup.-
D0e.sup.j.PHI.''.sup.D1)-V.sub.03(e.sup.j2'.PHI.''.sup.D1-e.sup.j2.PHI.'.s-
up.D0)+V.sub.04(e.sup.j.PHI.''.sup.D1-e.sup.j.PHI.''.sup.D0)/V.sub.01(e.su-
p.j.PHI.'.sup.D0e.sup.j2.PHI.'.sup.D1-e.sup.j2.PHI.'.sup.D0e.sup.j.PHI.'.s-
up.D1)-V.sub.02(e.sup.j2'.PHI..sup.D1-e.sup.j2.PHI.'.sup.D0)+V.sub.03(e.su-
p.j.PHI.'.sup.D1-e.sup.j.PHI.'.sup.D0) Performing the same
operations on equations (2'), (3') and (4') with the variables
M.sub.0X.sub.01, M.sub.1X.sub.11 and M.sub.2X.sub.21 and
.DELTA..sub.0 remains the same. The analysis is analogous and the
result is the following: M.sub.0e.sup.j.PHI..sup.D0=function of
(.PHI..sub.D1, .PHI..sub.D2) (6')
M.sub.1e.sup.j.PHI..sup.D1=function of (.PHI..sub.D0, .PHI..sub.D2)
(7) M2e.sup.j.PHI..sup.D2=function of .PHI..sub.D0, .PHI..sub.D1)
(8') Equation ( 6')/(6'), ( 7')/(7') and ( 8')/(8') (
6')/(6')=e.sup.j.PHI..sup.D0=function (.PHI..sub.D1,.PHI..sub.D2) (
7')/(7')=e.sup.j.PHI..sup.D1=function (.PHI..sub.D0, .PHI..sub.D2)
( 8)/(8')=e.sup.j.PHI..sup.D2=function (.PHI..sub.D0, .PHI..sub.D1)
Solving for .PHI..sub.D0, .PHI..sub.D1 and .PHI..sub.D2 and
substituting these values in equations (2), (3) and (4) we
determine M.sub.0X.sub.01, M1 X.sub.02 and M2X.sub.03
[0184] Taking the next set of equations as follows:
V''.sub.00=M.sub.0X.sub.02+M.sub.1X.sub.12+M.sub.1X.sub.22 Channel
2 Pulse data 2-M+1 Delay 1 (1'')
V''.sub.01=M.sub.0X.sub.02e.sup.j.PHI.'.sup.D0+M.sub.1X.sub.12e.sup.j.PHI-
.''.sup.D1+M.sub.2X.sub.22e.sup.j.PHI.''.sup.D2 Channel 2 Pulse
data 3-M+2 Delay 2 (2'')
V''.sub.02=M.sub.0X.sub.02e.sup.j2.PHI.''.sup.D0+M.sub.1X.sub.12e.sup.j2.-
PHI.''.sup.D1+M.sub.2X.sub.22e.sup.j2.PHI.''.sup.D2 Channel 2 Pulse
data 4-M+3 Delay 3 (3'')
V''.sub.03=M.sub.0X.sub.02e.sup.j3.PHI.''.sup.D0+M.sub.1X.sub.12e.sup.j3.-
PHI..sup.D1+M.sub.2X.sub.21e.sup.j3.PHI.''.sup.2 Channel 2 Pulse
data 5-M+4 Delay 4 (4'')
X.sub.02=X.sub.01e.sup.j(.PHI..sup.0.sup.+.DELTA.K.sup.D0.sup.X.sup.0.sup-
.)=X.sub.01e.sup.j(.theta..sup.0.sup.):
X.sub.12=X.sub.11e.sup.j(.PHI..sup.1.sup.+.DELTA.K.sup.D0.sup.X.sup.0.sup-
.)=X.sub.11e.sup.j(.theta..sup.1.sup.):X.sub.21=X.sub.21e.sup.j(.PHI..sup.-
2+K.sup.D0.sup.X.sup.0.sup.)=X.sub.21e.sup.j(.theta..sup.2.sup.)
Rewriting equations (1'' to 4'') we have the following:
V''.sub.00=M.sub.0X.sub.01e.sup.j.theta..sup.0+M.sub.1X.sub.11e.sup.j.the-
ta..sup.1+M.sub.2X.sub.12e.sup.j.theta..sup.2 Channel 2 Pulse data
2-M+1 Delay 1 (1'')
V''.sub.01=M.sub.0X.sub.01e.sup.j.theta..sup.0e.sup.j.PHI.''.sup.D0+M.sub-
.1X.sub.11e.sup.j.theta..sup.1e.sup.j.theta.'D1+M.sub.2X.sub.12e.sup.j.the-
ta..sup.2e.sup.j.PHI.''.sup.D2 Channel 2 Pulse data 3-M+2 Delay 2
(2'')
V''.sub.02=M.sub.0X.sub.01e.sup.j.theta..sup.0e.sup.j2.PHI.''.sup.D0+M.su-
b.1X.sub.11e.sup.j.theta..sup.1e.sup.j2.PHI.''.sup.D1+M.sub.2X.sub.12e.sup-
.j.theta..sup.2e.sup.j2.PHI..sup.D2 Channel 2 Pulse data 4-M+3
Delay 3 (3'')
V''.sub.03=M.sub.0X.sub.01e.sup.j.theta..sup.0e.sup.j3.PHI.'.sup.D-
0+M.sub.1X.sub.11e.sup.j.theta..sup.1e.sup.j3.PHI.'.sup.D1+M.sub.2X.sub.11-
e.sup.1.theta..sup.2e.sup.j3.PHI.'.sup.D2 Channel 2 Pulse data
5-M+4 Delay 4 (4'') Performing the same operations on equations
(1''), (2'') and (3'') with the variables
M.sub.0X.sub.01e.sup.j.theta..sup.0,
M.sub.1X.sub.11e.sup.j.theta..sup.1 and
M.sub.2X.sub.21e.sup.j.theta..sup.2 and .DELTA..sub.0 remains the
same. The analysis is analogous and the result is the following:
and .times. .times. solving .times. .times. for .times. .times. M 0
.times. X 01 .times. e j .times. .times. .theta. 0 _ = M 0 .times.
X 01 .times. e j .times. .times. .theta. 0 * .DELTA. 0 M 0 .times.
X 01 .times. e j .times. .times. .theta. 0 _ = .times. V 02 ''
.function. ( e j .times. .times. .PHI. D .times. .times. 1 '
.times. e j .times. .times. .PHI. .times. D .times. .times. 2 ' - e
j .times. .times. 2 .times. .times. .PHI. D .times. .times. 1 '
.times. e j .times. .times. .PHI. D .times. .times. 2 ' ) - .times.
V 03 '' .function. ( e j .times. .times. 2 ' .times. .PHI. D
.times. .times. 1 - e j .times. .times. 2 .times. .times. .PHI. D
.times. .times. 2 ' ) + V 04 '' .function. ( e j .times. .times.
.PHI. D .times. .times. 1 ' - e j .times. .times. .PHI. D .times.
.times. 2 ' ) = .times. function .times. .times. of .times. .times.
.PHI. D .times. .times. 1 '' .times. .times. and .times. .times.
.PHI. D .times. .times. 2 '' .times. .times. and .times. .times.
solving .times. .times. for .times. .times. M 1 .times. X 11
.times. e j .times. .times. .theta. 1 _ = M 1 .times. X 11 .times.
e j .times. .times. .theta. 1 * .DELTA. 0 ( 6 '' ) M 1 .times. X 11
.times. e j .times. .times. .theta. 1 _ = .times. V 02 .function. (
e j .times. .times. .PHI. D .times. .times. 0 '' .times. e j
.times. .times. 2 .times. .times. .PHI. .times. D .times. .times. 2
'' - e j .times. .times. 2 .times. .times. .PHI. D0 '' .times. e j
.times. .times. .PHI. D .times. .times. 2 '' ) - .times. V 03
.function. ( e j .times. .times. 2 '' .times. .PHI. D .times.
.times. 0 - e j .times. .times. 2 .times. .times. .PHI. D .times.
.times. 2 '' ) + V 04 .function. ( e j .times. .times. .PHI. D
.times. .times. 0 '' - e j .times. .times. .PHI. D .times. .times.
2 '' ) = .times. function .times. .times. of .times. .times. .PHI.
D .times. .times. 0 ' .times. .times. and .times. .times. .PHI. D
.times. .times. 2 ' .times. .times. and .times. .times. solving
.times. .times. for .times. .times. M 2 .times. X 21 .times. e j
.times. .times. .theta. 2 _ = M 2 .times. X 21 .times. e j .times.
.times. .theta. 2 * .DELTA. 0 ( 7 '' ) M 2 .times. X 21 .times. e j
.times. .times. .theta. 2 _ = .times. V 02 .function. ( e j .times.
.times. .PHI. D .times. .times. 0 '' .times. e j .times. .times. 2
.times. .times. .PHI. .times. D .times. .times. 1 '' - e j .times.
.times. 2 .times. .times. .PHI. D0 '' .times. e j .times. .times.
.PHI. D1 '' ) - .times. V 03 .function. ( e j .times. .times. 2 '
.times. .PHI. D .times. .times. 1 '' - e j .times. .times. 2
.times. .times. .PHI. D .times. .times. 0 '' ) + V 04 .function. (
e j .times. .times. .PHI. D .times. .times. 1 '' - e j .times.
.times. .PHI. D .times. .times. 0 '' ) = .times. function .times.
.times. of .times. .times. .PHI. D .times. .times. 0 '' .times.
.times. and .times. .times. .PHI. D .times. .times. 1 '' ( 8 ' )
##EQU4## Taking equation (6'')/(6') we have the following:
e.sup.j.theta..sup.0=M.sub.0X.sub.01e.sup.j.theta..sup.0/M.sub.0X.sub.01=-
V''.sub.02(e.sup.j.PHI.'.sup.D1e.sup.j2.PHI.'.sup.D2-e.sup.j2.PHI.'.sup.D1-
e.sup.j.PHI.'.sup.D2)-V''.sub.03(e.sup.j2'.PHI..sup.D1-e.sup.j2.PHI.'.sup.-
D2+V''.sub.04(e.sup.j.PHI.'.sup.D1-e.sup.1.PHI..sup.D'2)/V.sub.01(e.sup.j.-
PHI.'.sup.D1e.sup.j2.PHI.'.sup.D2-e.sup.j2.PHI.'.sup.D1e.sup.j.PHI.'.sup.D-
2)-V.sub.02(e.sup.j2'.PHI..sup.D1-e.sup.j2.PHI.'.sup.D2)+V.sub.03(e.sup.j.-
PHI.'.sup.D1-e.sup.j.PHI.'.sup.D2) (12) Taking equation (7'')/(7')
we have the following:
e.sup.j.theta..sup.1=M.sub.1X.sub.11e.sup.j.theta..sup.1/M.sub.1X.sub.11=-
V.sub.02(e.sup.j.PHI.''.sup.D0e.sup.j2.PHI.''.sup.D2-e.sup.j2.PHI.''.sup.D-
1e.sup.j.PHI.''.sup.D2)-V.sub.03(e.sup.j2''.PHI..sup.D1-e.sup.j2.PHI.''.su-
p.D2+V.sub.04(e.sup.j.PHI.''.sup.D1-e.sup.j.PHI..sup.D''2)/V.sub.01(e.sup.-
j.PHI.'.sup.D0e.sup.j2.PHI.'.sup.D2-e.sup.j2.PHI.'.sup.D0e.sup.j.PHI.'.sup-
.D2)-V.sub.02(e.sup.j2'.PHI..sup.D0-e.sup.j2.PHI.'.sup.D2)+V.sub.03(e.sup.-
j.PHI.'.sup.D0-e.sup.j.PHI.'.sup.D2) (13) Taking equation
(8'')/(8') we have the following:
e.sup.j.theta..sup.2=M.sub.2X.sub.21e.sup.j.theta..sup.2/M.sub.2X.sub.21=-
V.sub.02(e.sup.j.PHI.''.sup.D0e.sup.j2.PHI.''.sup.D1-e.sup.j2.PHI.''.sup.D-
0e.sup.j.PHI.''.sup.D1)-V.sub.03(e.sup.j2'.PHI.''.sup.D1-e.sup.j2.PHI.''.s-
up.D0)+V.sub.04(e.sup.j2'.PHI.''.sup.D1-e.sup.j.PHI.''.sup.D0)/V.sub.01
(e.sup.j.PHI..sup.D0e.sup.j2.PHI..sub.D1-e.sup.j.PHI..sup.D1e.sup.j2.PHI.-
.sup.D0)-V.sub.02(e.sup.j2.PHI..sup.D1-e.sup.j2.PHI..sup.D0)+V.sub.03(e.su-
p.j.PHI..sup.D1-e.sup.j.PHI..sup.D0) (14) Performing the same
operations on equations (2''), (3'') and (4'') with the variables
M.sub.0X.sub.01e.sup.j.sup.0, M.sub.1X.sub.11e.sup.j.theta..sup.1
and M.sub.2X.sub.21e.sup.j.theta..sup.2 and .DELTA..sub.0 remains
the same Substituting equation (13) into equation (12) we have the
following: The analysis is analogous and the result is the
following: M.sub.0e.sup.j.PHI..sup.D0=function of
(.PHI..sub.D1,.PHI..sub.D2) ( 6)
M.sub.1e.sup.j.PHI..sup.D1=function of (.PHI..sub.D0, .PHI..sub.D2)
( 7) M.sub.2e.sup.j.PHI..sup.D2=function of
(.PHI..sub.D0,.PHI..sub.D1) ( 8) Equation ( 6)/(6), ( 7)/(7) and (
8)/(8) ( 6)/(6)=e.sup.j.PHI..sup.D0=function (.PHI..sub.D1,
.PHI..sub.D2) ( 7)/(7)=e.sup.j.PHI..sup.D1=function .PHI..sub.D0,
.PHI..sub.D2) ( 8)/(8)=e.sup.j.PHI..sup.D2=function
(.PHI..sub.D0,.PHI..sub.D1) Solving for .PHI..sub.D0, .PHI..sub.D1
and .PHI..sub.D2 and substituting these values in equations (2),
(3) and (4) we determine M.sub.0X.sub.00e.sup.j.theta..sup.0
M.sub.1X.sub.01e.sup.j.theta..sup.1 and
M.sub.2X.sub.02e.sup.j.theta..sup.2
e.sup.j.theta..sup.0=M.sub.0X.sub.00e.sup.j.theta..sup.0/M.sub.0X.sub.00=-
function of .PHI..sub.D1 and .PHI..sub.D2
e.sup.j.theta..sup.1=M.sub.1X.sub.01e.sup.j.theta..sup.1/M.sub.1X.sub.01=-
function of .PHI..sub.D0 and .PHI..sub.D2
e.sup.j.theta..sup.2=M.sub.2X.sub.02e.sup.j.theta..sup.2/M.sub.2X.sub.02=-
function of .PHI..sub.D0 and .PHI..sub.D1
[0185] From the determination of M.sub.0X.sub.01,M.sub.1X.sub.11
and M.sub.2X.sub.21 and M.sub.0X.sub.00 e.sup.j.theta..sup.0,
M.sub.1X.sub.01e.sup.j.theta..sup.1 and
M.sub.2X.sub.02e.sup.j.theta..sup.2 we have determined
.theta..sub.1, .theta..sub.2 and .theta..sub.3 And
.theta..sub.0=.PHI..sub.0+.DELTA.K.sub.D0X.sub.0:
.theta..sub.1=.PHI..sub.1+.DELTA.K.sub.D0X.sub.1:.theta..sub.2=.PHI..sub.-
2+.DELTA.K.sub.D0X.sub.2 where everything is known except
.PHI..sub.0, .PHI..sub.1 and .PHI..sub.2 and X.sub.O, X.sub.1 and
X.sub.2 are determined as in two return case and having determined
.PHI..sub.D0 and .PHI..sub.D1 and .PHI..sub.D2 since
.PHI..sub.A0=.PHI..sub.D0-.PHI..sub.0:
.PHI..sub.A1=.PHI..sub.D1-.PHI..sub.1:.PHI..sub.A2=.PHI..sub.D2-.PHI..sub-
.2 the azimuth of the returns have been attained.
[0186] .PHI..sub.D0 and .PHI..sub.D1 and .PHI..sup.D2 in the three
sets of matrix data of three returns as follows Substituting in
equation .PHI..sub.D1 as a function of .PHI..sub.D0 and
.PHI..sub.D2 we have the following: .PHI..sub.D0 as a function of
.PHI..sub.D2
Substituting in equation .PHI..sub.D1 as a function of .PHI..sub.D0
and .PHI..sub.D2 we have the following: .PHI..sub.D0 as a function
of .PHI..sub.D2
Substituting equation .PHI..sub.D2 as a function of .PHI..sub.D0
and .PHI..sub.D1 we have the following: .PHI..sub.D1 as a function
of .PHI..sub.D0
Similarly substituting .PHI..sub.D1 as a function of .PHI..sub.D2
we have the following: .PHI..sub.1 as a function of
.PHI..sub.D0
Similarly substituting .PHI..sub.D1 as a function of .PHI..sub.D0
we have the following:
Similarly substituting .PHI..sub.D1 as a function of .PHI..sub.D0
we have the following:
.PHI..sub.1 as a function of .PHI..sub.D2
we have the following:
.PHI..sub.D1 as a function of .PHI..sub.D2
we have two equations two unknowns and solvable in .PHI..sub.D0 and
.PHI..sub.D2 and similarly for .PHI..sub.D1 and .PHI..sub.D2.and
.PHI..sub.D0 and .PHI..sub.D1 and .PHI..sub.D1, .PHI..sub.D2 and
.PHI..sub.D3
Thus we have solved for .theta..sub.1, .theta..sub.2 and
.theta..sub.3 twice.
B1 Assist in Processing Three or More Returns Per Detected Bin
[0187] We can perform these operations for the three sets of data
for the three returns and the solutions should be the same or close
to the same.
[0188] The methodology in simplifying and more robust solutions
when there are three or returns is the following: [0189] 1.
Determine from processing adjacent bins for the detection of other
returns that would also be detected in the processed bin such as
clutter then we have one or more known solutions. [0190] 2.
Employing the candidate solution technique, that is substituting
all possible solutions which are very limited in number (detected
only in the beamwidth of the antenna). [0191] 3. If radar returns
are received from more than one range Doppler bin then we know that
there is an object associated with the radar returns located in the
overlap from the adjacent range Doppler bins (i.e., narrowing the
possible location of the object). Thus, multiple objects in a
single bin are easier to locate when overlap from other range
Doppler bins is also considered. [0192] 4. The solution entails
.PHI..sub.D1, .PHI..sub.D2, .PHI..sub.D3, etc where the amplitudes
are equal. From the second set of data a small frequency change
from the first set of data this gives the same .PHI..sub.D1,
.PHI..sub.D2 and .PHI..sub.D3 for the solution but different
M.sub.0, M.sub.1 and M.sub.2. The ratios of the
M'.sub.0/M.sub.0,M'.sub.1/M.sub.1 and M'.sub.2/M.sub.2 should give
a good estimate of where the position .PHI..sub.D0 and .PHI..sub.D1
and .PHI..sub.D2 are detected at their peak in that RDB and a check
on the solutions determined. From this the azimuth of the returns
are determined. From the ratio of the second set of data to the
first set of data we obtain XF0 and XF1 and XF2 from which is the
ratio of M'.sub.0/M.sub.0=X.sub.F0 and M'.sub.1/M.sub.1=X.sub.F1
and M'.sub.2/M.sub.2=X.sub.F2 where all other terms are known. From
the previous determinations of the estimate .PHI..sub.D0 and
.PHI..sub.D1 and .PHI..sub.D2 which is the position in the filter
where the returns are detected at there peak in the RDB. This gives
a good estimate of the azimuth of the returns. To get more accurate
determinations other close frequency points to initially processed
data are processed.
[0193] From XF0 an estimate of where the returns are detected at
there peak in the RDB. From the following equation
.PHI..sub.0A=.PHI..sub.D0-.PHI..sub.0 where .PHI..sub.0A is the
phase of the return proportional to the azimuth of the return, and
.PHI..sub.D1, .PHI..sub.D2 and .PHI..sub.D3 is the phase of the
return proportional to the peak of the return where, .PHI..sub.0 is
the phase of the return proportional to the velocity of the
return.
[0194] Similarly this is performed for XF1 and XF2 hence finding
the azimuth of the second and third return.
[0195] Analogously a small change in range bin may be taken and we
determine XR0, XR1 and XR2 which determines where the peak of the
returns in range, this does not help in the evaluation in azimuth.
If and evaluation in resolving velocity ambiguity with the taking
of meaning delay in time and processing again. Thus we can
determine the peak of each return in range and azimuth to obtain
the maximum amplitude for each return for further use.
[0196] A more accurate determination of .PHI..sub.D0, .PHI..sub.D1
and .PHI..sub.D2 is determined by taking the four sets of equations
and employing the candidate .PHI. technique substituting all
possible solutions which are restricted to the values that can be
in only one range doppler bin (RDB) but for when greater accuracy
is required the number of candidate solutions increase. The
candidate solutions should be very close in value for all four sets
of data giving very robust and accurate solutions which determines
all the parameters of the returns.
[0197] Also another correlating and checking operation is to repeat
the processing with a close frequency and the results should be
very close plus obtaining and obtaining change in return vector
(XF). This would be the same for all sets of four sets of data and
also would be a check on the .PHI..sub.D0, .PHI..sub.D1 and
.PHI..sub.D2 solutions. This is illustrated in FIG. 12.
[0198] Analogously this would process a close sample in the range
direction and also for processing other linear arrays. Attaining
the precise range, azimuth, height, unambiguous radial velocity and
vertical and tangential velocity is performed the same as in other
single channel many pulse systems. RECAPPING--We have determined
all .PHI.s, in the two return and three return case and as
consequently it may be performed for more than three .PHI.s. The
significance of this development is as each RDB that is processed
clutter, target, noise, and other returns may be detected and
thresholded for importance and later post processed to determine if
clutter, movers, sidelobes, multipath targets, and others.
Correlation Factors
1--Time delay as many pulses at a time as the number of returns and
process data determine all the .PHI.s
2--Additional time delay processed again and all (Ds should
agree
3--Other RDB processed that have the same return data related to
each such as mover should agree
4--IF more than two channels other dual channels is processed and
results should agree.
5--Other techniques that are related as to be shown later in
document and results should agree
6--If a planar array is implemented all other linear arrays should
obtain the same results and height and vertical tangential velocity
obtained.
[0199] The aforementioned system has many advantages such as the
following:
1--No clutter cancellation of any kind is required therefore as
follows:
[0200] a) no clutter covariance matrix; [0201] b) no training data;
and [0202] c) no special clutter knowledge required. 2--No channel
matching required 3--Returns and clutter do not compete with each
other in there detection and therefore clutter and returns are
thresholded separately and returns are ideally are competing with
white noise only and make for an excellent return ratio to noise.
4--Very simple system-less storage-less processing-less hardware
and less dwell time and very accurate. 5--Full transmit and receive
antenna employed with full antenna gains [0203] a) smaller antenna
sidelobes; [0204] b) full antenna gain; and [0205] c) narrow
clutter band width 6--May be applied to two arrays and two arrays
or three arrays. Each dual array processed as two channel system
and should have same results and correlated. 7--Correlation factors
as stated in previous paragraph. 8--The significance of the ability
to process many returns in same RDB and determining there amplitude
and phases and radial velocity gives the ability to separate
clutter and either returns such as bona fide targets, moving
clutter, multi path returns, etc. Knowledge aided information would
aid in categorizing these returns. IIII. Two channel "M" Pulses-Two
return analyses-DPCA TYPE OPERATION The following analysis may be
applied for a one transmit with the two or more receive antennae
(channels) utilizing DPCA techniques to find the range, radial
velocity and azimuth. This set of equations is for a two channel
.DELTA.T system. A--This development is for two(2) returns with
DPCA operation. V.sub.00=M.sub.0+M.sub.1 Channel 1 Pulse data 1-M
Delay 0 (1) V.sub.01=M.sub.0X.sub.01+M.sub.1X.sub.11 Channel 2
Pulse data 1-M Delay 0 (2)
V.sub.02=M.sub.0X.sub.02e.sup.j.theta..sup.0+M.sub.1X.sub.11e.sup.j-
.theta..sup.0 Channel 2 Pulse data 2-M+1 Delay 1 (3)
V.sub.03=M.sub.0X.sub.03e.sup.j2.theta..sup.0+M.sub.1X.sub.11e.sup.j2.the-
ta..sup.1 Channel 2 Pulse data 3-M+2 Delay 2 (4)
X.sub.01=e.sup.1D.PHI..sup.0/W.sub.M0 where
D=0:X.sub.01=e.sup.j(K.sup.D0.sup.X.sup.0.sup.)/W.sub.M0 (5)
X.sub.11=e.sup.jD.PHI..sup.1/W.sub.M1 where
D=0:X.sub.11=e.sup.j(K.sup.D0.sup.X.sup.1.sup.)/W.sub.M1 (6)
X.sub.02=e.sup.jD.PHI..sup.0.sup.+.DELTA.K.sup.D0.sup.X.sup.0/W.sub.M0
where
D=1:X.sub.01e.sup.j(.PHI..sup.0.sup.+.DELTA.K.sup.D0.sup.X.sup.0.su-
p.) (7)
X.sub.12=e.sup.j.PHI..sup.0.sup.+.DELTA.K.sup.D0.sup.X.sup.1/W.s-
ub.M1 where D=1:X.sub.11e.sup.1.PHI.K.sup.D0.sup.X.sup.1.sup.) (8)
X.sub.03=e.sup.jD(.PHI..sup.0.sup.+.DELTA.K.sup.D0.sup.X.sup.0.sup.)/W.su-
b.M0 where
D=2:X.sub.01e.sup.j2(.PHI..sup.0.sup.+K.sup.D0.sup.X.sup.0.sup.- )
(9)
X.sub.13=e.sup.jD(.PHI..sup.1.sup.+K.sup.D0.sup.X.sup.1.sup.)/W.su-
b.M1 where
D=2:X.sub.11e.sup.j2(.PHI..sup.0.sup.+K.sup.D0.sup.X.sup.1.sup.- )
(10)
[0206] Rewriting equations (1) to (4) incorporating development
above we have the following: V.sub.00=M.sub.0+M.sub.1 Channel 1
Pulse data 1-M Delay 0 (1) V.sub.01=M.sub.0X.sub.01+M.sub.1X.sub.11
Channel 2 Pulse data 1-M Delay 0 (2)
V.sub.02=M.sub.0X.sub.02e.sup.j.theta..sup.0+M.sub.1X.sub.11e.sup.j.theta-
..sup.0 Channel 2 Pulse data 2-M+1 Delay 1 (3)
V.sub.03=M.sub.0X.sub.03e.sup.j2.theta..sup.0+M.sub.1X.sub.11e.sup.j2.the-
ta..sup.1 (Channel 2 Pulse data 3-M+2 Delay 2 (4) where
.theta..sub.0=.DELTA.K.sub.D0X.sub.0 and
.theta..sub.1=.DELTA.K.sub.D0X.sub.1 All terms previously defined
except X.sub.01 and X.sub.11 where X.sub.01 and X.sub.02 is the
DPCA factor plus that which makes the channel 1 and channel 2 equal
and where A.sub.M0 is the amplitude matching antenna factor and
.PSI..sub.M0 is are the phase matching factor and K.sub.D0X.sub.0
is the factor of the detection is from the center of filter. AMO
and .PSI..sub.M0 represents the imperfect matching between channel
1 and 2. K.sub.D0X.sub.0 is the factor that corrects if the return
is not detected in the center of the filter. K.sub.D0 is the DPCA
constant that corrects off for mismatch from center of filter.
X.sub.0 is the distance the return is detected from the center of
filter. X.sub.1 and analogously the same as for W.sub.M1. A.sub.M1
is the amplitude factor and .PSI..sub.M1 and K.sub.D0 X.sub.1 are
the phase factor. A.sub.M1 and W.sub.M1 represent the imperfect
matching between channel and 2. K.sub.D0X.sub.1 is the factor that
corrects if the return is not detected in the center of the filter.
K.sub.D0 is the DPCA constant that corrects off center of filter.
X1 is the distance the return is detected from the center of
filter. Equation (1) is the first channel and equation (2) is the
second channel delayed no time delay. Equation (3) is second
channel delayed one times.
[0207] Taking equations (2) and (3) and treating M.sub.0X.sub.01
and M.sub.1X.sub.11 as the variables and vying for M.sub.0X.sub.01
and M.sub.1X.sub.11 we have:
Taking equations (3) and (4) and treating
M.sub.0X.sub.0e.sup.j.theta..sup.0 and
M.sub.1X.sub.1e.sup.j.theta..sup.1 as the variables and solving for
M.sub.0X.sub.0e.sup.j.theta..sup.0 and
M.sub.1X.sub.1e.sup.j.theta..sup.1 we have:
M.sub.0X.sub.0e.sup.j.theta..sup.0=(V.sub.02e.sup.j.theta..sup.1-V.sub.03-
)/(e.sup.j.theta..sup.1-e.sup.j.theta..sup.0) (2''')
M.sub.1X.sub.1e.sup.j.theta..sup.1=(V.sub.02=V.sub.03e.sup.j.theta..sup.0-
)/(e.sup.j.theta..sup.1-e.sup.j.theta..sup.0) (3''') Equation
(2''')/Equation (2'') and equation (3''')/equation (3'') is the
following:
e.sup.j.theta..sup.0=(V.sub.02e.sup.j.theta..sup.1-V.sub.03)/(V.sub.01e.s-
up.j.theta..sup.1-V.sub.02) (4)
e.sup.j.theta..sup.1=(V.sub.02-V.sub.03e.sup.j.theta..sup.0)/(V.sub.01-V.-
sub.02e.sup.j.theta..sup.0) (5) Equation (4) or Equation (5) is
easily solved for .theta..sub.0 and .theta..sub.1 which are solved
for .PHI..sub.0 and .PHI..sub.1 proportional to the radial velocity
of return 0 and return 1 respectively. If return "Mo" is clutter
then .PHI..sub.0=0 corresponding to clutter having zero (0)
velocity. Now employing equations (2) and (3) and solving for MoXo
and M1X1 knowing .PHI..sub.0 and .PHI..sub.1 we are now to find
.PHI..sub.D0 and .PHI..sub.D1 (defined previously) which are
proportional to return 0 and return 1 respectively where they are
detected in there filter. We have determined .PHI..sub.0 and
.PHI..sub.1 and MoXo and M1X1 and both returns are detected in the
same RDB but the location in that RDB is not known. If the location
is taken at the center of the filter the error in determination of
azimuth is plus or minus a half a RDB. If a more accurate
determination is desired a point of frequency close to first filter
is created and processed like that of first filter. This gives the
same .PHI..sub.0 and .PHI..sub.1 and different M.sub.0 and M.sub.1
and the ratio of the M.sub.0 and M.sub.1 should give a good
estimate of where the position .PHI..sub.D0 and .PHI..sub.D1 is
detected at in the RDB. From this an estimate of azimuth of both
returns determined. To get a more accurate determination another
frequency may be processed or a slight change in the range
processed and results correlated for best results. From a second
set of data a small known change in frequency from the first set of
data. We assume there will be no change in the channel balancing
terms A.sub.M0,.PSI..sub.M0 which are the amplitude and phase term
but a known DPCA term .DELTA.K.sub.D0 X.sub.0 where X.sub.0 is
unknown position of new filter and .DELTA.K.sub.D0 DPCA known
constant therefore the term is unknown and performing a small
change in frequency as done previously second set of data, the
solutions is then determined for .PHI..sub.1 and .PHI..sub.0 and
the changes are in X.sub.01 to X.sub.02
e.sup.j.DELTA.X.sup.0.sup.*.DELTA.K.sup.D0 where the phase term is
known and represents the known change in frequency and known
position change in peak of filter. The same is for the second
return X.sub.11 to X.sub.12e.sup.j.DELTA.K.sup.D0.sup.X.sup.1 and
analogous definitions of terms. The returns change due to frequency
change from M.sub.0 to M'.sub.0 where X.sub.F0=M'.sub.0/M.sub.0 and
M.sub.1 to M'.sub.1 where X.sub.F1=M'.sub.1/M.sub.1 and solving for
M.sub.0X.sub.0 and M.sub.0X.sub.0e.sup.j(K.sup.D1.sup.X.sup.0.sup.)
in the first and second set of data and dividing the terms we get
X.sub.F0 e.sup.j(K.sup.D1.sup.X.sup.0.sup.)=M'.sub.0/M.sub.0
e.sup.j(K.sup.D1.sup.X.sup.0.sup.). Therefore we have determined
the ratio of the returns from which we estimate the position of the
peak where is the first return and from that calculate the azimuth
of the return. We can analogously perform that for the second
return. The aforementioned analysis may be applied to many returns
per RDB but as the number of returns increases the difficulty of
determining the phases of the returns becomes much more difficult
up to four and more returns is cumbersome are complicated. More
said about that later in the document. B--This development is for
three (3) returns with DPCA operation.
V.sub.00=M.sub.0+M.sub.1+M.sub.2 CHANNEL 1-TIME 1 (1')
V.sub.01=M.sub.0X.sub.01+M.sub.1X.sub.11+M.sub.2X.sub.21CHANNEL
2-TIME 1 (2')
V.sub.02=M.sub.0X.sub.02e.sup.j.theta..sup.0+M.sub.12X.sub.12e.sup.-
j.PHI..sup.1+M.sub.2X.sub.12e.sup.j.PHI..sup.2 CHANNEL 2-TIME 2
(3')
V.sub.03=M.sub.0X.sub.03e.sup.j2.PHI..sup.0+M.sub.13X.sub.13e.sup.j2.PHI.-
.sup.1+M.sub.2X.sub.23e.sup.j2.PHI..sup.2 CHANNEL 2-TIME 3 (4')
V.sub.04=M.sub.0X.sub.04e.sup.j3.PHI..sup.0+M.sub.14X.sub.14e.sup.j3.PHI.-
.sup.1+M.sub.2X.sub.24e.sup.j3.PHI..sup.1 CHANNEL 2-TIME 4 (5')
X.sub.01=e.sup.j.PHI..sup.0/W.sub.M0=e.sup.j.PHI..sup.0/A.sub.M0e.sup.j(.-
PSI..sup.M0.sup.+K.sup.D0.sup.X.sup.0.sup.) where .PHI..sub.0=0
(6')
X.sub.11=e.sup.j.theta..sup.0/W.sub.M1=e.sup.j.PHI..sup.1/W.sub.M1=e.sup.-
j.PHI..sup.1/A.sub.M1e.sup.j(.PSI..sup.M1.sup.+K.sup.D0.sup.X.sup.1.sup.)
where .PHI..sub.1=0 (7')
X.sub.12=e.sup.j.PHI..sup.2/W.sub.M2=e.sup.j.PHI..sup.2/A.sub.M2e.sup.j(.-
PSI..sup.M2.sup.+K.sup.D0.sup.X.sup.2.sup.) where .PHI..sub.2=0
(8')
X.sub.02=X.sub.01e.sup.j.PHI..sup.0/W.sub.M0=1/A.sub.M0e.sup.j(.PHI..sup.-
0.sup.-.DELTA.K.sup.D0.sup.X.sup.0-.PSI..sup.M0.sup.) (9')
X.sub.12=e.sup.j.PHI..sup.1/W.sub.M1=e.sup.j.PHI..sup.1/A.sub.M1e.sup.j(.-
PHI..sup.1.sup.-.DELTA.K.sup.D0.sup.X.sup.1-.PSI..sup.M1.sup.)
(10')
X.sub.22=e.sup.j.PHI..sup.2/W.sub.M2=e.sup.j.PHI..sup.2/A.sub.M2e.sup.j(.-
PHI..sup.2.sup.-.DELTA.K.sup.D0.sup.X.sup.2-.PSI..sup.M2.sup.)
(11')
X.sub.03=X.sub.01e.sup.j.PHI..sup.1/W.sub.M0=1/A.sub.M0e.sup.j2(.PHI..sup-
.0.sup.-.DELTA.K.sup.D0.sup.X.sup.0.sup.) -.PSI..sup.M0.sup.) (12')
X.sub.13=e.sup.j.PHI..sup.1/W.sub.M1=e.sup.j.PHI..sup.1/A.sub.M1e.sup.j2(-
.PHI..sup.1.sup.-.DELTA.K.sup.D0.sup.X.sup.1.sup.)-.PSI..sup.M1.sup.)
(13')
X.sub.23=e.sup.j.PHI..sup.2/W.sub.M2=e.sub.j.PHI..sup.2/AM2e.sup.j-
2(.PHI..sup.2.sup.-.DELTA.K.sup.D0.sup.X.sup.2.sup.)-.PSI..sup.M2.sup.)
(14')
[0208] Rewriting equations (1) to (5) incorporating development
above we have the following: V.sub.00=M.sub.0+M.sub.1+M.sub.2
CHANNEL 1-TIME 1 (1')
V.sub.01=M.sub.0X.sub.01+M.sub.1X.sub.11+M.sub.2X.sub.21CHANNEL
2-TIME 1 (2')
V.sub.02=M.sub.0X.sub.02e.sup.j2.theta..sup.0+M.sub.12X.sub.12e.sup.j.the-
ta..sup.1+M.sub.2X.sub.12e.sup.j.theta..sup.2 CHANNEL 2-TIME 2 (3')
V.sub.03=M.sub.0X.sub.03e.sup.j2.theta..sup.0+M.sub.13X.sub.13e.sup.j2.th-
eta..sup.1+M.sub.2X.sub.23e.sup.j2.theta..sup.2 CHANNEL 2-TIME 3
(4')
V.sub.04=M.sub.0X.sub.04e.sup.j3.theta..sup.0+M.sub.14X.sub.14e.sup.j3.th-
eta..sup.1+M.sub.2X.sub.24e.sup.j3 .theta..sup.1 CHANNEL 2-TIME 4
(5')
[0209] Taking equations (2') and (3') and (4') and treating
M.sub.0X.sub.0 and M.sub.1X.sub.1 and M.sub.2X.sub.2 as the
variables and solving the determinant equation for .DELTA..sub.0 we
have: .DELTA. 0 = .times. e j.theta. 0 1 .times. e j.theta. 1 1
.times. e j.theta. 2 1 = .times. 1 .times. e j.theta. 1 .times. e
j.theta. 2 - 1 .times. e j.theta. 0 .times. e j.theta. 2 + .times.
1 .times. e j.theta. 0 .times. e j.theta. 1 .times. e j2.theta. 0
.times. e j2.theta. 1 .times. e j2.theta. 2 .times. e j2.theta. 1
.times. e j2.theta. 2 .times. e j2.theta. 0 .times. e j2.theta. 2
.times. e j2.theta. 0 .times. e j2.theta. 1 = .times. e j.theta. 1
.times. e j2.theta. 2 - e j.theta. 2 .times. e j2.theta. 1 - e
j.theta. 0 .times. e j2.theta. 2 + e j.theta. 2 .times. e j2.theta.
0 + .times. e j.theta. 0 .times. e j2.theta. 1 - e j.theta. 1
.times. e j2.theta. 0 = .times. function .times. .times. of .times.
.times. .theta. 0 , .theta. 1 .times. .times. and .times. .times.
.theta. 2 .times. .times. and .times. .times. solving .times.
.times. for .times. .times. M 0 .times. X 01 _ = M 0 .times. X 01 *
.DELTA. 0 .times. .times. M 0 .times. X 01 _ = V 02 V 01 .times. e
j.theta. 1 1 .times. e j.theta. 2 1 = V 01 .times. e j.theta. 1
.times. e j.theta. 2 - V 02 .times. 1 .times. .times. 1 .times.
.times. V 03 .times. 1 .times. .times. 1 .times. .times. V 03
.times. e j2.theta. 1 .times. e j2.theta. 2 .times. e j2.theta. 1
.times. e j2.theta. 2 .times. e j2.theta. 1 .times. e j2.theta. 2
.times. e j2.theta. 1 .times. e j2.theta. 2 M 0 .times. X 01 _ =
.times. V 01 .function. ( e j.theta. 1 .times. e j2.theta. 2 - e
j.theta. 2 .times. e j2.theta. 1 ) - .times. V 02 .function. ( e
j2.theta. 2 - e j2.theta. 1 ) + V 03 .function. ( e j.theta. 1 - e
j.theta. 2 ) = .times. function .times. .times. of .times. .times.
.theta. 1 .times. .times. and .times. .times. .theta. 2 .times.
.times. and .times. .times. solving .times. .times. for ( 6 ) M 1
.times. X 11 _ = .times. M 1 .times. X 11 * .DELTA. 0 = .times. V
02 .function. ( e j.theta. 0 .times. e j2.theta. 2 - e j.theta. 2
.times. e j2.theta. 0 ) - .times. V 03 .function. ( e j2.theta. 2 -
e j2.theta. 0 ) + V 04 .function. ( e j.theta. 2 - e j.theta. 0 ) =
.times. function .times. .times. of .times. .times. .theta. 0
.times. .times. and .times. .times. .theta. 2 .times. .times. and
.times. .times. solving .times. .times. for .times. .times. M 2
.times. X 21 _ = .times. M 2 .times. X 21 * .DELTA. 0 = .times. V
02 .function. ( e j.theta. 0 .times. e j2.theta. 1 - e j.theta. 1
.times. e j2.theta. 0 ) - .times. V 03 .function. ( e j2.theta. 1 -
e j2.theta. 0 ) + V 04 .function. ( e j.theta. 1 - e j.theta. 0 ) =
.times. function .times. .times. of .times. .times. .theta. 0
.times. .times. and .times. .times. .theta. 1 .times. .times. M 2
.times. X 21 _ = e j.theta. 0 1 .times. e j.theta. 1 1 .times. V 02
V 02 = V 01 .times. e j.theta. 0 .times. e j.theta. 1 - V 02
.times. 1 .times. .times. 1 + V 03 .times. 1 .times. .times. 1
.times. .times. e j2.theta. 0 .times. e j2.theta. 1 .times. V 03
.times. e j2.theta. 0 .times. e j2.theta. 1 .times. e j2.theta. 0
.times. e j2.theta. 1 .times. e j.theta. 0 .times. e j.theta. 1 ( 7
) M 2 .times. X 21 _ = .times. V 01 .function. ( e j.theta. 0
.times. e j2.theta. 1 - e j.theta. 1 .times. e j2.theta. 0 ) - V 02
.times. ( e j2.theta. 1 - e j2.theta. 0 ) + .times. V 03 .function.
( e j.theta. 1 - e j.theta. 0 ) = .times. function .times. .times.
of .times. .times. .theta. 1 .times. .times. and .times. .times.
.theta. 2 ( 8 ) ##EQU5## Performing the same operations on
equations (3), (4) and (5) with the variables M.sub.0X.sub.01
e.sup.j.theta..sup.0, M.sub.1X.sub.11e.sup.j.theta..sup.1 and
M.sub.2X.sub.12e.sup.j.theta..sup.0 and .DELTA..sub.0 remains the
same. The analysis is analogous and the result will be the
following: and .times. .times. solving .times. .times. for .times.
.times. M 0 .times. X 01 .times. e j.theta. 0 _ = M 0 .times. X 01
.times. e j.theta. 0 * .DELTA. 0 M 0 .times. X 01 _ .times. e
j.theta. 0 _ = .times. V 02 .function. ( e j.theta. 1 .times. e
j2.theta. 2 - e j.theta. 2 .times. e j2.theta. 1 .times. 1 ) -
.times. V 03 .function. ( e j2.theta. 2 - e j2.theta. 1 ) + V 04
.function. ( e j.theta. 2 - e j.theta. 1 ) = .times. function
.times. .times. of .times. .times. .theta. 1 .times. .times. and
.times. .times. .theta. 2 .times. .times. and .times. .times.
solving .times. .times. for .times. .times. M 1 .times. X 11
.times. e j.theta. 1 _ = M 1 .times. X 11 .times. e j.theta. 1 *
.DELTA. 0 ( 9 ) M 1 .times. X 11 _ .times. e j.theta. 1 _ = .times.
V 02 .function. ( e j.theta. 0 .times. e j2.theta. 2 - e j.theta. 2
.times. e j2.theta. 0 ) - .times. V 03 .function. ( e j2.theta. 2 -
e j2.theta. 0 ) + V 04 .function. ( e j.theta. 2 - e j.theta. 0 ) =
.times. function .times. .times. of .times. .times. .theta. 0
.times. .times. and .times. .times. .theta. 2 .times. .times. and
.times. .times. solving .times. .times. for .times. .times. M 2
.times. X 21 .times. e j.theta. 2 _ = M 2 .times. X 21 .times. e
j.theta. 2 * .DELTA. 0 ( 10 ) M 2 .times. X 21 _ .times. e j.theta.
2 _ = .times. V 02 .function. ( e j.theta. 0 .times. e j2.theta. 1
- e j.theta. 1 .times. e j2.theta. 0 ) - .times. V 03 .function. (
e j2.theta. 1 - e j2.theta. 0 ) + V 04 .function. ( e j.theta. 1 -
e j.theta. 0 ) = .times. function .times. .times. of .times.
.times. .theta. 0 .times. .times. and .times. .times. .theta. 1 (
11 ) ##EQU6## Taking the equations (9)/(6) and solve we have the
following: e j.theta. 0 = .times. V 03 .function. ( e j.theta. 1
.times. e j2.theta. 2 - e j.theta. 2 .times. e j2.theta. 1 ) - V 04
.function. ( e j2.theta. 2 - e j2.theta. 1 ) + .times. V 05
.function. ( e j2.theta. 2 - e j2.theta. 1 ) / .times. V 02
.function. ( e j.theta. 1 .times. e j2.theta. 2 - e j.theta. 2
.times. e j2.theta. 1 ) - V 03 .function. ( e j2.theta. 2 - e
j2.theta. 1 ) + .times. V 04 .function. ( e j2.theta. 2 - e
j2.theta. 1 ) = .times. function .times. .times. of .times. .times.
.theta. 1 .times. .times. and .times. .times. .theta. 2 ( 12 '' )
##EQU7## Taking the previous equations (10)/(7) and solve we have
the following: e j.theta. 1 = .times. V 03 .function. ( e j.theta.
0 .times. e j2.theta. 2 - e j.theta. 2 .times. e j2.theta. 0 ) - V
04 .function. ( e j2.theta. 2 - e j2.theta. 0 ) + .times. V 05
.function. ( e j2.theta. 2 - e j2.theta. 0 ) / .times. V 02
.function. ( e j.theta. 0 .times. e j2.theta. 2 - e j.theta. 2
.times. e j2.theta. 0 ) - V 03 .function. ( e j2.theta. 2 - e
j2.theta. 0 ) + .times. V 04 .function. ( e j2.theta. 2 - e
j2.theta. 0 ) = .times. function .times. .times. of .times. .times.
.theta. 0 .times. .times. and .times. .times. .theta. 2 ( 13 '' )
##EQU8## Taking the previous equation (11)/(8) and solve we have
the following: e j.theta. 2 = .times. V 03 .function. ( e j.theta.
0 .times. e j2.theta. 1 - e j.theta. 1 .times. e j2.theta. 0 ) - V
04 .function. ( e j2.theta. 1 - e j2.theta. 0 ) + .times. V 05
.function. ( e j2.theta. 1 - e j2.theta. 0 ) / .times. V 02
.function. ( e j.theta. 0 .times. e j2.theta. 1 - e j.theta. 1
.times. e j2.theta. 0 ) - V 03 .function. ( e j2.theta. 1 - e
j2.theta. 0 ) + .times. V 04 .function. ( e j2.theta. 1 - e
j2.theta. 0 ) = .times. function .times. .times. of .times. .times.
.theta. 0 .times. .times. and .times. .times. .theta. 2 ( 14 '' )
##EQU9## Substituting equation (13'') into equation (12'') we have
the following: .theta..sub.0 as a function of .theta..sub.2
Substituting equation (13'') into equation (14'') we have the
following: .theta..sub.0 as a function of .theta..sub.2 we have two
equations two unknowns and solvable in .PHI..sub.0 and .PHI..sub.2.
Substituting equation (12'') into equation (13'') we have the
following: .theta..sub.1 as a function of .theta..sub.2
Substituting equation (12'') into equation (14'') we have the
following: .theta..sub.1 as a function of .theta..sub.2 we have two
equations two unknowns and solvable in .PHI..sub.1 as a function of
.PHI..sub.2. Substituting equation (14'') into equation (13'') we
have the following: .theta..sub.0 as a function of .theta..sub.1
Substituting equation (14'') into equation (12'') we have the
following: .theta..sub.0 as a function of .theta..sub.1 C1--Same as
Assist in Section B1 for Assist in Determining Solutions for
.theta..sub.0, .theta..sub.1, .theta..sub.2, ETC for More Two
Returns Instead of .PHI..sub.D0, .PHI..sub.D1, .PHI..sub.D2, Etc we
have two equations two unknowns and solvable in .theta..sub.0 as a
function of .theta..sub.1 Thus we have solved for .theta..sub.2
twice
[0210] From a second set of data a small known change in frequency
from the first set of data. We assume there will be no change in
the channel balancing terms A.sub.M0,.PSI..sub.M0 which are the
amplitude and phase term but a known DPCA term
.DELTA.K.sub.D0X.sub.0 where X.sub.0 is the unknown change in
position of new filter and K.sub.D0 DPCA known constant therefore
the term is known. Performing the operations on the second set of
data, the solutions are the same for .theta..sub.1 and
.theta..sub.2 and the changes are in X.sub.01 to X.sub.01
e.sup.j(.DELTA.K.sup.D0.sup.X.sup.0.sup.) where the phase term is
known and represents the known change in frequency and known
position change in peak of filter. The same is for the second and
third return X.sub.11 to
X.sub.11e.sup.j.DELTA.X.sup.1.sup.*.DELTA.K.sup.D0 and X.sub.21 to
X.sub.21e.sup.j.DELTA.X.sup.2.sup.*.DELTA.K.sup.D0 and analogous
definitions of terms. The returns change due to frequency change
from M.sub.0 to M'.sub.0 where X.sub.F0=M'.sub.0/M.sub.0 and
M.sub.1 to M'.sub.1 where X.sub.F1=M'.sub.1/M.sub.1 and solving for
M.sub.0X.sub.01 and
M.sub.0X.sub.01e.sup.j(K.sup.D0.sup.*.DELTA.X.sup.0.sup.) in the
first and second set of data and dividing the terms we get X.sub.F0
e.sup.j(K.sup.D0.sup.*.DELTA.X.sup.0.sup.)=M'.sub.0/M.sub.0e.sup.j(K.sup.-
D0.sup.*.DELTA.X.sup.0.sup.). Therefore we have determined the
ratio of the returns from which we estimate the position of the
peak where is the first return and from that calculate the azimuth
of the return. We can analogously perform that for the second and
third return. The aforementioned analysis may be applied to many
returns per RDB but as the number of returns increase the
difficulty of determining the phases of the returns becomes much
more difficult up to four or more returns is cumbersome is
complicated. More said about that later in the document.
C2--Combining techniques of section III--Two channels "M" pulse
system .PHI..sub.D technique and section IIII--.DELTA.T
technique-DPCA-Two channel "M" pulse system
[0211] The two techniques employ the same data and may be processed
in any manner to facilitate a solution. The following is a list of
common solutions and attributes.
[0212] 1. Same solutions for all parameters such as the following:
[0213] a) .PHI..sub.D s, .PHI..sub.A s and .PHI.s and M s and
X.sub.F s, X.sub.R s and X.sub.H s [0214] b) .PHI..sub.D s have
many same solutions in the .PHI..sub.D technique [0215] c)
solutions for position and velocity of respective returns [0216] 2.
.PHI..sub.D technique is more effective but requires more storage
and processing but requires one less delay in data
[0217] 3. Accuracy and robustness of solutions are enhanced
[0218] 4. Appearance of a very practical system
[0219] D--Analyzing the relationship (Duality) between one and two
pulse systems to that of the one and two channel systems. The one
and two channel systems employ many pulses in time which the
spectrum (transformed to frequency) are obtained while the one and
two pulse systems employ many channels (space elements) which the
spectrum (transformed to frequency) are obtained.
[0220] 1. The many pulse system and the many channel system the
detection of clutter is the azimuth of detection while movers have
two components one due to there azimuth and the other due to their
radial velocity. The total frequency component is the addition of
these components.
[0221] 2. The many pulse system processes all detections of returns
in the same RDB and the many channel system processes all
detections of returns in the same RAB.
[0222] 3. The many pulse system processes to determine velocity of
returns and then calculates azimuth. The many channel system
processes to determine azimuth of returns and then calculates
velocity.
[0223] 4. Calculation of DPCA and channel balancing factors are a
duality since one works on space elements transformed while the
other works on time elements transformed. Although one works with
space but other works with time they have the same form and lend
themselves to analogous equations and solutions. The channel
balancing terms are in both systems depending on the azimuth of the
returns. The DPCA terms depend on respective delays one in time and
other in space but are analogous. Consequently they are analyzed in
that manner.
[0224] 5. FIGS. 7 and 8 illustrate in the multipulse systems the
number of parameters that could be correlated if n additional sets
of data are processed which also applies to the multichannel
systems. FIG. 9 illustrates the type of operations to be performed
in implementing the multichannel system.
V One Pulse and One Channel Systems
[0225] This STAP methodology employs one or more pulse or channel
data but one pulse at a time or one channel at a time, process them
into its frequency spectrum and consequently localize clutter into
its own range azimuth bin (RAB) or range doppler bin (RDB) together
with any other returns such as target, thermal noise, and
others.
[0226] The subsequent processing of each bin will separate out
clutter doppler since clutter has zero (0) radial velocity and
other returns detected in the same bin will have different
velocities. Determining the azimuth and the velocity of the returns
will be calculated therefore no additional data is required.
[0227] The knowledge aided STAP will be involved to determine from
the detected returns which are the targets of interest, sidelobe
returns, land sea interface, thermal noise, etc.
[0228] The knowledge aided STAP will not be involved in canceling
clutter but in the post processing of the returns of interest so
they may be detected and there parameters measured and determine
the nature of the return.
[0229] The following sections will be an analysis of various
techniques with there mathematical development to accomplished
these ends. It is assumed the channel or time data has been
processed by FFT into there individual range azimuth bins (RABs) or
(RDBs) respectively where there exist in the cases of interest
clutter (0--velocity) and other returns (non "0" velocity).
Initially two (2) returns will be developed; it may be clutter and
moving target or two moving targets.
[0230] More returns detected in one bin will be considered such as
three returns, or more.
[0231] VA1--Two Returns Only Employing Two Sets of Data Common to
all One Channel and One Pulse Systems V.sub.00=M.sub.0+M.sub.1 (1)
V.sub.01=M.sub.0e.sup.j.PHI..sup.D0+M.sub.1.sup.j.PHI..sup.D1 (2)
V.sub.02=M.sub.0e.sup.j2.PHI..sup.D0+M.sub.1.sup.j2.PHI..sup.D1
(3)
[0232] VA1--One Channel Many Pulse Odd-Even Data and Apertures
[0233] EQUATIONS (1),(2) and (3) and (1'),(2') and (3') represented
as follows: TABLE-US-00001 (1)-channel 1 -aperture 1-time data 1,
3, 5, - - - , m - 1 odd data (2)- 3, 5, 7, - - - , m + 1 (3) 5, 7,
9, - - - , m + 3 (1') -aperture 2 2, 4, 6, - - - , m even data (2')
4, 6, 8, - - - , m + 2 (3') 6, 8, 1O, - - - , m + 4
[0234] VA2--One Channel Many Pulse No Odd-Even Data and
Simultaneous Apertures
[0235] EQUATIONS (1), (2) and (3) and (1'), (2') and (3')
represents as follows: TABLE-US-00002 (1)-channel 1 -aperture
1-time data 1, 2, 3, - - - , m (2)- 1, 2, 3, - - - , m (3) 1, 2, 3,
- - - , m (1')- -aperture 2 1, 2, 3, - - - , m (2') 1, 2, 3, - - -
, m (3') 1, 2, 3, - - - , m
[0236] VA3--One Pulse Many Channels Odd-Even Data and Apertures
EQUATIONS (1),(2) and (3) and (1'),(2') and (3') represents as
follows: TABLE-US-00003 (1)-PULSE 1 -aperture 1, 3, 5, - - - , N -
1 odd data 1-CHANNEL data (2)- 3, 5, 7, - - - , N + 1 (3) 5, 7, 9,
- - - , N + 3 (1') -aperture 2 2, 4, 6, - - - , N even data (2') 4,
6, 8, - - - , N + 2 (3') 6, 8, 10, - - - , N + 4
[0237] VA4--One Pulse Many Channels No Odd-Even Data and
Simultaneous Apertures
[0238] a) EQUATIONS (1),(2) and (3) and (1'),(2') and (3')
represents as follows: TABLE-US-00004 (1)-PULSE 1 -aperture
1-CHANNEL data 1, 2, 3, - - - , N (2)- 1, 2, 3, - - - , N (3) 1, 2,
3, - - - , N (1')- -aperture 2 1, 2, 3, - - - , N (2') 1, 2, 3, - -
- , N (3') 1, 2, 3, - - - , N
[0239] Taking equations (1) and (2) and treating M.sub.0 and
M.sub.1 as the variables and solving for M.sub.0 and M.sub.1 we
have:
M.sub.0=(V.sub.00e.sup.j.PHI..sup.D1-V.sub.01)/(e.sup.j.PHI..sup.D1-e.sup-
.j.PHI..sup.D0) (5)
M.sub.1=(V.sub.01-e.sup.j.PHI..sup.D0V.sub.00)/(e.sup.j.PHI..sup.D1-e.sup-
.j.PHI..sup.D0) (6)
[0240] Taking equations (2) and (3) and solving for M.sub.0
e.sup.j.PHI..sup.D0 and M.sub.1.sup.j.PHI..sup.D1 we have the
following:
M.sub.0e.sup.j.PHI..sub.D0=(V.sub.01e.sup.j.PHI..sup.D1=V.sub.02)/(e.sup.-
j.PHI..sup.D1-e.sup.j.PHI..sup.D0) (7)
M.sub.1e.sup.j.PHI..sup.D1=(V.sub.02-e.sup.j.PHI..sup.D0V.sub.01)/(e.sup.-
j.PHI..sup.D1-e.sup.j.PHI..sup.D0) (8) Dividing equations (7)/(5)
and equations (8)/(6) we have the following:
e.sup.j.PHI..sup.D0=(V.sub.01e.sup.j.PHI..sup.D1-V.sub.02)/(V.sub.00e.sup-
.j.PHI..sup.D1-V.sub.01) (9)
e.sup.j.PHI..sup.D1=(V.sub.02-e.sup.j.PHI..sup.D0V.sub.01)/(V.sub.01-e.su-
p.j.PHI..sup.D0V.sub.00) (10)
[0241] Solving equation (9) and (10) for .PHI..sub.D0 and
.PHI..sub.D1 and substituting these values into equation (1) and
(2) and determine M.sub.0 and M.sub.1.
[0242] Now we have another set of equations for aperture (antenna)
2 formulated a beam width away from the first aperture (it can be
any reasonable distance away). V'.sub.00=M'.sub.0+M'.sub.1 (1')
V'.sub.01=M'.sub.0e.sup.j.PHI.'.sup.D0+M'.sub.1j.PHI.'.sup.D1 (2')
V'.sub.02=M'.sub.0e.sup.j2.PHI.'.sup.D0+M'.sub.1j2.PHI.'.sup.D1
(3')
[0243] Taking equations (1'), (2') and (3') and performing the
identical operations as on equations (1), (2) and (3) and solving
for .PHI.'.sub.DO and .PHI.'.sub.D1 and M'.sub.0+M'.sub.1 and where
.PHI.'.sub.DO=.PHI..sub.DO and .PHI.'.sub.D1=.PHI..sub.D1
K.sub.M0e.sup.j.alpha..sup.0=M'.sub.0/M.sub.0=(V'.sub.00e.sup.j.PHI.'.sup-
.D1-V'.sub.01)/(V.sub.00e.sup.j.PHI.'.sup.D1-V.sub.01) (12)
K.sub.M1e.sup.j.PHI..alpha.1=M'.sub.1/M.sub.1=(V'.sub.01-V'.sub.00e.sup.j-
.PHI.'.sup.D0)/(V.sub.01-V.sub.00e.sup.j.PHI.'.sup.D0) (13) b) From
the data in the significant clutter only area in the antennas we
have the equation for clutter only data as follows:
[0244] The returns from a prior measurement of the ratio of return
output of aperture 2, even data to aperture 1 data, odd
data-vs-azimuth or real time measurement of significant clutter
only data, their ratio of two apertures-vs-azimuth and compared
with ratios calculated in the processing which is the position in
the filter where the returns are detected.
[0245] The methodology of producing this curve from real time data
is as follows: [0246] a) chose only relatively large amplitude
clutter only data [0247] b) determine its azimuth from its
measurement and its amplitude and phase ratio of the return of
apertures [0248] c) measure ratio of ratio of the amplitude and
phase from each aperture which is
K.sub.M0e.sup.j.alpha..sup.0=M'.sub.0/M.sub.0 and
K.sub.M1e.sup.j.PHI..alpha..sup.1=M'.sub.1/M.sub.1 [0249] d) note:
clutter only data is at its azimuth position--no radial velocity
[0250] e) perform this with as much data as to obtain a very good
estimate of the curve of c) by any fitting statistical methodology
[0251] f) thus we have obtained a very good estimate of curve
desired
[0252] Now having generated from the real time data the curve of
ratio of even divided by odd-vs-azimuth the candidate .PHI.
technique is employed where all the possible phases are substituted
(which are very limited in number, in equation (12) or (13) and the
solutions are compared to the curve for the ratio of aperture data
as a function of azimuth and where there is a match this is the
solution. The solution for equations (12) and (13) should agree and
they are a check on each other. Having attained the solution for
azimuth .PHI..sub.A and having the solution for .PHI..sub.D then
.PHI.=.PHI..sub.D-.PHI..sub.A, the solution for radial velocity of
the returns.
[0253] From the ratio of the second set of data to the first set of
data we obtain K.sub.M0e.sup.j.alpha..sup.0 and
K.sub.M1e.sup.j.alpha..sup.1 which is the ratio of
M'.sub.0/M.sub.0=K.sub.M0e.sup.j.alpha..sup.0 and
M'.sub.1/M.sub.1=K.sub.M1e.sup.j.alpha..sup.1 where all other terms
are known.
c) A close range is now processed. This is processed to yield a
second set of equations and processing similar to first set of
data.
[0254] Now employing equations (1) and (2) and solving for M.sub.0
and M.sub.1 knowing .PHI..sub.A0 and .PHI..sub.A1 we are now to
find .PHI..sub.R0 and .PHI..sub.R1 which is the detected position
of 0 and 1 return is at its peak in the range bin, are proportional
to range of return 0 and return 1 respectively. and M.sub.0 and
M.sub.1 and both returns are detected in the same range bin (RB)
but the location in that RB is not known. If the location is taken
at the center of the filter the error in determination of range is
plus or minus a half a RB. If a more accurate determination is
desired a point of range close to first filter is created and
processed like that of first data set this will be used to a more
accurate determination of the range of both returns.
[0255] This gives the same .PHI..sub.A0 and .PHI..sub.A1 and
different M.sub.0 and M.sub.1 and the ratios of the M.sub.0 and
M.sub.1 should give a good estimate of where the position
.PHI..sub.R0 and .PHI..sub.R1 is detected in the RB. From this an
estimate of better range of both returns is determined. To get a
more accurate determination, another range or ranges may be
processed or a slight change in the range processed and results
correlated for best results. The ratio of second set of data for
close in range we will obtain a much more accurate range.
[0256] The linear array height amplitude and phase changes in the
different linear arrays should be the same.
[0257] The X.sub.R and X.sub.H should be all equal in the both sets
of data and is another determination of the correct results
[0258] Up to this point all sections VA1-VA4 have a common set of
equations and solutions.
[0259] In the one channel system if the time data is delayed a
significant time and processed like the first set of data the
amplitude and phase change of the range will give the unambiguous
velocity from which the ambiguous velocity is calculated and will
be a check on the velocity that has been determined. This may be
performed as many times as necessary and may eliminate the need for
another PRF to increase the ambiguous velocity.
[0260] Processing similarly for change in doppler frequency will
give the horizontal tangential velocity and for height change in
the linear arrays will give vertical tangential velocity.
[0261] Thus range, azimuth and radial velocity unambiguously and
vertical and horizontal tangential velocity has been attained.
[0262] In the one pulse system the precise range and height will be
as in the one channel system but precise frequency will not be the
same meaning. The significant delay in channel will give these
parameters as a function of channel change.
[0263] Additional aids in one pulse and one channel systems the
attaining the solutions are to employ another delayed set of data
and results should agree with the first set of data processed.
Further if another close range bin is processed the change in range
in both sets of data processed should be the same. This holds for
the height and doppler or azimuth change is the same.
[0264] VB--Three Returns Only Employing Three Sets of Data Common
To all One Channel and One Pulse Systems
V.sub.00=M.sub.0+M.sub.1+M.sub.2 (1)
V.sub.01=M.sub.0e.sup.j.PHI..sup.D0+M.sub.1.sup.j.PHI..sup.D1+M.sub.2j.PH-
I..sup.D2 (2)
V.sub.02=M.sub.0e.sup.j2.PHI..sup.D0+M.sub.1.sup.j2.PHI..sup.D1+M.sub.2.s-
up.j2.PHI..sup.D2 (3)
V.sub.03=M.sub.0e.sup.j3.PHI..sup.D0+M.sub.1.sup.j3.PHI..sup.D1+M.sub.2.s-
up.j3.PHI..sup.D2 (4) VB1--One Channel Many Pulse Odd-Even Data and
Apertures
[0265] EQUATIONS (1),(2),(3) and (4) and (1'),(2'),(3') and (4')
represented as follows: TABLE-US-00005 (1)-channel 1 -aperture
1-time data 1, 3, 5, - - - , m - 1 odd data (2)- 3, 5, 7, - - - , m
+ 1 (3) 5, 7, 9, - - - , m + 3 (4) 7, 9, 11, - - - , m + 5 (1')
-aperture 2 2, 4, 6, - - - , m even data (2') 4, 6, 8, - - - , m +
2 (3') 6, 8, 10, - - - , m + 4 (4') 8, 10, 12, - - - , m + 6
VB2--One Channel Many Pulse No Odd-Even Data and Simultaneous
Apertures
[0266] EQUATIONS (1), (2), (3) and (4) and (1'), (2'), (3') and
(4') represented as follows: TABLE-US-00006 (1)-channel 1 -aperture
1-time data 1, 2, 3, - - - , m (2)- 1, 2, 3, - - - , m (3) 1, 2, 3,
- - - , m (4) 1, 2, 3, - - - , m (1')- -aperture 2 1, 2, 3, - - - ,
m (2') 1, 2, 3, - - - , m (3') 1, 2, 3, - - - , m (4') 1, 2, 3, - -
- , m
VB3--One Pulse Many Channels Odd-Even Data and Apertures
[0267] EQUATIONS (1),(2),(3) and (4) and (1'),(2'),(3') and (4')
represented as follows: TABLE-US-00007 (1)-PULSE 1 -aperture 1, 3,
5, - - - , N - 1 odd data 1-CHANNEL data (2)- 3, 5, 7, - - - , N +
1 (3) 5, 7, 9, - - - , N + 3 (4) 7, 9, 11 - - - , N + 5 (1')
-aperture 2 2, 4, 6, - - - , N even data (2') 4, 6, 8, - - - , N +
2 (3') 6, 8, 10, - - - , N + 4 (4') 8, 10, 12 - - - , N + 6
VB4--One Pulse Many Channels No Odd-Even Data and Simultaneous
Apertures
[0268] EQUATIONS (1),(2),(3) and (4) and (1'),(2'),(3') and (4')
represented as follows: TABLE-US-00008 (1)-PULSE 1 -aperture
1-CHANNEL data 1, 2, 3, - - - , N (2)- 1, 2, 3, - - - , N (3) 1, 2,
3, - - - , N (4) 1, 2, 3, - - - , N (1')- -aperture 2 1, 2, 3, - -
- , N (2') 1, 2, 3, - - - , N (3') 1, 2, 3, - - - , N (4') 1, 2, 3,
- - - , N
[0269] Taking equations (1) and (2) and (3) and treating M.sub.0
and M.sub.1 and M.sub.2 as the variables and solving the
determinant equation for .DELTA..sub.0 we have: .DELTA. 0 = e
j.PHI. D .times. .times. 0 1 .times. e j.PHI. D .times. .times. 1 1
.times. e j.PHI. D .times. .times. 2 1 = 1 .times. .times. e j.PHI.
D .times. .times. 1 .times. e j.PHI. D .times. .times. 2 - 1
.times. .times. e j.PHI. D .times. .times. 0 .times. e j.PHI. D
.times. .times. 2 + 1 .times. .times. e j.PHI. D .times. .times. 0
.times. e j.PHI. D .times. .times. 1 .times. .times. e j2.PHI. D
.times. .times. 0 .times. e j2.PHI. D .times. .times. 1 .times. e
j2.PHI. D .times. .times. 2 .times. .times. e j2.PHI. D .times.
.times. 1 .times. e j2.PHI. D .times. .times. 2 .times. .times. e
j2.PHI. D .times. .times. 0 .times. e j2.PHI. D .times. .times. 2
.times. .times. e j2.PHI. D .times. .times. 0 .times. e j2.PHI. D
.times. .times. 1 .times. .times. .DELTA. 0 = .times. e j.PHI. D
.times. .times. 1 .times. e j2.PHI. D .times. .times. 2 - e j2.PHI.
D .times. .times. 1 .times. e j.PHI. D .times. .times. 2 - e j.PHI.
D .times. .times. 0 .times. e j2.PHI. D .times. .times. 2 + .times.
e j.PHI. D .times. .times. 2 .times. e j2.PHI. D .times. .times. 0
+ e j.PHI. D .times. .times. 0 .times. e j2.PHI. D .times. .times.
1 - e j.PHI. D .times. .times. 1 .times. e j2.PHI. D .times.
.times. 0 = .times. function .times. .times. of .times. .times.
.PHI. D .times. .times. 0 , .PHI. D .times. .times. 1 .times.
.times. and .times. .times. .PHI. D .times. .times. 2 .times.
.times. and .times. .times. solving .times. .times. for .times.
.times. M 0 _ = M 0 * .DELTA. 0 M 0 _ = V 01 V 00 .times. e j.PHI.
D .times. .times. 1 1 .times. e j.PHI. D .times. .times. 2 1 = V 00
.times. e j.PHI. D .times. .times. 1 .times. e j.PHI. D .times.
.times. 2 - V 01 .times. 1 .times. .times. 1 + V 02 .times. 1
.times. .times. 1 .times. .times. V 02 .times. e j2.PHI. D .times.
.times. 1 .times. V .times. .times. e j2.PHI. D .times. .times. 2
.times. .times. e j2.PHI. D .times. .times. 1 .times. e j2.PHI. D
.times. .times. 2 .times. .times. e j2.PHI. D .times. .times. 1
.times. e j2.PHI. D .times. .times. 1 .times. .times. e j.PHI. D
.times. .times. 1 .times. e j.PHI. D .times. .times. 2 .times.
.times. M 0 _ = .times. V 00 .function. ( e j.PHI. D .times.
.times. 1 .times. e j2.PHI. D .times. .times. 2 - e j.PHI. D
.times. .times. 2 .times. e j2.PHI. D .times. .times. 1 ) - .times.
V 01 ( e j2.PHI. D .times. .times. 2 - e j2.PHI. D .times. .times.
1 ) + V 02 .function. ( e j.PHI. D .times. .times. 2 - e j.PHI. D
.times. .times. 1 ) = .times. function .times. .times. of .times.
.times. .times. .PHI. D .times. .times. 1 .times. .times. and
.times. .times. .PHI. D .times. .times. 2 .times. .times. and
.times. .times. solving .times. .times. for .times. .times. M 1 _ =
M 1 * .DELTA. 0 ( 6 ) M 1 _ = e j.PHI. D .times. .times. 0 1
.times. V 01 V 00 .times. e j.PHI. D .times. .times. 2 1 = V 00
.times. e j.PHI. D .times. .times. 0 .times. e j.PHI. D .times.
.times. 2 - V 01 .times. 1 .times. .times. 1 + V 02 .times. 1
.times. .times. 1 .times. .times. e j2.PHI. D .times. .times. 0
.times. V 02 .times. e j2.PHI. D .times. .times. 2 .times. .times.
e j2.PHI. D .times. .times. 0 .times. e j2.PHI. D .times. .times. 2
.times. .times. e j2.PHI. D .times. .times. 0 .times. e j2.PHI. D
.times. .times. 2 .times. .times. e j.PHI. D .times. .times. 0
.times. e j.PHI. D .times. .times. 2 .times. .times. M 1 _ =
.times. V 01 .function. ( e j.PHI. D .times. .times. 0 .times. e
j2.PHI. D .times. .times. 2 - e j2.PHI. D .times. .times. 0 .times.
e j.PHI. D .times. .times. 2 ) - .times. V 01 ( e j2.PHI. D .times.
.times. 2 - e j2.PHI. D .times. .times. 0 ) + V 02 .function. ( e
j.PHI. D .times. .times. 2 - e j.PHI. D .times. .times. 0 ) =
.times. function .times. .times. of .times. .times. .PHI. D .times.
.times. 0 .times. .times. and .times. .times. .times. .PHI. D
.times. .times. 2 .times. .times. and .times. .times. solving
.times. .times. for .times. .times. M 2 _ = M 2 * .DELTA. 0 ( 7 ) M
2 _ = e j.PHI. D .times. .times. 0 1 .times. e j.PHI. D .times.
.times. 1 1 .times. V 01 V 00 = V 00 .times. e j.PHI. D .times.
.times. 0 .times. e j.PHI. D .times. .times. 1 - V 01 .times. 1
.times. .times. 1 + V 02 .times. 1 .times. .times. 1 .times.
.times. e j2.PHI. D .times. .times. 0 .times. e j2.PHI. D .times.
.times. 1 .times. V 02 .times. .times. e j2.PHI. D .times. .times.
0 .times. e j2.PHI. D .times. .times. 1 .times. .times. e j2.PHI. D
.times. .times. 0 .times. e j2.PHI. D .times. .times. 1 .times.
.times. e j.PHI. D .times. .times. 0 .times. e j.PHI. D .times.
.times. 1 .times. .times. M 2 _ = .times. V 00 .function. ( e
j.PHI. D .times. .times. 0 .times. e j2.PHI. D .times. .times. 1 -
e j2.PHI. D .times. .times. 1 .times. e j.PHI. D .times. .times. 0
) - .times. V 01 ( e j2.PHI. D .times. .times. 1 - e j2.PHI. D
.times. .times. 0 ) + V 02 .function. ( e j.PHI. D .times. .times.
1 - e j.PHI. D .times. .times. 0 ) = .times. function .times.
.times. of .times. .times. .PHI. D .times. .times. 0 .times.
.times. and .times. .times. .times. .PHI. D .times. .times. 2 ( 8 )
##EQU10##
[0270] Taking equation (2), (3) and (4) and performing the
identical operations as in equation (1), (2) and (3) we have the
following: M 0 _ .times. e j.PHI. D .times. .times. 0 _ = .times. V
01 .function. ( e j.PHI. D .times. .times. 1 .times. e j2.PHI. D
.times. .times. 2 - e j.PHI. D .times. .times. 2 .times. e j2.PHI.
D .times. .times. 1 ) - .times. V 02 .function. ( e j2.PHI. D
.times. .times. 2 - e j2.PHI. D .times. .times. 1 ) + V 03
.function. ( e j.PHI. D .times. .times. 2 - e j.PHI. D .times.
.times. 1 ) = .times. function .times. .times. ( .PHI. D .times.
.times. 1 .times. .times. and .times. .times. .PHI. D .times.
.times. 2 ) ( 9 ) M 1 _ .times. e j.PHI. D .times. .times. 1 _ =
.times. V 01 .function. ( e j.PHI. D .times. .times. 0 .times. e
j2.PHI. D .times. .times. 2 - e j.PHI. D .times. .times. 0 .times.
e j2.PHI. D .times. .times. 2 ) - .times. V 02 .function. ( e
j2.PHI. D .times. .times. 2 - e j2.PHI. D .times. .times. 0 ) + V
03 .function. ( e j.PHI. D .times. .times. 2 - e j.PHI. D .times.
.times. 0 ) = .times. function .times. .times. ( .PHI. D .times.
.times. O .times. .times. and .times. .times. .PHI. D .times.
.times. 1 ) ( 10 ) M 2 _ .times. e j.PHI. D .times. .times. 2 _ =
.times. V 01 .function. ( e j.PHI. D .times. .times. 0 .times. e
j2.PHI. D .times. .times. 1 - e j.PHI. D .times. .times. 1 .times.
e j2.PHI. D .times. .times. 0 ) - .times. V 02 .function. ( e
j2.PHI. D .times. .times. 1 - e j2.PHI. D .times. .times. 0 ) + V
03 .function. ( e j.PHI. D .times. .times. 1 - e j.PHI. D .times.
.times. 0 ) = .times. function .times. .times. ( .PHI. D .times.
.times. 0 .times. .times. and .times. .times. .PHI. D .times.
.times. 1 ) ( 11 ) ##EQU11##
[0271] Dividing equation (9)/(6) and (10)/(7) and (11)/(8) we have
the following: e .times. j.PHI. D .times. .times. 0 = .times. V 01
.function. ( e j.PHI. D .times. .times. 1 .times. e j2.PHI. D
.times. .times. 2 - e j.PHI. D .times. .times. 2 .times. e j2.PHI.
D .times. .times. 1 ) - .times. V 02 .function. ( e j2.PHI. D
.times. .times. 2 - e j2.PHI. D .times. .times. 1 ) + V 03
.function. ( e j.PHI. D .times. .times. 2 - e j.PHI. D .times.
.times. 1 ) / .times. V 00 .function. ( e j.PHI. D .times. .times.
1 .times. e j2.PHI. D .times. .times. 2 - e j.PHI. D .times.
.times. 2 .times. e j2.PHI. D .times. .times. 1 ) - .times. V 01
.function. ( e j2.PHI. D .times. .times. 2 - e j2.PHI. D .times.
.times. 1 ) + V 02 .function. ( e j.PHI. D .times. .times. 2 - e
j.PHI. D .times. .times. 1 ) = .times. function .times. .times. (
.PHI. D .times. .times. 1 , .PHI. D .times. .times. 2 ) ( 12 ) e
.times. j.PHI. D .times. .times. 1 = .times. V 01 .function. ( e
j.PHI. D .times. .times. 0 .times. e j2.PHI. D .times. .times. 2 -
e j.PHI. D .times. .times. 0 .times. e j2.PHI. D .times. .times. 2
) - .times. V 02 .function. ( e j2.PHI. D .times. .times. 2 - e
j2.PHI. D .times. .times. 0 ) + V 03 .function. ( e j.PHI. D
.times. .times. 2 - e j.PHI. D .times. .times. 0 ) / .times. V 01
.function. ( e j.PHI. D .times. .times. 0 .times. e j2.PHI. D
.times. .times. 2 - e j.PHI. D .times. .times. 0 .times. e j2.PHI.
D .times. .times. 2 ) - .times. V 01 .function. ( e j2.PHI. D
.times. .times. 2 - e j2.PHI. D .times. .times. 0 ) + V 02
.function. ( e j.PHI. D .times. .times. 2 - e j.PHI. D .times.
.times. 0 ) = .times. function .times. .times. ( .PHI. D .times.
.times. 0 , .PHI. D .times. .times. 2 ) ( 13 ) e .times. j.PHI. D
.times. .times. 2 = .times. V 01 .function. ( e j.PHI. D .times.
.times. 0 .times. e j2.PHI. D .times. .times. 1 - e j.PHI. D
.times. .times. 1 .times. e j2.PHI. D .times. .times. 0 ) - .times.
V 02 .function. ( e j2.PHI. D .times. .times. 1 - e j2.PHI. D
.times. .times. 0 ) + V 03 .function. ( e j.PHI. D .times. .times.
1 - e j.PHI. D .times. .times. 0 ) / .times. V 00 .function. ( e
j.PHI. D .times. .times. 0 .times. e j2.PHI. D .times. .times. 1 -
e j.PHI. D .times. .times. 1 .times. e j2.PHI. D .times. .times. 0
) - .times. V 01 .function. ( e j2.PHI. D .times. .times. 1 - e
j2.PHI. D .times. .times. 0 ) + V 02 .function. ( e j.PHI. D
.times. .times. 1 - e j.PHI. D .times. .times. 0 ) = .times.
function .times. .times. ( .PHI. D .times. .times. 0 , .PHI. D
.times. .times. 1 ) ( 14 ) ##EQU12##
[0272] The equations for the other data as follows:
V'.sub.00=M'.sub.0+M'.sub.1+M'.sub.2 (1')
V'.sub.01=M'.sub.0e.sup.j.PHI.'.sup.D0+M'.sub.1.sup.j.PHI.'.sup.D1+M'.sub-
.2.sup.j2.PHI.'.sup.D2 (2')
V'.sub.02=M'.sub.0e.sup.j2.PHI.'.sup.D0+M'.sub.1.sup.j2.PHI.'.sup.D1+M'.s-
ub.2.sup.j3.PHI.'.sup.D2 (3')
V'.sub.03=M'.sub.0e.sup.j3.PHI.'.sup.D0+M'.sub.1.sup.j3.PHI.'.sup.D1+M'.s-
ub.2j3.PHI.'.sup.D2 (4')
[0273] Taking equations (1' to 4') and solving identical to
equations (1) to (4) we have the following: e .times. j .times.
.times. .PHI. D .times. .times. 0 ' = .times. V 01 ' ( e j.PHI. D
.times. .times. 1 ' .times. e j2.PHI. D .times. .times. 2 ' - e
j.PHI. D .times. .times. 2 ' .times. e j2.PHI. D .times. .times. 1
' ) - .times. V 02 ' ( e j2.PHI. D .times. .times. 2 ' - e j2.PHI.
D .times. .times. 1 ' ) + V 03 ' ( e j.PHI. D .times. .times. 2 ' -
e j.PHI. D .times. .times. 1 ' ) / .times. V 00 ' ( e j.PHI. D
.times. .times. 1 ' .times. e j2.PHI. D .times. .times. 2 ' - e
j.PHI. D .times. .times. 2 ' .times. e j2.PHI. D .times. .times. 1
' ) - .times. V 01 ' ( e j2.PHI. D .times. .times. 2 ' - e j2.PHI.
D .times. .times. 1 ' ) + V 02 ' ( e j.PHI. D .times. .times. 2 ' -
e j.PHI. D .times. .times. 1 ' ) = .times. function .times. .times.
( .PHI. D .times. .times. 1 ' , .PHI. D .times. .times. 2 ' ) ( 12
' ) e .times. j.PHI. D .times. .times. 1 ' = .times. V 01 ' ( e
j.PHI. D .times. .times. 0 ' .times. e j2.PHI. D .times. .times. 2
' - e j.PHI. D .times. .times. 0 ' .times. e j2.PHI. D .times.
.times. 2 ' ) - .times. V 02 ' ( e j2.PHI. D .times. .times. 2 ' -
e j2.PHI. D .times. .times. 0 ' ) + V 03 ' ( e j.PHI. D .times.
.times. 2 ' - e j.PHI. D .times. .times. 0 ' ) / .times. V 01 ' ( e
j.PHI. D .times. .times. 0 ' .times. e j2.PHI. D .times. .times. 2
' - e j.PHI. D .times. .times. 0 ' .times. e j2.PHI. D .times.
.times. 2 ' ) - .times. V 01 ' ( e j2.PHI. D .times. .times. 2 ' -
e j2.PHI. D .times. .times. 0 ' ) + V 02 ' ( e j.PHI. D .times.
.times. 2 ' - e j.PHI. D .times. .times. 0 ' ) = .times. function
.times. .times. ( .PHI. D .times. .times. 0 ' , .PHI. D .times.
.times. 2 ' ) ( 13 ' ) e .times. j.PHI. D .times. .times. 2 ' =
.times. V 01 ' ( e j.PHI. D .times. .times. 0 ' .times. e j2.PHI. D
.times. .times. 1 ' - e j.PHI. D .times. .times. 1 ' .times. e
j2.PHI. D .times. .times. 0 ' ) - .times. V 02 ' ( e j2.PHI. D
.times. .times. 1 ' - e j2.PHI. D .times. .times. 0 ' ) + V 03 ' (
e j.PHI. D .times. .times. 1 ' - e j.PHI. D .times. .times. 0 ' ) /
.times. V 00 ' ( e j.PHI. D .times. .times. 0 ' .times. e j2.PHI. D
.times. .times. 1 ' - e j.PHI. D .times. .times. 1 ' .times. e
j2.PHI. D .times. .times. 0 ' ) - .times. V 01 ' ( e j2.PHI. D
.times. .times. 1 ' - e j2.PHI. D .times. .times. 0 ' ) + V 02 ' (
e j.PHI. D .times. .times. 1 ' - e j.PHI. D .times. .times. 0 ' ) =
.times. function .times. .times. ( .PHI. D .times. .times. 0 ' ,
.PHI. D .times. .times. 1 ' ) .times. .times. where .times. .times.
.PHI. D .times. .times. 0 = .PHI. D .times. .times. 0 ' ; .PHI. D
.times. .times. 1 = .PHI. D .times. .times. 1 ' .times. .times. and
.times. .times. .PHI. D .times. .times. 2 = .PHI. D .times. .times.
2 ' ( 14 ' ) ##EQU13##
[0274] Taking equations (12) to (14) and equations (12') to (14')
and solving in both sets of equations for .PHI..sub.D0,
.PHI..sub.D1 and .PHI..sub.D2 solution which should be equal is the
following procedure:
[0275] Substituting equation (12) or (12') into equation (13) or
(13') we have the following:
.PHI..sub.D0 as a function of .PHI..sub.D2
Substituting equation (13) or (13') into equation (14) or (14') we
have the following:
.PHI..sub.D0 as a function of .PHI..sub.D2
Substituting equation (14) or (14') into equation (12) or (12') we
have the following: .PHI..sub.D0 as a function of .PHI..sub.D1
substituting equation (14) or (14') into equation (13) or (13') we
have the following:
.PHI..sub.D0 as a function of .PHI..sub.D1
[0276] Similarly we have two equations two unknowns and solvable in
.PHI..sub.D0 and .PHI..sub.D2 and similarly for .PHI..sub.D1 and
.PHI..sub.D2.
[0277] Thus we have solved for .PHI..sub.D1, .PHI..sub.D2 and
.PHI..sub.D3 twice.
[0278] From the second set of data a small frequency change from
the first set of data this gives the same .PHI..sub.D1,
.PHI..sub.D2 and .PHI..sub.D3 and different M.sub.0, M.sub.1 and
M.sub.2 and the ratios of the M'.sub.0/M.sub.0,M'.sub.1/M.sub.1 and
M'.sub.2/M.sub.2 should give a good check of where the position
.PHI..sub.D0 and .PHI..sub.D1 and .PHI..sub.D2 is detected at that
RDB or RAB and a check on the solutions determined. From this the
azimuth of the returns are determined.
[0279] A methodology in simplifying solutions where there are three
or more returns detected in RDB or RAB. Determine from processing
adjacent RDB or RAB detection of returns that will be detected in
the processed bin. Then by employing candidate solution
methodology, that is substituting all possible solutions which are
very limited in number, and knowing one or more solutions. The
solutions must have the known solution as one of its solutions.
This makes it much simpler solution and more robust and
accurate
[0280] Calculating from real time data a curve of the ratio of
amplitude of returns at the two different apertures-vs-azimuth.
Chose relatively significant clutter only detected in same bin in
both apertures.
[0281] The methodology of producing this curve from real time data
is as follows: [0282] a) chose only relatively large amplitude
clutter only data. [0283] b) determine its azimuth from its
measurement and its amplitude and phase of the return in each
aperture. [0284] c) measure ratio of ratio of the amplitude and
phase from each aperture which is
K.sub.M0e.sup.j.alpha..sup.0=M'.sub.0/M.sub.0 and
K.sub.M1e.sup.j.PHI..alpha..sup.1=M'.sub.1/M.sub.1 etc. [0285] d)
perform this with as much data as to obtain a very good estimate of
the curve by any fitting statistical methodology. [0286] e) thus we
have obtained a very good estimate of curve desired.
[0287] Now having generated from the real time data the curve of
ratio of even divided by odd-vs-azimuth the candidate .PHI.
technique is employed where all the possible phases are substituted
(which are very limited in number, in equations and the solutions
are compared to the curve for the ratio of aperture data as a
function of azimuth and where there is a match this is the
solution. The solution for equations should agree and they are a
check on each other. Having attained the solution for azimuth,
.PHI..sub.A, and having the solution for .PHI..sub.D then
.PHI.=.PHI..sub.D-.PHI..sub.A, the solution for radial velocity of
the returns.
[0288] Determine its azimuth position and measure its ratio between
apertures. Perform this for all clutter that meets the criteria and
obtain a best statistical estimate of the said curve.
[0289] Dealing with three unknown returns or more an aid in finding
the .PHI..sub.D S will be very helpful and obtain a more robust
solutions. There are not many cases where there will be three or
more returns are detected in the same RDB or RAB but in those cases
the aid in processing first if there is clutter or other return
detected close to processed bin to be detected in processed bin
also. To continue to find as many possible solutions from all the
close bins processed. If so you know at least one of the solutions
assume you that returns solution is known and a great deal more
robust and accurate.
[0290] Employing the possible candidate solutions, only a
restricted number of solutions are possible, with the known
solution or solutions, vary the other candidate solutions until the
solution is
M'.sub.0/M.sub.0=K.sub.M0e.sup.j.alpha..sup.0 or
M'.sub.1/M.sub.1=K.sub.M1e.sup.j.alpha..sup.1 or
M'.sub.2/M.sub.2=K.sub.M2e.sup.j.alpha..sup.2 etc.
The agreement with curve of ratio of returns ratio-vs-azimuth and
the azimuth of each return has been determined. Since
.PHI..sub.0=.PHI..sub.D0-.PHI..sub.A0 and
.PHI..sub.1=.PHI..sub.D1-.PHI..sub.A1 and
.PHI..sub.2=.PHI..sub.D2-.PHI..sub.A2 etc. we solve for all returns
radial velocity.
[0291] From the ratio of the second set of data to the first set of
data we obtain XF0 and XF1 and XF2 from which is the ratio of
[0292] M'.sub.0/M.sub.0=X.sub.F0 and M'.sub.1/M.sub.1=X.sub.F1 and
M'.sub.2/M.sub.2=X.sub.F2 where all other terms are known. From the
previous determinations of the .PHI..sub.D0 and .PHI..sub.D1 and
.PHI..sub.D2 which is the position in the filter where the returns
are detected at there peak in the RDB or RAB where .PHI..sub.0A is
the phase of the return proportional to the azimuth of the return,
and .PHI..sub.D0 is the phase of the return proportional to the
peak of the return, .PHI..sub.0, is the phase of the return
proportional to the velocity of the return.
[0293] In the one channel system:
[0294] A small change in doppler bin may be taken and its
determined XF0, XF1 and XF2 which determines where the peak of the
returns in doppler, this does not help in the evaluation in
azimuth.
[0295] A small change in range bin may be taken and we determine
XR0, XR1 and XR2 which determines where the peak of the returns in
range, this does not help in the evaluation in azimuth. Resolving
velocity ambiguity is taking a meaning delay in time and processing
again. Thus we can determine the peak of each return in range and
azimuth to obtain the maximum amplitude for each return for further
use.
[0296] Other linear arrays are processed may be taken and its
determine XH0, XH1 and XH2 which determines where the peak of the
returns in height, this does not help in the evaluation in
azimuth.
[0297] Resolving velocity ambiguity with the taking of meaningful
delay in time and processing again. Thus we can determine the peak
of each return in range and azimuth to obtain the maximum amplitude
for each return for further use. The change in amplitude and phase
of the range bin in conjunction with a delay in time gives an
accurate determination of radial velocity which will resolve
velocity ambiguity. This will also be for doppler change give the
horizontal tangential velocity and with an analogous technique in a
planar array giving vertical tangential velocity therefore an
estimate of total velocity and estimate of pointing angle of the
return. Which is the following: The previous analysis was with two
returns possible per RAB processed though three (3) or more returns
per RAB may be processed and determine the solution
[0298] From the analysis for the one channel system there is
determined all the parameters of the returns the accurate position
in range, azimuth and velocity and radial velocity, horizontal and
vertical tangential velocity, mover, noise, and other returns may
be detected and thresholded for importance and later processed to
determine if sidelobes, multipath targets, etc.
[0299] One Pulse System
[0300] The analysis indicates the same solutions for range,
velocity, azimuth and precise range and height are obtained but not
the other parameters.
[0301] Obtaining curve of ratio of aperture 2 divided by aperture 1
M'/M=|K.sub.M|e.sup.j.alpha.-vs-azimuth as detailed in previous
cases, we perform the candidate solution technique we substitute
each candidate solution for right side of equations above and when
the right solution is entered the left side will equal the correct
Km and phase. This performed for all three equations and the
solutions should correlate. Employ analogous techniques as in other
three return cases in the one pulse technique to find all the same
solutions.
[0302] RECAPPING--We have determined all .PHI.s, in the two return
and three return case and as consequently it may be performed for
many .PHI.s. The significance of this development is as each RDB
that is processed clutter, target, noise, and other returns may be
detected and thresholded for importance and later processed to
determine if sidelobes, multipath targets, etc.
[0303] Employ analogous techniques as other three return and three
sets of data cases to find all the same solutions.
VC--One Pulse--One Aperture System--.DELTA.C Technique
[0304] The analysis may be performed with a one antenna transmit
and many (channel) receive system. This system is called .DELTA.C
technique with one aperture formulated where the data will be
delayed as desired to solve the problem. We will consider two
returns clutter and mover and the channel data has been spectrum
processed into its individual RABs and each will be treated as
follows:
Referenced previous delayed one data point, each channel the data
point is delayed it is multiplied by a suitable weighting function
and its spectrum is obtained with such as FFT. In processing a
particular RAB we may have the following:
V.sub.00=M.sub.0+M.sub.1PULSE 1-APERTURE 1-CHANNEL 1-N (1)
V.sub.01=M.sub.0e.sup.j.PHI..sup.D0+M.sub.1.sup.j.PHI..sup.D1 PULSE
1-APERTURE 1-CHANNEL 2-N+1-DELAYED ONE CHANNEL (2)
V.sub.02=M.sub.0e.sup.j2.PHI..sup.D0+M.sub.1.sup.j2.PHI..sup.D1
PULSE 1-APERTURE 1-CHANNEL 3-N+2-DELAYED TWO CHANNELS (3)
V.sub.03=M.sub.0e.sup.j3.PHI..sup.D0+M.sub.1.sup.j3.PHI..sup.D1
PULSE 1-APERTURE 1 CHANNEL 4-N+3-DELAYED THREE CHANNELS (4) Above
equations are for two returns where V.sub.00--is the return in the
RAB being processed at delayed data 1 at PULSE 1 V.sub.01--is the
return in the RAB being processed at delayed data 2 at PULSE 1
V.sub.02--is the return in the RAB being processed at delayed data
3 at PULSE 1 V.sub.03--is the return in the RAB being processed at
delayed data 4 at PULSE 1 M.sub.0--is the first return vector
M.sub.1--is the second return vector .PHI..sub.D0 --is the phase of
the first return where the phase is proportional to the azimuth
plus velocity of the return .PHI..sub.D1--is the phase of the
second return where the phase is proportional to the azimuth plus
velocity of the return
[0305] Taking equations (1) and (2) and treating M.sub.0 and
M.sub.1 as the variables and solving for M.sub.0 and M.sub.1 we
have:
M.sub.0=(V.sub.00e.sup.j.PHI..sup.D1-V.sub.01)/(e.sup.j.PHI..sup.D1-e.sup-
.j.PHI..sup.D0) (5)
M.sub.1=(V.sub.00-e.sup.j.PHI..sup.D0V.sub.01)/(e.sup.j.PHI..sup.D1-e.sup-
.j.PHI..sup.D0) (6) Taking equations (2) and (3) and treating
M.sub.0e.sup.j.PHI..sup.D0 and M.sub.1e.sup.j.PHI..sup.D1 as the
variables and solving for M.sub.0e.sup.j.PHI..sup.D0 and
M.sub.1e.sup.j.PHI..sup.D1 we have:
M.sub.0e.sup.j.PHI..sup.D0=(V.sub.01e.sup.j.PHI..sup.D1-V.sub.02)/(e.sup.-
j.PHI..sup.D1-e.sup.j.PHI..sup.D0) (5')
M.sub.1e.sup.j.PHI..sup.D1=(V.sub.01-e.sup.j.PHI..sup.D0V.sub.02)/(e.sup.-
j.PHI..sup.D1-e.sup.j.PHI..sup.D0) (6') Equation (5')/Equation (5)
and (6')/(6) are the following:
e.sup.j.PHI..sup.D0=(V.sub.01e.sup.j.PHI..sup.D1-V.sub.02)/V.sub.00e.sup.-
j.PHI..sup.D1-V.sub.01) (7')
e.sup.j.PHI..sup.D1=(V.sub.01-e.sup.j.PHI..sup.D0V.sub.02)/(V.sub.00-e.su-
p.j.PHI..sup.D0V.sub.01) (8') Equation (7') or Equation (8') is
easily solved for .PHI..sub.D0 and .PHI..sub.D1 which are
proportional to the azimuth plus velocity of return 0 and return 1
respectively. Now employing equations (1) and (2) and solving for
M.sub.0 and M.sub.1 knowing .PHI..sub.D0 and .PHI..sub.D1 we are
now to find .PHI..sub.A0 and .PHI..sub.A1 which are proportional to
total phase of the azimuth return 0 and return 1 respectively and
M.sub.0 and M.sub.1 and both returns are detected in the same RAB.
Now we have another set of equations for another close azimuth bin
from the first azimuth bin processed. V'.sub.00=M'.sub.0+M'.sub.1
PULSE 1-AZIMUTH BIN 2-CHANNEL 1-N (1')
V'.sub.01=M'.sub.0e.sup.j.PHI.'.sup.D0+M'.sub.1.sup.j.PHI.'.sup.D1
PULSE 1-AZIMUTH BIN 2-CHANNEL 2-N+1-DELAYED ONE CHANNEL (2')
V'.sub.02=M'.sub.0e.sup.j2.PHI.'.sup.D0+M'.sub.1j.sup.2.PHI.'.sup.D1
PULSE 1-AZIMUTH BIN 2-CHANNEL 3-N+2-DELAYED TWO CHANNELS (3')
V'.sub.03=M.sub.0e.sup.j3.PHI.'.sup.D0+M'.sub.1.sup.j3.PHI.'.sup.D1
PULSE 1-AZIMUTH BIN 2-CHANNEL 4-N+3-DELAYED THREE CHANNELS (4')
This gives the same .PHI..sub.A0 and .PHI..sub.A1 and different
M.sub.0 and M.sub.1 and the ratios of the M.sub.0 and M.sub.1
should give a good estimate of where the position .PHI..sub.D0 and
.PHI..sub.D1 is detected at in the RAB. .PHI..sub.D0 and
.PHI..sub.D1 is the peak position of return 0 and 1 are detected in
the RDB processed.
[0306] From the ratio of the second set of data to the first set of
data we obtain |A.sub.Z0|and |A.sub.Z1|which is the ratio of
M'.sub.0/M.sub.0=|A.sub.Z0|and M'.sub.1/M.sub.1=|A.sub.Z1|where all
other terms are known.
[0307] A small change in the azimuth bin may be taken and we
determine |A.sub.Z0|and |A.sub.Z1|which determines where the peak
of the returns is in azimuth, this helps in the determination in
tangential velocity. If attaining tangential velocity is desired
then the taking of meaningful delay in time and processing again.
Thus we can determine the peak of each return in azimuth to obtain
the .PHI..sub.A0 and .PHI..sub.A1 of each return for further use in
determining the radial velocity
.PHI..sub.0=.PHI..sub.D0-.PHI..sub.A0 and
.PHI..sub.1=.PHI..sub.D1-.PHI..sub.A1 change in amplitude and phase
of the azimuth bin in conjunction with a delay in time gives an
accurate determination of radial velocity. This will also be for
and an analogous technique in a planar array giving vertical
tangential velocity therefore an estimate of total velocity and
estimate of pointing angle of the return which is the following:
The previous analysis was with two returns possible per RAB
processed though three (3) or more returns per RAB may be processed
and determine the solution
[0308] From the previous analysis for the one pulse system there is
determined all the parameters of the returns the accurate position
in range, azimuth and height and ambiguous radial velocity.
[0309] VD--One Channel--Multiple Time Data-Change in Time-One
Aperture
[0310] The system is a transmission from a fixed transmission array
and one or more receive antennas This STAP methodology process the
data into its frequency spectrum and consequently localize clutter
into its own range doppler bin (RDB) together with any other
returns such as target, thermal noise, and others.
[0311] The subsequent processing of each RDB will separate out
clutter doppler since clutter has zero (0) radial velocity and
other returns in the same (RDB) will have different velocities.
From determining the velocity of the returns the azimuth will be
calculated therefore no additional data is required.
[0312] The knowledge aided STAP will be involved to determine from
the detected returns which are targets of interest, sidelobe
returns, land sea interface, thermal noise, etc.
[0313] The knowledge aided STAP will be not involved in canceling
clutter but in the post processing of the returns of interest so
they may be detected and there parameters measured and determine
the nature of the return.
[0314] Two returns in one RDB will be considered initially and such
as three moving returns, or more will be dealt with as analogously
as other techniques. V.sub.00=M.sub.0+M.sub.1 TIME DATA (1)
V.sub.01=M.sub.0e.sup.j.PHI..sup.D0+M.sub.1.sup.j.PHI..sup.D1 TIME
DATA DELAYED ONE TIME (2)
V.sub.02=M.sub.0e.sup.j2.PHI..sup.D0+M.sub.1.sup.j2.PHI..sup.D1
DELAYED TWO TIMES (3)
V.sub.03=M.sub.0e.sup.j3.PHI..sup.D0+M.sub.1.sup.j3.PHI..sup.D1
DELAYED THREE TIMES (4) Above equations are for two returns where
V00--is the return in the RDB being processed at data 1
V.sub.01--is the return in the RDB being processed at data 2
V.sub.02--is the return in the RDB being processed at data 3
V.sub.03--is the return in the RDB being processed at data 4
M.sub.0--is the first return vector. M.sub.1--is the second return
vector. .PHI..sub.D0--is the phase of the first return where the
phase is proportional to the azimuth plus velocity of the return.
.PHI..sub.D1--is the phase of the second return where the phase is
proportional to the azimuth plus velocity of the return.
[0315] Taking equations (1) and (2) and treating M.sub.0 and
M.sub.1 as the variables and solving for M.sub.0 and M.sub.1 we
have:
M.sub.0=(V.sub.00e.sup.j.PHI..sup.D1-V.sub.01)/(e.sup.j.PHI..sup.D1-e.sup-
.j.PHI..sup.D0) (5)
M.sub.1=(V.sub.00-e.sup.j.PHI..sup.D0(V.sub.01)/(e.sup.j.PHI..sup.D1-e.su-
p.j.PHI..sup.D0) (6) Taking equations (2') and (3') and treating
M.sub.0e.sup.j.PHI..sup.D0 and M.sub.1e.sup.j.PHI..sup.D1 as the
variables and solving for M.sub.0 e.sup.j.PHI..sup.D0 and
M.sub.1e.sup.j.PHI..sup.D1 we have:
M.sub.0e.sup.j.PHI..sup.D0=(V.sub.01e.sup.j.PHI..sup.D1-V.sub.02)/(e.sup.-
j.PHI..sup.D1-e.sup.j.PHI..sup.D0) (5')
M.sub.1e.sup.j.PHI..sup.D1=(V.sub.01-e.sup.j.PHI..sup.D0V.sub.02)/(e.sup.-
j.PHI..sup.D1-e.sup.j.PHI..sup.D0) (6') Equation (5')/Equation (5)
and (6')/(6) are the following:
e.sup.j.theta.D0=(V.sub.01e.sup.j.PHI..sup.D1-V.sub.02)/V.sub.00e.sup.j.P-
HI..sup.D1-V.sub.01) (7')
e.sup.j.PHI..sup.D1=(V.sub.01-e.sup.j.PHI..sup.D0V.sub.02)/(V.sub.00-e.su-
p.j.PHI..sup.D0V.sub.01) (8')
[0316] Equation (7') or Equation (8') is easily solved for
.PHI..sub.D0 and .PHI..sub.D1 which are proportional to the azimuth
plus velocity of return 0 and return 1 respectively. A close range
is processed. This is processed to yield a second set of equations
and processing similar to first set of data.
V'.sub.00=M'.sub.0+M'.sub.1 NO DELAY IN DATA (1')
V'.sub.01=M'.sub.0e.sup.j.PHI..sup.0+M'.sub.1.sup.j.PHI.'.sup.D1
DELAYED ONE TIME (2')
V'.sub.02=M'.sub.0e.sup.j2.PHI.'.sup.D0+M'.sub.1.sup.j2.PHI.'.sup.D1
DELAYED THREE TIMES (3')
V'.sub.03=M'.sub.0e.sup.j3.PHI.'.sup.D0+M'.sub.1.sup.j3.PHI.'.sup.D1
DELAYED FOUR TIMES (4')
[0317] Now employing equations (1') to (4') and solving in same
manner as equation (1) to (4) for M'.sub.0, M'.sub.1 and
.PHI.'.sub.D0, .PHI.'.sub.D1 in which .PHI.'.sub.D0=.PHI..sub.D0
and .PHI.'.sub.D1=.PHI..sub.D1 we are now to find
M'.sub.0/M.sub.0=X.sub.RO and M'.sub.1/M.sub.1=X.sub.RO which is
the detected position of 0 and 1 return gives estimate of peak in
the range bin, are proportional to range of return 0 and return 1
respectively and M.sub.0 and M.sub.1 and both returns are detected
in the same range bin (RB).
[0318] To get a more accurate determination, another range or
ranges may be processed or a slight change in the range processed
and results correlated for best results. The ratio of second set of
data for close in range we will obtain a much more accurate range.
Now we have another set of equations after a significant delay in
time and perform the same operations as first set of data and
determine the amplitude and phase change of the determination of
the range bin data will give an estimate of the unambiguous
velocity of the returns and from this the known peak of the returns
the azimuth of the returns are calculated.
VE--Combination of multi pulse techniques where processing
significant time later (multi-aperture and .DELTA.R techniques)
[0319] The two techniques may employ the same data since in multi
aperture technique each aperture data the .DELTA.R techniques may
be implemented and may be processed in any manner to correlate with
other solutions. The following is a list of common solutions.
[0320] 1. Same solutions for all parameters such as the following:
[0321] a) .PHI..sub.D s,.PHI..sub.A s and .PHI..sub.s and M s and
X.sub.F s, X.sub.R s and X.sub.H s [0322] b) solutions for position
and velocity of respective returns
[0323] 2. Accuracy and robustness of solutions are enhanced
VF-Combination of multi channel technique (multi-aperture and
.DELTA.Z--change in azimuth-techniques)
The two techniques may employ the same data since in multi aperture
technique each aperture data the .DELTA.Z techniques may be
implemented and may be processed in any manner to facilitate a
solution. The following is a list of common solutions.
[0324] 2. Same solutions for all parameters such as the following:
[0325] a) .PHI..sub.D s, .PHI..sub.A s and .PHI..sub.s and M s and
X.sub.F s, X.sub.R s and X.sub.H s [0326] b) solutions for position
and velocity of respective returns
[0327] 3. Accuracy and robustness of solutions are enhanced
[0328] From the previous analysis for the one pulse system and that
for the one channel system there is determined all the parameters
of the returns the accurate position in range, azimuth and velocity
and unambiguous radial velocity, horizontal and vertical tangential
velocity, mover, noise, and other returns may be detected and
thresholded for importance and later processed to determine if
sidelobes, multipath targets, etc.
VG--Correlation Factors
1--Time delay as many pulses and process data and determines all
.PHI.s.
2--Additional time delay data processed again and all .PHI.s should
agree
3--Other RDB processed have same return data related to each such
as mover should agree
4--Other techniques as to be shown later in document and results
should agree
VH--The aforementioned system has many advantages but the
outstanding are as the following
[0329] 1--Channel matching is not a problem since only one channel
is employed
[0330] 2--Dwell Time is reduced dramatically due to the minimum of
only one pulse required limited by the processor to perform the
necessary functions.
[0331] 3--Returns and clutter do not compete with each other in the
resulting processing and therefore clutter and returns are
thresholded separately and returns are ideally are competing with
white noise only and make for an excellent return ratio to
noise.
[0332] 4--One pulse system is very simple system-less storage-less
processing-more hardware due to RF front end and A/D converter
required for every channel or groups of channels.
[0333] 5--May be applied to one pulse or two or more pulses to give
more than one solution and they should be very close to each other.
Each processed as one pulse system and should have same results and
correlated.
[0334] 6--The significance of the ability to process many returns
in same RDB and determining there amplitude and phases and radial
velocity gives the ability to separate clutter and other returns
such as bona fide movers, moving clutter, multi path returns, etc.
Data base of returns and the mathematical basis and knowledge aided
information would aid in categorizing these returns.
[0335] 7--If more than one pulse implemented than the results of
each pulse should be the same or close to the same. If a different
transmission frequency is accompanied by another pulse they can be
close in time and process as another one pulse system without
interfering with each other.
[0336] 8--If a number of pulses and a number of channels are
employed with the delta T and delta C technique and correlated
would make for excellent results.
[0337] 9. FIG. 10 illustrates the detection of two returns in the
same bin.
VI--A Two PULSES at a Time-"N"-Channels of Data-Two
Returns-.PHI..sub.D Technique
[0338] The analysis may be performed with a one antenna transmit
and two pulse system. This system is called .DELTA.C methodology
where the data will be delayed one or more channel increments in
pulse 2 as required for a solution. We will consider two returns
clutter and target and the "N" channel data (channel data) has been
spectrum processed into its individual range azimuth bins (RABs)
and each will be treated as follows: Each set of data, channel data
point is delayed it is multiplied by a suitable weighting function
and its spectrum is obtained with such as FFT. In processing a
particular RAB where we have two returns we have the following
equations: V.sub.00=M.sub.0+M.sub.1 PULSE 1 CHANNEL data 1-N Delay
0 (1)
V.sub.01=M.sub.0e.sup.j.PHI..sup.D0+M.sub.1e.sup.j.PHI..sup.D1
PULSE 1 CHANNEL data 2-N+1 Delay 1 (2)
V.sub.02=M.sub.0e.sup.j2.PHI..sup.D0+M.sub.1e.sup.j2.PHI..sup.D1
PULSE 1 CHANNEL data 3-N+2 Delay 2 (3)
V.sub.03=M.sub.0e.sup.j3.PHI..sup.D0+M.sub.1e.sup.j3.PHI..sup.D1
PULSE 1 CHANNEL data 4-N+3 Delay 3 (4) Above equations are for two
returns where V.sub.00--is the return in the RAB being processed at
time 1 V.sub.01--is the return in the RAB being processed at time 2
V.sub.02--is the return in the RAB being processed at time 3
V.sub.03--is the return in the RAB being processed at time 4
M.sub.0--is the first return vector M.sub.1--is the second return
vector .PHI..sub.D0--is the phase of the first return where the
phase is proportional to the phase due to radial velocity plus that
due to the azimuth of the return. .PHI..sub.D1--is the phase of the
second return where the phase is proportional to the radial
velocity plus that due to the azimuth of the return
[0339] It is noted with each delay in channel data the vectors of
the returns phase is increased proportional to the delay which
represents the phase of the return proportional to the velocity
plus that due to its azimuth in the antenna beam. Zero velocity
returns such as clutter will have phase shift equal to zero due to
its velocity but one due to its azimuth position in the antenna
beam and other returns will have phase shifts directly proportional
to their radial velocity and one due to its azimuth position in the
main beam. When returns are detected in the same RAB the sum of
their phases (.PHI..sub.D0 or .PHI..sub.D1) (frequency) are in the
same RAB and it is on this basis the returns are analyzed,
processed and separated out.
[0340] Taking equations (1) and (2) and treating M.sub.0 and
M.sub.1 as the variables and solving for M.sub.0 and M.sub.1 we
have:
M.sub.0=(V.sub.00e.sup.j.PHI..sup.D1-V.sub.01)/(e.sup.j.PHI..sup.D1-e.sup-
.j.PHI..sup.D0) (1')
M.sub.1=(V.sub.00-V.sub.01e.sup.j.PHI..sup.D0)/(e.sup.j.PHI..sup.D1-e.sup-
.j.PHI..sup.D0) (2') Taking equations (2) and (3) and treating
M.sub.0e.sup.j.PHI..sup.D0 and M.sub.1e.sup.j.PHI..sup.D1 as the
variables and solving for M.sub.0e.sup.j.PHI..sup.D0 and
M.sub.1e.sup.j.PHI..sup.D1 we have:
M.sub.0e.sup.j.PHI..sup.D0=(V.sub.01e.sup.j.PHI..sup.D1-V.sub.02)/(e.sup.-
j.PHI..sup.D1-e.sup.j.theta.D0) (1'')
M.sub.1e.sup.j.PHI..sup.D1=(V.sub.01-V.sub.02e.sup.j.PHI..sup.D0)/(e.sup.-
j.PHI..sup.D1-e.sup.j.PHI..sup.D0) (2'') Equation (2'')/Equation
(2') or Equation (1'')/Equation (1') are the following:
e.sup.j.PHI..sup.D0=(V.sub.01e.sup.j.PHI..sup.D1-V.sub.02)/(V.sub.00e.sup-
.j.PHI..sup.D1-V.sub.01) (3')
e.sup.j.PHI..sup.D1=(V.sub.02-V.sub.01e.sup.j.PHI..sup.D0)/(V.sub.01-V.su-
b.00e.sup.j.PHI..sup.D0) (4') Equation (3') or Equation (4') is
easily solved for .PHI..sub.D0 and .PHI..sub.D1 which are
proportional to the total phase of return 0 and return 1
respectively. If return "Mo" is clutter then .PHI..sub.0=0
corresponding to clutter having zero (0) velocity. Now employing
equations (1) and (2) and solving for M.sub.0 and M.sub.1 knowing
.PHI..sub.D0 and .PHI..sub.D1 we are now to find .PHI..sub.0 and
.PHI..sub.1 which are proportional to velocity of return 0 and
return 1 respectively. M.sub.0 and M.sub.1 and both returns that
are detected in the same RAB.
[0341] Having the second channel data and performing the same
operations as in channel 1 and the equations are as follows:
V'.sub.00=M.sub.0X.sub.01+M.sub.1X.sub.11 PULSE 2 CHANNEL data 1-N
Delay 0 (1')
V'.sub.01=M.sub.0X.sub.01e.sup.j.PHI.'.sup.D0+M.sub.1X.sub.11e.s-
up.j.PHI.'.sup.D1 PULSE 2 CHANNEL data 2-N+1 Delay 1 (2')
V'.sub.02=M.sub.0X.sub.01e.sup.j2.PHI.'.sup.D0+M.sub.1X.sub.11e.sup.j2.PH-
I.'.sup.D1 PULSE 2 CHANNEL data 3-N+2 Delay 2 (3')
V'.sub.03=M.sub.0X.sub.01e.sup.j3.PHI.'.sup.D0+M.sub.1X.sub.11e.sup.j3.PH-
I.'.sup.D1 PULSE 2 CHANNEL data 4-N+3 Delay 3 (4')
X.sub.01=e.sup.jD.PHI..sup.A0e.sup.jK.sup.D0.sup.X.sup.0/W.sub.M0=|1/A.su-
b.M0|e.sup.j(K.sup.D0.sup.X.sup.0-.PSI..sup.M0.sup.) where
D=0X.sub.01=e.sup.jK.sup.D0.sup.X.sup.0/W.sub.M0=|1/A.sub.M0|e.sup.j(K.su-
p.D0.sup.X.sup.0-.PSI..sup.M0.sup.)
X.sub.11=e.sup.jD.PHI..sup.A1e.sup.jK.sup.D0.sup.X.sup.1/W.sub.M1=|1/A.su-
b.M1|e.sup.j(K.sup.D0.sup.X.sup.1-.PSI..sup.M1.sup.) where
D=0X.sub.11=e.sup.jK.sup.D0.sup.X.sup.1/W.sub.M1=|1/A.sub.M1|e.sup.j(K.su-
p.D0.sup.X.sup.1-.PSI..sup.M1.sup.)
[0342] Solving equations (1') to (4') in the same manner as
equations (1) to (4) we solve for .PHI.'.sub.D0 and .PHI.'.sup.D1
and M.sub.0X.sub.01 and M.sub.1X.sub.11. .PHI.'.sub.D0 and
.PHI.'.sup.D1 Solution should be the same as for .PHI..sub.D0 and
.PHI..sub.D1 since in pulse 2 we have the same returns detected in
the same RAB with the same velocity components.
solution for M.sub.0X.sub.01 and M.sub.1X.sub.11 in pulse 2/solving
for M.sub.0 and M.sub.1 in pulse 1 yields X.sub.01 and X.sub.11
Having the second pulse data delayed and performing the same
operations as in channel 1 and 2 and the equations are as follows:
V''.sub.00=M.sub.0X.sub.02+M.sub.1X.sub.12 PULSE 2 CHANNEL data
2-N+1 Delay 1 (1'')
V''.sub.01=M.sub.0X.sub.02e.sup.j.PHI.''.sup.D0+M.sub.1X.sub.12e.sup.j.PH-
I.''.sup.D1 PULSE 2 CHANNEL data 3-N+2 Delay 2 (2'')
V''.sub.02=M.sub.0X.sub.02e.sup.j2.PHI.''.sup.D0+M.sub.1X.sub.12e.sup.j2.-
PHI.''.sup.D1 PULSE 2 CHANNEL data 4-N+3 Delay 3 (3'')
V''.sub.03=M.sub.0X.sub.02e.sup.j3.PHI.''.sup.D0+M.sub.1X.sub.12e.sup.j3.-
PHI.''.sup.D1 PULSE 2 CHANNEL data 5-N+4 Delay 4 (4'')
X.sub.02=X.sub.01e.sup.j(.PHI..sup.A0.sup.+.DELTA.K.sup.D0.sup.X.sup.0.su-
p.)=X.sub.01e.sup.j(.gamma..sup.0.sup.):
X.sub.12=X.sub.11e.sup.j(.PHI..sup.A1.sup.+.DELTA.K.sup.D0.sup.X.sup.1.su-
p.)=X.sub.11e.sup.j(.gamma..sup.1.sup.)
[0343] Rewriting equations (1'') to (4'') we have the following:
V''.sub.00=M.sub.0X.sub.01e.sup.j.gamma..sup.0+M.sub.1X.sub.12e.sup.j.gam-
ma..sup.1 PULSE 2 CHANNEL data 2-N+1 Delay 1 (1'')
V''.sub.01=M.sub.0X.sub.01e.sup.j.gamma..sup.0e.sup.j.PHI.''.sup.D0+M.sub-
.1X.sub.12e.sup.j.gamma..sup.1e.sup.j.PHI.''.sup.D1 PULSE 2 CHANNEL
data 3-N+2 Delay 2 (2'')
V''.sub.02=M.sub.0X.sub.01e.sup.j.gamma..sup.0e.sup.j2.PHI.''.sup.D0+M.su-
b.1X.sub.12e.sup.j.gamma..sup.1e.sup.j2.PHI.'.sup.D1 PULSE 2
CHANNEL data 4-N+3 Delay 3 (3'')
V''.sub.03=M.sub.0X.sub.01e.sup.j.gamma..sup.0e.sup.j3.PHI.''.sup.D0+M.su-
b.1X.sub.12e.sup.j.gamma..sup.1e.sup.j3.PHI.''.sup.D1 PULSE 2
CHANNEL data 5-N+4 Delay 4 (4'') Solving equations (1'') to (4'')
the same manner as equations (1) to (4) we solve for .PHI.'.sub.D0
and .PHI.'.sub.D1 and M.sub.0X.sub.01 and M.sub.1X.sub.11.
.PHI.''.sub.D0 and .PHI.''.sub.D1 Solution should be the same.
solution for M.sub.0X.sub.01e.sup.j.gamma..sup.0 and
M.sub.1X.sub.11e.sup.j.gamma..sup.1 in channel 2 delayed/solving
for M.sub.0X.sub.01 and M.sub.1X.sub.11 in channel 2 yields
e.sup.j.gamma..sup.0 and e.sup.j.gamma..sup.1 and
.gamma..sub.0=.PHI..sub.A0+.DELTA.K.sub.D0X.sub.0 where X.sub.0 is
unknown and .gamma..sub.0 is known and therefore .PHI..sub.A0 has
to be determined .gamma..sub.1=.PHI..sub.A1+.DELTA.K.sub.D0X.sub.1
where X.sub.1 is unknown and .gamma..sub.1 are known and therefore
.PHI..sub.A1 has to be determined.sub.1 Solving for phase
proportional to velocity in both returns we have the following:
[0344] Finding .PHI..sub.D0 and .PHI..sub.D1 as in the channel
technique and finding
.PHI..sub.O=.PHI..sub.D0-.PHI..sub.A0 and
.PHI..sub.1=.PHI..sub.D1-.PHI..sub.A1
Definition of terms not defined previously:
ALL "V" TERMS ARE MEASURED TERMS.--
X01--CHANNEL 2 TERM THAT makes relates channel 2 to channel 1 for
return 1
X02--CHANNEL 2 TERM THAT makes relates channel 2 to channel 1 for
return 2
.DELTA.K.sub.D0--The difference factor for different delays for
return 1 and 2
X.sub.0--The azimuth position in filter factor for return 1
.gamma..sub.0--The difference in angle between different delayed
data of return 1
.gamma..sub.1--The difference in angle between different delayed
data of return 2
.PHI..sub.AO--phase proportional to azimuth of return 1
.PHI..sub.A1--phase proportional to azimuth of return 2
A.sub.M0--Amplitude balancing term between channel 1 and 2 for
return 1
A.sub.M1--Amplitude balancing term between channel 1 and 2 for
return 2
.PSI..sub.M0--Phase balancing term between channel 1 and 2 for
return 1
.PSI..sub.M1--Phase balancing term between channel 1 and 2 for
return 2
[0345] Comments and observations on technique
1--All solutions
.PHI..sub.D0, .PHI.'.sub.D0, .PHI.''.sub.D0 should be equal and
.PHI..sub.D1, .PHI.'.sub.D1, .PHI.''.sub.D1 should be equal
2--Solving for M0 and M1 by this approach solves for the location
of their peaks therefore they have a phase shift equal to zero at
this point.
3--To solve for the channel balancing terms three sets of equations
are required but for solving for velocity and azimuth only last two
sets are required.
4--Correlate with other .DELTA.C technique in the following
manner:
[0346] a) Same solution [0347] b) All variables are the same value
such as M0, M1, ETC [0348] c) .DELTA.F, .DELTA.R and .DELTA.H
Results should correlate Analogously a small change in range bin
may be taken and we determine X.sub.R0 and X.sub.R1 which
determines where the peak of the returns in range, this does not
help in the evaluation in azimuth. Resolving velocity ambiguity
with the taking of meaningful delay in time and processing again.
Thus we can determine the peak of each return in range and azimuth
to obtain the maximum amplitude for each return for further use.
The change in amplitude and phase of the range bin in conjunction
with a delay in time gives an accurate determination of velocity
which will resolve velocity ambiguity.
[0349] The change in amplitude and phase of the doppler bin in
conjunction with a delay in time gives an accurate determination of
horizontal tangential velocity.
[0350] The change in amplitude and phase in the different linear
arrays of the doppler bin in conjunction with a delay in time gives
an accurate determination of vertical tangential velocity.
[0351] Thus we have obtained the three dimensional position and
velocity of all returns.
B. Two pulse "N" channel data in time-three returns-.PHI..sub.D
technique
[0352] The previous analysis was for two returns possible per RAB
processed; this will be for three (3) returns per RAB.
V.sub.00=M.sub.0+M.sub.1+M.sub.2 PULSE 1 CHANNEL data 1-N Delay 0
(1)
V.sub.01=M.sub.0e.sup.j.PHI..sup.D0+M.sub.1e.sup.j.PHI..sup.D1+M.sub.2e.s-
up.j.PHI..sup.D2 PULSE 1 CHANNEL data 2-N+1 Delay 1 (2)
V.sub.02=M.sub.0e.sup.j2.PHI..sup.D0+M.sub.1e.sup.j2.PHI..sup.D1+M.sub.2e-
.sup.j2.PHI..sup.D2 PULSE 1 CHANNEL data 3-N+2 Delay 2 (3)
V.sub.03=M.sub.0e.sup.j3.PHI..sup.D0+M.sub.1e.sup.j3.PHI..sup.D1+M.sub.2e-
.sup.j3.PHI..sup.D2PULSE 1 CHANNEL data 4-N+3 Delay 3 (4) All terms
previously defined except the following: M--Third return
.PHI..sub.D2--phase proportional to radial velocity plus azimuth of
third return .PHI..sub.A2--phase proportional to azimuth of third
return .PHI..sub.2--phase proportional to radial velocity of third
return Taking equations (1) and (2) and (3) and treating M.sub.0
and M.sub.1 and M.sub.2 as the variables and solving the
determinant equation for .DELTA..sub.0 we have: .DELTA. 0 = e
j.PHI. D .times. .times. 0 1 .times. e j.PHI. D .times. .times. 1 1
.times. e j.PHI. D .times. .times. 2 1 = 1 .times. .times. e j.PHI.
D .times. .times. 1 .times. e j.PHI. D .times. .times. 2 - 1
.times. .times. e j.PHI. D .times. .times. 0 .times. e j.PHI. D
.times. .times. 2 + 1 .times. .times. e j.PHI. D .times. .times. 0
.times. e j.PHI. D .times. .times. 1 .times. .times. e j2.PHI. D
.times. .times. 0 .times. e j2.PHI. D .times. .times. 1 .times. e
j2.PHI. D .times. .times. 2 .times. .times. e j2.PHI. D .times.
.times. 1 .times. e j2.PHI. D .times. .times. 2 .times. .times. e
j2.PHI. D .times. .times. 0 .times. e j2.PHI. D .times. .times. 2
.times. .times. e j2.PHI. D .times. .times. 0 .times. e j2.PHI. D
.times. .times. 1 .times. .times. .DELTA. 0 = .times. e j.PHI. D
.times. .times. 1 .times. e j2.PHI. D .times. .times. 2 - e j2.PHI.
D .times. .times. 1 .times. e j.PHI. D .times. .times. 2 - e j.PHI.
D .times. .times. 0 .times. e j2.PHI. D .times. .times. 2 + .times.
e j.PHI. D .times. .times. 2 .times. e j2.PHI. D .times. .times. 0
+ e j.PHI. D .times. .times. 0 .times. e j2.PHI. D .times. .times.
1 - e j.PHI. D .times. .times. 1 .times. e j2.PHI. D .times.
.times. 0 = .times. function .times. .times. of .times. .times.
.PHI. D .times. .times. 0 , .PHI. D .times. .times. 1 .times.
.times. and .times. .times. .PHI. D .times. .times. 2 .times.
.times. and .times. .times. solving .times. .times. for .times.
.times. M 0 _ = M 0 * .DELTA. 0 M 0 _ = V 01 V 00 .times. e j.PHI.
D .times. .times. 1 1 .times. e j.PHI. D .times. .times. 2 1 = V 00
.times. e j.PHI. D .times. .times. 1 .times. e j.PHI. D .times.
.times. 2 - V 01 .times. 1 .times. .times. 1 + V 02 .times. 1
.times. .times. 1 .times. .times. V 02 .times. e j2.PHI. D .times.
.times. 1 .times. V .times. .times. e j2.PHI. D .times. .times. 2
.times. .times. e j2.PHI. D .times. .times. 1 .times. e j2.PHI. D
.times. .times. 2 .times. .times. e j2.PHI. D .times. .times. 1
.times. e j2.PHI. D .times. .times. 1 .times. .times. e j.PHI. D
.times. .times. 1 .times. e j.PHI. D .times. .times. 2 .times.
.times. M 0 _ = .times. V 00 .function. ( e j.PHI. D .times.
.times. 1 .times. e j2.PHI. D .times. .times. 2 - e j.PHI. D
.times. .times. 2 .times. e j2.PHI. D .times. .times. 1 ) - .times.
V 01 ( e j2.PHI. D .times. .times. 2 - e j2.PHI. D .times. .times.
1 ) + V 02 .function. ( e j.PHI. D .times. .times. 2 - e j.PHI. D
.times. .times. 1 ) = .times. function .times. .times. of .times.
.times. .times. .PHI. D .times. .times. 1 .times. .times. and
.times. .times. .PHI. D .times. .times. 2 .times. .times. and
.times. .times. solving .times. .times. for .times. .times. M 1 _ =
M 1 * .DELTA. 0 ( 6 ) M 1 _ = e j.PHI. D .times. .times. 0 1
.times. V 01 V 00 .times. e j.PHI. D .times. .times. 2 1 = V 00
.times. e j.PHI. D .times. .times. 0 .times. e j.PHI. D .times.
.times. 2 - V 01 .times. 1 .times. .times. 1 + V 02 .times. 1
.times. .times. 1 .times. .times. e j2.PHI. D .times. .times. 0
.times. V 02 .times. e j2.PHI. D .times. .times. 2 .times. .times.
e j2.PHI. D .times. .times. 0 .times. e j2.PHI. D .times. .times. 2
.times. .times. e j2.PHI. D .times. .times. 0 .times. e j2.PHI. D
.times. .times. 2 .times. .times. e j.PHI. D .times. .times. 0
.times. e j.PHI. D .times. .times. 2 .times. .times. M 1 _ =
.times. V 01 .function. ( e j.PHI. D .times. .times. 0 .times. e
j2.PHI. D .times. .times. 2 - e j2.PHI. D .times. .times. 0 .times.
e j.PHI. D .times. .times. 2 ) - .times. V 01 ( e j2.PHI. D .times.
.times. 2 - e j2.PHI. D .times. .times. 0 ) + V 02 .function. ( e
j.PHI. D .times. .times. 2 - e j.PHI. D .times. .times. 0 ) =
.times. function .times. .times. of .times. .times. .PHI. D .times.
.times. 0 .times. .times. and .times. .times. .times. .PHI. D
.times. .times. 2 .times. .times. and .times. .times. solving
.times. .times. for .times. .times. M 2 _ = M 2 * .DELTA. 0 ( 7 ) M
2 _ = e j.PHI. D .times. .times. 0 1 .times. e j.PHI. D .times.
.times. 1 1 .times. V 01 V 00 = V 00 .times. e j.PHI. D .times.
.times. 0 .times. e j.PHI. D .times. .times. 1 - V 01 .times. 1
.times. .times. 1 + V 02 .times. 1 .times. .times. 1 .times.
.times. e j2.PHI. D .times. .times. 0 .times. e j2.PHI. D .times.
.times. 1 .times. V 02 .times. .times. e j2.PHI. D .times. .times.
0 .times. e j2.PHI. D .times. .times. 1 .times. .times. e j2.PHI. D
.times. .times. 0 .times. e j2.PHI. D .times. .times. 1 .times.
.times. e j.PHI. D .times. .times. 0 .times. e j.PHI. D .times.
.times. 1 .times. .times. M 2 _ = .times. V 00 .function. ( e
j.PHI. D .times. .times. 0 .times. e j2.PHI. D .times. .times. 1 -
e j2.PHI. D .times. .times. 1 .times. e j.PHI. D .times. .times. 0
) - .times. V 01 ( e j2.PHI. D .times. .times. 1 - e j2.PHI. D
.times. .times. 0 ) + V 02 .function. ( e j.PHI. D .times. .times.
1 - e j.PHI. D .times. .times. 0 ) = .times. function .times.
.times. of .times. .times. .PHI. D .times. .times. 0 .times.
.times. and .times. .times. .times. .PHI. D .times. .times. 1 ( 8 )
##EQU14## Solving for .PHI..sub.D0, .PHI..sub.D1 and .PHI..sub.D2
and substituting these values in equations (1), (2) and (3) we
determine M.sub.0, M.sub.1 and M.sub.2. Taking equations (2), (3)
and (4) and treating M.sub.0e.sup.jD.PHI..sup.0,
M.sub.1e.sup.jD.PHI..sup.1 and M.sub.2e.sup.jD.PHI..sup.2 as the
variables and solving the determinant equation for .DELTA..sub.0 is
the same and performing the same operations as with the first set
of equations we have the following:
M.sub.0e.sup.j.PHI..sup.D0=function of (.PHI..sub.D1,.PHI..sub.D2)
( 6) M.sub.1e.sup.j.PHI..sup.D1=function of
(.PHI..sub.D0,.PHI..sub.D2) ( 7) M2e.sup.j.PHI..sup.D2=function of
(.PHI..sub.D0,.PHI..sub.D1) ( 8) Equation ( 6)/(6), ( 7)/(7) and (
8)/(8) ( 6)/(6)=e.sup.j.PHI..sup.D0=function
(.PHI..sub.D1,.PHI..sub.D2) ( 7)/(7)=e.sup.j.PHI..sup.D1=function
(.PHI..sub.0,.PHI..sub.D2) ( 8)/(8)=e.sup.j.PHI..sup.D2=function
(.PHI..sub.D0,.PHI..sub.D1) Solving for .PHI..sub.D0,.PHI..sub.D1
and .PHI..sub.D2 and substituting these values in equations (2),
(3) and (4) we determine M.sub.0e.sup.jD.PHI..sup.0,
M.sub.1e.sup.jD.PHI..sup.1 and M.sub.2e.sup.jD.PHI..sup.2.
V'.sub.00=M.sub.0X.sub.01+M.sub.1X.sub.11+M.sub.2X.sub.21 PULSE 2
CHANNEL data 1-N Delay 0 (1)
V'.sub.01=M.sub.0X.sub.01e.sup.j.PHI.'.sup.D0+M.sub.1X.sub.11e.sup.j.PHI.-
'.sup.D1+M.sub.2X.sub.21e.sup.j.PHI.'.sup.D2 PULSE 2 CHANNEL data
2-N+1 Delay 1 (2)
V'.sub.02=M.sub.0X.sub.01e.sup.j2.PHI.'.sup.D0+M.sub.1X.sub.11e.sup.j2.PH-
I.'.sup.D1+M.sub.2X.sub.21e.sup.j2.PHI.'.sup.D2 PULSE 2 CHANNEL
data 3-N+2 Delay 2 (3')
V'.sub.03=M.sub.0X.sub.01e.sup.j3.PHI.'.sup.D0+M.sub.1X.sub.11e.sup.j3.PH-
I.'.sup.D1+M.sub.2X.sub.21e.sup.j3.PHI.'.sup.D2 PULSE 2 CHANNEL
data 4-N+3 Delay 3 (4)
X.sub.01=e.sup.jD.PHI..sup.A0e.sup.jK.sup.D0.sup.X.sup.0/W.sub.M0=|1/A.su-
b.M0|e.sup.j(K.sup.D0.sup.X.sup.0-.PSI..sup.M0.sup.) where
D=0X.sub.01=e.sup.jK.sup.D0.sup.X.sup.0/W.sub.M0=|1/A.sub.M0|e.sup.j(K.su-
p.D0.sup.X.sup.0-.PSI..sup.M0.sup.)
X.sub.11=e.sup.jD.PHI..sup.A1e.sup.jK.sup.D0.sup.X.sup.1/W.sub.M1=|1/A.su-
b.M1|e.sup.j(K.sup.D0.sup.X.sup.1-.PSI..sup.M1.sup.) where
D=0X.sub.11=e.sup.jK.sup.D0.sup.X.sup.1/W.sub.M1=|1/A.sub.M1|e.sup.j(K.su-
p.D0.sup.X.sup.1-.PSI..sup.M1.sup.)
X.sub.21=e.sup.jD.PHI..sup.A2e.sup.jK.sup.D0.sup.X.sup.2/W.sub.M2=|1/A.su-
b.M2|e.sup.j(K.sup.D0.sup.X.sup.2-.PSI..sup.M2.sup.) where
D=0X.sub.21=e.sup.jK.sup.D0.sup.X.sup.2/W.sub.M2=|1/A.sub.M2|e.sup.j(K.su-
p.D0.sup.X.sup.2-.PSI..sup.M2.sup.)
[0353] Performing the same operations on equations (1'), (2') and
(3') with the variables M.sub.0X.sub.01, M.sub.1X.sub.11 and
M.sub.2X.sub.21 and .DELTA..sub.0 remains the same. The analysis is
analogous and the result is the following: and .times. .times.
solving .times. .times. for .times. .times. M 0 .times. X 01 _ = M
0 .times. X 01 * .DELTA. 0 M 0 .times. X 01 _ = .times. V 01
.function. ( e j .times. .times. .PHI. D .times. .times. 1 '
.times. e j .times. .times. 2 .times. .times. .PHI. .times. D
.times. .times. 2 ' - e j .times. .times. 2 .times. .times. .PHI. D
.times. .times. 1 ' .times. e j .times. .times. .PHI. D .times.
.times. 2 ' ) - .times. V 02 .function. ( e j .times. .times. 2 '
.times. .PHI. D .times. .times. 1 - e j .times. .times. 2 .times.
.PHI. D .times. .times. 2 ' ) + V 03 .function. ( e j .times.
.times. .PHI. D .times. .times. 1 ' - e j .times. .times. .PHI. D
.times. .times. 2 ' ) = .times. function .times. .times. of .times.
.times. .PHI. D .times. .times. 1 ' .times. .times. and .times.
.times. .PHI. D .times. .times. 2 ' .times. .times. and .times.
.times. solving .times. .times. for .times. .times. M 1 .times. X
11 _ = M 1 .times. X 11 * .DELTA. 0 ( 6 ' ) V 01 .function. ( e j
.times. .times. .PHI. D .times. .times. 0 ' .times. e j .times.
.times. 2 .times. .times. .PHI. .times. D .times. .times. 2 ' - e j
.times. .times. 2 .times. .times. .PHI. D .times. .times. 0 '
.times. e j .times. .times. .PHI. D .times. .times. 2 ' ) - V 02
.function. ( e j .times. .times. 2 ' .times. .PHI. D .times.
.times. 0 - e j .times. .times. 2 .times. .PHI. D .times. .times. 2
' ) + V 03 .function. ( e j .times. .times. .PHI. D .times. .times.
0 ' - e j .times. .times. .PHI. D .times. .times. 2 ' ) = function
.times. .times. of .times. .times. .PHI. D .times. .times. 0 '
.times. .times. and .times. .times. .PHI. D .times. .times. 2 '
.times. .times. and .times. .times. solving .times. .times. for
.times. .times. M 2 .times. X 21 _ = M 2 .times. X 21 * .DELTA. 0 (
7 ' ) M 2 .times. X 21 _ = V 01 .function. ( e j .times. .times.
.PHI. D .times. .times. 0 ' .times. e j .times. .times. 2 .times.
.times. .PHI. .times. D .times. .times. 1 ' - e j .times. .times. 2
.times. .times. .PHI. D .times. .times. 0 ' .times. e j .times.
.times. .PHI. D .times. .times. 1 ' ) - V 02 .function. ( e j
.times. .times. 2 ' .times. .PHI. D .times. .times. 1 - e j .times.
.times. 2 .times. .PHI. D .times. .times. 0 ' ) + V 03 .function. (
e j .times. .times. .PHI. D .times. .times. 1 ' - e j .times.
.times. .PHI. D .times. .times. 0 ' ) = function .times. .times. of
.times. .times. .PHI. D .times. .times. 0 ' .times. .times. and
.times. .times. .PHI. D .times. .times. 1 ' ( 8 ' ) ##EQU15##
Taking equation (6')/(6) we have the following:
X.sub.01=M.sub.0X.sub.01/M.sub.0
[0354] Taking equation (7')/(7) we have the following:
X.sub.11=M.sub.1X.sub.11/M.sub.1 Taking equation (8')/(8) we have
the following: X.sub.21=M.sub.2X.sub.21/M.sub.2 Performing the same
operations on equations (2'), (3') and (4') with the variables
M.sub.0X.sub.01, M.sub.1X.sub.11 and M.sub.2X.sub.21 and
.DELTA..sub.0 remains the same. The analysis is analogous and the
result is the following: M.sub.0e.sup.j.PHI..sup.D0=function of
(.PHI..sub.D1,.PHI..sub.D2) ( 6')
M.sub.1e.sup.j.PHI..sup.D1=function of (.PHI..sub.D0,.PHI..sub.D2)
( 7) M.sub.2e.sup.j.PHI..sup.D2=function of
(.PHI..sub.D0,.PHI..sub.D1) ( 8') Equation ( 6)/(6'), ( 7)/(7') and
( 8')/(8') ( 6')/(6')=e.sup.j.PHI..sup.D0=function
(.PHI..sub.D1,.PHI..sub.D2) ( 7')/(7)=e.sup.j.PHI..sup.D1=function
(.PHI..sub.D0,.PHI..sub.D2) ( 8')/(8')=e.sup.j.PHI..sup.D2=function
(.PHI..sub.D0,.PHI..sub.D1) Solving for .PHI..sub.D0, .PHI..sub.D1
and .PHI..sub.D2 and substituting these values in equations (2),
(3) and (4) we determine M.sub.0X.sub.01, M.sub.1X.sub.02 and
M.sub.2X.sub.03.
[0355] Taking the next set of equations as follows:
V''.sub.00=M.sub.0X.sub.02+M.sub.1X.sub.12+M.sub.2X.sub.22 PULSE 2
CHANNEL data 2-N+1 Delay 1 (1'')
V''.sub.01=M.sub.0X.sub.02e.sup.j.PHI.''.sup.D0+M.sub.1X.sub.12e.sup.j.PH-
I.''.sup.D1+M.sub.2X.sub.22e.sup.j.PHI.''.sup.D2 PULSE 2CHANNEL
data 3-N+2 Delay 2 (2'')
V''.sub.02=M.sub.0X.sub.02e.sup.j2.PHI.''.sup.D0+M.sub.1X.sub.12e.sup.j2.-
PHI.''.sup.D1+M.sub.2X.sub.22e.sup.j2.PHI.''.sup.D2 PULSE 2CHANNEL
data 4-N+3 Delay 3 (3'')
V''.sub.03=M.sub.0X.sub.02e.sup.j3.PHI.''.sup.D0+M.sub.1X.sub.12e.sup.j3.-
PHI.''.sup.D1+M.sub.2X.sub.22e.sup.j3.PHI.''.sup.D2 PULSE 2CHANNEL
data 5-N+4 Delay 4 (4'')
X.sub.02=X.sub.01e.sup.j(.PHI..sup.A0.sup.+.DELTA.K.sup.D0.sup.X.sup.0.su-
p.)=X.sub.01e.sup.j(.gamma..sup.0.sup.):X.sub.12=X.sub.11e.sup.j(.PHI..sup-
.A1.sup.+.DELTA.K.sup.D0.sup.X.sup.0.sup.)=X.sub.11e.sup.j(.gamma..sup.1.s-
up.):X.sub.22=X.sub.21e.sup.j(.PHI..sup.A2.sup.+.DELTA.K.sup.D0.sup.X.sup.-
0.sup.)=X.sub.21e.sup.j(.gamma..sup.0.sup.) Rewriting equations
(1'' to 4'') we have the following:
V''.sub.00=M.sub.0X.sub.01e.sup.j.gamma..sup.0+M.sub.1X.sub.11e.sup.j.gam-
ma..sup.1+M.sub.2X.sub.12e.sup.j.gamma..sup.2 PULSE 2 CHANNEL data
2-N+1 Delay 1 (1'')
V''.sub.01=M.sub.0X.sub.01e.sup.j.gamma..sup.0e.sup.j.PHI.''.sup.D0+M.sub-
.1X.sub.11e.sup.j.gamma..sup.1e.sup.j.PHI.''.sup.D1+M.sub.2X.sub.12e.sup.j-
.gamma..sup.2e.sup.j.PHI.''.sup.D2 PULSE 2 CHANNEL data 3-N+2 Delay
2 (2'')
V''.sub.02=M.sub.0X.sub.01e.sup.j.gamma..sup.0e.sup.j2.PHI.''.sup.-
D0+M.sub.1X.sub.11e.sup.j.gamma..sup.1e.sup.j2.PHI.''.sup.D1+M.sub.2X.sub.-
12e.sup.j.gamma..sup.2e.sup.j2.PHI.''.sup.D2 PULSE 2 CHANNEL data
4-N+3 Delay 3 (3'')
V''.sub.03=M.sub.0X.sub.01e.sup.j.gamma..sup.0e.sup.j3.PHI.''.sup.D0+M.su-
b.1X.sub.11e.sup.j.gamma..sup.1e.sup.j3.PHI.''.sup.D1+M.sub.2X.sub.12e.sup-
.j.gamma..sup.2e.sup.j3.PHI.''.sup.D2 PULSE 2 CHANNEL data 5-N+4
Delay 4 (4'') Performing the same operations on equations (1''),
(2'') and (3'') with the variables
M.sub.0X.sub.01e.sup.j.gamma..sup.0,
M.sub.1X.sub.11e.sup.j.gamma..sup.1 and
M.sub.2X.sub.21e.sup.j.gamma..sup.2 and .DELTA..sub.0 remains the
same. The analysis is analogous and the result is the following:
and .times. .times. solving .times. .times. for .times. .times.
.times. M 0 .times. X 01 _ .times. e j.UPSILON. 0 _ = M 0 .times. X
01 .times. e j.UPSILON. 0 * .DELTA. 0 .times. .times. M 0 .times. X
01 _ .times. e j.UPSILON. 0 _ = .times. V 02 '' .function. ( e
j.PHI. D .times. .times. 1 ' .times. e j2.PHI. D .times. .times. 2
' - e j2.PHI. D .times. .times. 1 ' .times. e j.PHI. D .times.
.times. 2 ' ) - .times. V 03 '' .function. ( e j2 ' .times. .PHI. D
.times. .times. 1 - e j2.PHI. D .times. .times. 2 ' ) + V 04 ''
.function. ( e j.PHI. D .times. .times. 1 ' - e j.PHI. D .times.
.times. 2 ' ) = .times. function .times. .times. of .times. .times.
.PHI. D .times. .times. 1 '' .times. .times. and .times. .times.
.PHI. D .times. .times. 2 '' .times. .times. and .times. .times.
solving .times. .times. for .times. .times. M 1 .times. X 11 _
.times. e j.UPSILON. 1 _ = M 1 .times. X 11 .times. e j.UPSILON. 1
* .DELTA. 0 ( 6 '' ) M 1 .times. X 11 _ .times. e j.UPSILON. 1 _ =
.times. V 02 .function. ( e j.PHI. D .times. .times. 0 '' .times. e
j2.PHI. D .times. .times. 2 '' - e j2.PHI. D .times. .times. 0 ''
.times. e j2.PHI. D .times. .times. 2 '' ) - .times. V 03
.function. ( e j2 '' .times. .PHI. D .times. .times. 0 - e j2.PHI.
D .times. .times. 2 '' ) + V 04 .function. ( e j.PHI. D .times.
.times. 0 '' - e j.PHI. D .times. .times. 2 '' ) = .times. function
.times. .times. of .times. .times. .PHI. D .times. .times. 0 '
.times. .times. and .times. .times. .PHI. D .times. .times. 2 '
.times. .times. and .times. .times. solving .times. .times. for
.times. .times. M 2 .times. X 21 _ .times. e j.UPSILON. 2 _ = M 2
.times. X 21 .times. e j.UPSILON. 2 * .DELTA. 0 ( 7 '' ) M 2
.times. X _ 21 .times. e j.UPSILON. 2 _ = .times. V 02 ( e j.PHI. D
.times. .times. 0 '' .times. e j2.PHI. D .times. .times. 1 '' - e
j2.PHI. D .times. .times. 0 '' .times. e j.PHI. D .times. .times. 1
'' ) - .times. V 03 ( e j2 ' .times. .PHI. D .times. .times. 1 '' -
e j2.PHI. D .times. .times. 0 '' ) + V 04 .function. ( e j.PHI. D
.times. .times. 1 '' - e j.PHI. D .times. .times. 0 '' ) = .times.
function .times. .times. of .times. .times. .PHI. D .times. .times.
0 '' .times. .times. and .times. .times. .PHI. D .times. .times. 1
'' ( 8 '' ) ##EQU16## Taking equation (6'')/(6') we have the
following:
e.sup.j.gamma..sup.0=M.sub.0X.sub.01e.sup.j.gamma..sup.0/M.sub.0X.sub.01=-
V''.sub.02(e.sup.j.PHI.'.sup.D1e.sup.j2.PHI.'.sup.D2-e.sup.j2.PHI.'.sup.D1-
e.sup.j.PHI.'.sup.D2)-V''.sub.03(e.sup.j2'.PHI..sup.D1-e.sup.j2.PHI.'.sup.-
D2)+V''.sub.04(e.sup.j.PHI.'.sup.D1-j.PHI.'.sup.D2)/V.sub.01(e.sup.j.PHI.'-
.sup.D1e.sup.j2.PHI.'.sup.D2-e.sup.j2.PHI.'.sup.D1e.sup.j.PHI.'.sup.D2)-V.-
sub.02(e.sup.j2'.PHI..sup.D1-e.sup.j2.PHI.'.sup.D2)+V.sub.03(e.sup.j.PHI.'-
.sup.D1-e.sup.j.PHI.'.sup.D2) (12) Taking equation (7'')/(7') we
have the following:
e.sup.j.gamma..sup.1=M.sub.1X.sub.11e.sup.j.gamma..sup.1/M.sub.1X.sub.11=-
V.sub.02(e.sup.j.PHI.''.sup.D0e.sup.j2.PHI.''.sup.D2-e.sup.j2.PHI.''.sup.D-
0e.sup.j.PHI.''.sup.D2)-V.sub.03(e.sup.j2''.PHI..sup.D0-e.sup.j2.PHI.''.su-
p.D2)+V.sub.04(e.sup.j.PHI.''.sup.D0-j.PHI.''.sup.D2)/V.sub.01(e.sup.j.PHI-
.'.sup.D0e.sup.j2.PHI.'.sup.D2-e.sup.j2.PHI.'.sup.D0e.sup.j.PHI.'.sup.D2)--
V.sub.02(e.sup.j2'.PHI..sup.D0-e.sup.j2.PHI.'.sup.D2)+V.sub.03(e.sup.j.PHI-
.'.sup.D0-e.sup.j.PHI.'.sup.D2) (13) Taking equation (8'')/(8') we
have the following:
e.sup.j.gamma..sup.2=M.sub.2X.sub.21e.sup.j.gamma..sup.2/M.sub.2X.sub.21=-
V.sub.02(e.sup.j.PHI.''.sup.D0e.sup.j2.PHI.''.sup.D1-e.sup.j2.PHI.''.sup.D-
0e.sup.j.PHI.''.sup.D1)-V.sub.03(e.sup.j2''.PHI..sup.D1-e.sup.j2.PHI.''.su-
p.D0)+V.sub.04(e.sup.j.PHI.''.sup.D1-j.PHI.''.sup.D0)/V.sub.01(e.sup.j.PHI-
.'.sup.D0e.sup.j2.PHI.'.sup.D2-e.sup.j2.PHI.'.sup.D0e.sup.j.PHI.'.sup.D2)--
V.sub.02(e.sup.j2'.PHI..sup.D0-e.sup.j2.PHI.'.sup.D2)+V.sub.03(e.sup.j.PHI-
.'.sup.D0-e.sup.j.PHI.'.sup.D2) (14) Performing the same operations
on equations (2''), (3'') and (4'') with the variables
M.sub.0X.sub.01e.sup.j.theta..sup.0,
M.sub.1X.sub.11e.sup.j.theta..sup.1 and
M.sub.1X.sub.21e.sup.j.theta..sup.2 and .DELTA..sub.0 remains the
same Substituting equation (13) into equation (12) we have the
following: The analysis is analogous and the result is the
following: M.sub.0e.sup.j.PHI..sup.D0=function of
(.PHI..sub.D1,.PHI..sub.D2) ( 6')
M.sub.1e.sup.j.PHI..sup.D1=function of (.PHI..sub.D0,.PHI..sub.D2)
( 7') M.sub.2e.sup.j.PHI..sup.D2=function of
(.PHI..sub.0,.PHI..sub.D1) ( 8'') Equation ( 6')/(6''), ( 7')/(7'')
and ( 8')/(8-) ( 6'')/(6'')=e.sup.j.PHI..sup.D0=function
(.PHI..sub.D1,.PHI..sub.D2) (
7'')/(7'')=e.sup.j.PHI..sup.D1=function (.PHI..sub.D0,.PHI..sub.D2)
( 8'')/(8'')=e.sup.j.PHI..sup.D2=function
(.PHI..sub.D0,.PHI..sub.D1) Solving for .PHI..sub.D0, .PHI..sub.D1
and .PHI..sub.D2 and substituting these values in equations (2),
(3) and (4) we determine M.sub.0X.sub.00e.sup.j.gamma..sup.0,
M.sub.1X.sub.01e.sup.j.gamma..sup.1 and
M.sub.2X.sub.02e.sup.j.gamma..sup.2 and we have determined
.gamma..sub.1, .gamma..sub.2 and .gamma..sub.3 and
.gamma..sub.0=.PHI..sub.A0+.DELTA.K.sub.D0X.sub.0:.gamma..sub.1=.PHI..sub-
.A1+.DELTA.K.sub.D0X.sub.1:.gamma..sub.2=.PHI..sub.A2+.DELTA.K.sub.D0X.sub-
.2 where everything is known except .PHI..sub.A0, .PHI..sub.A1 and
.PHI..sub.A2 are easily determined and having to determine
.PHI..sub.D0 and .PHI..sub.D1 and .PHI..sub.D2 as in the two return
case since .PHI..sub.0=.PHI..sub.D0-.PHI..sub.A0:
.PHI..sub.1=.PHI..sub.D1-.PHI..sub.A1:.PHI..sub.2=.PHI..sub.D2-.PHI..sub.-
A2 the velocity of the returns have been attained.
e.sup.j.gamma..sup.0=M.sub.0X.sub.00e.sup.j.gamma..sup.0/M.sub.0X.sub.00
e.sup.j.gamma..sup.1=M.sub.1X.sub.01e.sup.j.gamma..sup.1/M.sub.1X.sub.01
e.sup.j.gamma..sup.2=M.sub.2X.sub.02e.sup.j.gamma..sup.2/M.sub.2X.sub.02
Substituting equation (13) into equation (12) we have the
following: Same solution as in two channel section BI for
.PHI..sub.0, .PHI..sub.1 and .PHI..sub.2 and for the Assist in
Determining Solutions when the Number of Returns are Three or More
M.sub.0, M.sub.1 and M.sub.2 and the ratios of the
M'.sub.0/M.sub.0,M'.sub.1/M.sub.1 and M'.sub.2/M.sub.2 should give
a good estimate of where the position .PHI..sub.D0 and .PHI..sub.D1
and .PHI..sub.D2 is detected at that RAB. From this an estimate of
velocity of the returns are determined. From the ratio of the
second set of data to the first set of data we obtain XF0 and XF1
and XF2 from which is the ratio of M'.sub.0/M.sub.0=X.sub.F0 and
M'.sub.1/M.sub.1=X.sub.F1 and M'.sub.2/M.sub.2=X.sub.F2 where all
other terms are known. From the previous determinations of the
estimate .PHI..sub.D0 and .PHI..sub.D1 and .PHI..sub.D2 which is
the position in the filter where the returns are detected at there
peak in the RAB. This gives a good estimate of the azimuth of the
returns. To get more accurate determinations other close frequency
points to initially processed data are processed.
[0356] From XF0 an estimate of where the returns are detected at
there peak in the RDB. From the following equation
.PHI..sub.0=.PHI..sub.D0-.PHI..sub.A0 where .PHI..sub.0A is the
phase of the return proportional to the azimuth of the return, and
.PHI..sub.D0 is the phase of the return proportional to the peak of
the return, .PHI..sub.0
is the phase of the return proportional to the velocity of the
return.
[0357] Similarly this is performed for XF1 and XF2 hence finding
the azimuth of the second and third return.
[0358] Analogously a small change in range bin may be taken and we
determine XR0, XR1 and XR2 which determines where the peak of the
returns in range, this does not help in the evaluation in azimuth.
Resolving velocity ambiguity with the taking of meaning delay in
time and processing again. Thus we can determine the peak of each
return in range and azimuth to obtain the maximum amplitude for
each return for further use. A more accurate determination of
.PHI..sub.D0, .PHI..sub.D1 and .PHI..sub.D2 is determined by taking
the four sets of equations and employing the candidate .PHI.
technique substituting all possible solutions which are restricted
to the values that can be in only one range azimuth bin (RAB) but
for when greater accuracy is required the number of candidate
solutions increase. The candidate solutions should be very close in
value for all four sets of data giving very robust and accurate
solutions which determines all the parameters of the returns.
[0359] Also another correlating and checking operation is to repeat
the processing with a close frequency and the results should be
very close plus obtaining and obtaining change in return vector
(XF). This would be the same for all sets of four sets of data and
also would be a check on the .PHI..sub.D0, .PHI..sub.D1 and
.PHI..sub.D2 solutions.
[0360] Analogously this would process a close sample in the range
direction and also for processing other linear arrays.
[0361] RECAPPING--We have determined all .PHI.s, in the two return
and three return case and as consequently it may be performed for
many .PHI.s. The significance of this development is as each RAB
that is processed clutter, target, noise, and other returns may be
detected and thresholded for importance and later processed to
determine if sidelobes, multipath targets, etc.
CORRELATION FACTORS
[0362] 1--Time delay as many pulses at a time as the number of
returns and process data determine all the .PHI.s.
[0363] 2--Additional channel delay processed again and all .PHI.s
should agree
[0364] 3--Other RAB processed have same return data related to each
such as mover should agree
[0365] 4--IF more than two pulses other dual pulses is processed
and results should agree.
[0366] 5--Other techniques as to be shown later in document and
results should agree
[0367] 6--If a planar array is implemented all other linear arrays
should obtain the same results and height and vertical tangential
velocity obtained.
[0368] The aforementioned system has many advantages such as the
following:
[0369] 1--No clutter cancellation of any kind is required therefore
as follows: [0370] a) no clutter covariance matrix [0371] b) no
training data [0372] c) no special clutter knowledge required
[0373] 2--No channel matching required
[0374] 3--Returns and clutter do not compete with each other in
there detection and therefore clutter and returns are thresholded
separately and returns are ideally are competing with white noise
only and make for an excellent return ratio to noise.
[0375] 4--Disadvantage many channels-radar receiver front end and
a/d converter for each channel
[0376] 5--Full transmit and receive antenna employed with there
full antenna gains [0377] a) smaller antenna sidelobes [0378] b)
full antenna gain [0379] c) narrow clutter band width
[0380] 6--May be applied to two pulses and two pulses or three
pulses. Each dual pulse processed as two pulse system and should
have same results and correlated.
[0381] 7--Correlation factors as stated in previous paragraph.
[0382] 8--The significance of the ability to process many returns
in same RAB and determining there amplitude and phases and radial
velocity gives the ability to separate clutter and either returns
such as bona fide targets, moving clutter, multi path returns, etc.
Knowledge aided information would aid in categorizing these
returns.
VII--A Dual Pulse at a Time Many Channel System-Second Pulse
Channel Delay-Delta C-DPCA Like Operation
[0383] As in the two channel-many pulse system the two pulse many
channel system described previously as the relation between them as
a duality this is also true in this case and will be illustrated
here for the two return case only. The dual pulse many channel
system is a duality with the dual channel many pulse system.
[0384] Same comments as at end of two return case.
[0385] We will now analyze the various DPCA type delay in the
.DELTA.C methodologies, where only two pulses will be employed. The
second pulse will have a number of DPCA type delays .DELTA.C and
starting at zero ("0") and going up to two (2). It does not have to
start at zero; it may start at any convenient delay and continue to
as many as required. Only two returns will be considered in this
analysis.
Mathematic Development (Two Returns) V.sub.00=M.sub.0+M.sub.1 PULSE
1-- (1) V.sub.01=M.sub.0X.sub.01+M.sub.1X.sub.11 PULSE 2-.DELTA.C
DELAY 0 (2)
V.sub.02=M.sub.0X.sub.02e.sup.j.PHI..sup.A0+M.sub.1X.sub.12e.sup.j.P-
HI..sup.A1 PULSE 2-.DELTA.C DELAY 1 (3)
V.sub.03=M.sub.0X.sub.03e.sup.j2.PHI..sup.A0+M.sub.1X.sub.13e.sup.j2.PHI.-
.sup.A1 PULSE 2-.DELTA.C DELAY 2 (4)
V.sub.04=M.sub.0X.sub.04e.sup.j3.PHI..sup.A0+M.sub.1X.sub.14e.sup.j3.PHI.-
.sup.A1 PULSE 2-.DELTA.C DELAY 3 (5)
[0386] The following is the further definition of Xs in light of
the different DPCA delays. X.sub.01=e.sup.jD.PHI..sup.A0/W.sub.M0
at
D=0:A.sub.0=1/W.sub.M0=1/A.sub.M0e.sup.-j(.PSI..sup.M0.sup.+K.sup.D0.sup.-
X.sup.0.sup.) X.sub.01=A.sub.0
X.sub.02=A.sub.0e.sup.j(.PHI..sup.A0.sup.+.DELTA.K.sup.D0.sup.X.sup.0.sup-
.)=A.sub.0e.sup.j.gamma..sup.0
X.sub.03=A.sub.0e.sup.j2.gamma..sup.0
X.sub.04=A.sub.0e.sup.j3.gamma..sup.0 Also in similar manner
X.sub.11=e.sup.jD.PHI..sup.A1/W.sub.M1 at
D=0:A.sub.1=1/W.sub.M1=1/A.sub.M1e.sup.-j(.PSI..sup.M1.sup.+K.sup.DO.sup.-
X.sup.1.sup.) X.sub.11=A.sub.1
X.sub.12=A.sub.1e.sup.j(.PHI..sup.A1.sup.+.DELTA.K.sup.DO.sup.X.sup.1.sup-
.)=A.sub.1e.sup.j.gamma..sup.1
X.sub.13=A.sub.1e.sup.j2.gamma..sup.1
X.sub.14=A.sub.1e.sup.j3.gamma..sup.1 We will now rewrite the five
equations above with it incorporated. V.sub.00=M.sub.0+M.sub.1
PULSE 1-TIME 1 (1') V.sub.01=M.sub.0A.sub.0+M.sub.1A.sub.1 PULSE
2-.DELTA.C-DPCA DELAY 0 (2')
V.sub.02=M.sub.0A.sub.0e.sup.j.gamma..sup.0+M.sub.1A.sub.1e.sup.j.gamma..-
sup.1 PULSE 2-.DELTA.C-DPCA DELAY 1 (3')
V.sub.03=M.sub.0A.sub.0e.sup.j2.gamma..sup.0+M.sub.1A.sub.1e.sup.j2.gamma-
..sup.1 PULSE 2-.DELTA.C-DPCA DELAY 2 (4')
V.sub.04=M.sub.0A.sub.0e.sup.j3.gamma..sup.0+M.sub.1A.sub.1e.sup.j3.gamma-
..sup.1 PULSE 2-.DELTA.C-DPCA DELAY 3 (5') Employing equations (2')
and (3') and the variables MoAo and M1A1 and solving for
.gamma..sub.0 and .gamma..sub.1 we have the following:
M.sub.0A.sub.0=(V.sub.01e.sup.j.gamma..sup.1-V.sub.02)/(e.sup.j.gamma..su-
p.1-e.sup.j.gamma..sup.0) (2'')
M.sub.1A.sub.1=(V.sub.02-V.sub.01e.sup.j.gamma..sup.0)/(e.sup.j.theta..su-
p.1-e.sup.j.gamma..sup.0) (3'') Employing equations (3') and (4')
and the variables MoAo e.sup.j.gamma..sup.0 and M1A1
e.sup.j.gamma..sup.1 and solving for .gamma..sub.0 and
.gamma..sub.1 we have the following:
M.sub.0A.sub.0e.sup.j.gamma..sup.0=(V.sub.02e.sup.j.gamma..sup.1-V.sub.03-
)/(e.sup.j.gamma..sup.1-e.sup.j.gamma..sup.0) (2''')
M.sub.1A.sub.1e.sup.j.gamma..sup.1=(V.sub.03-V.sub.02e.sup.j.gamma..sup.0-
)/(e.sup.j.gamma..sup.1-e.sup.j.gamma..sup.0) (3''') Next take
equation (2''')/(2'') and equation (3''')/(3'') we have the
following:
e.sup.j.gamma..sup.0=(V.sub.02e.sup.j.gamma..sup.1-V.sub.03)/(V.sub.01e.s-
up.j.gamma..sup.1-V.sub.02) (6')
e.sup.j.gamma..sup.1=(V.sub.03-V.sub.02e.sup.j.gamma..sup.0)/(V.sub.02-V.-
sub.01e.sup.j.gamma..sup.0) (7') Equation (6') or equation (7') may
be solved for .gamma..sub.0 and .gamma..sub.1 and consequently
.PHI..sub.A0 and .PHI..sub.A1 and at this point the velocity may be
determined with maximum error of a half of a azimuth bin since the
returns peak within a halve of a doppler bin where detected.
processing like the first frequency. Taking equation (2'') and
solving for MoAo since everything is known on right side of
equation To attain much greater accuracy the returns position of
there peaks will be endeavored to be found. This will be performed
by inserting to zero fill and processing to attain a frequency
close to first frequency and taking equivalent equation in second
frequency and solving for M'oA'o since everything is known on right
side of this equation. The ratio of M'o/Mo equals XF0 which is the
response to return in the RDB and gives an estimate where the peak
of the return is in that RAB.
[0387] The ratio of A'o/Ao equals the difference between where
frequencies are processed in that RDB. The actual distance is
known.
A.sub.0=1/W.sub.M0=1/A.sub.M0e.sup.-j(.PSI..sup.M0.sup.+K.sup.D0.sup.X.su-
p.0.sup.)
A'.sub.0=1/W.sub.M0=1/A.sub.M0e.sup.-j(.PSI..sup.M0.sup.+K.sup.-
D0.sup.(X.sup.0.sup.+.DELTA.X.sup.0.sup.)) Solving equation
(2'')=K.sub.0e.sup.j.beta..sup.0 Solving equivalent equation
(2''')=K'.sub.0e.sup.j.beta.'.sup.0 M'.sub.0/M.sub.0=X.sub.F0
A'.sub.0M'.sub.0/A.sub.0M.sub.0=X.sub.F0e.sup.j.DELTA.K.sup.CM.sup..DELTA-
..sup.xo Therefore |X.sub.F0|=|K'.sub.0/K.sub.0|and angle of
(M'.sub.0/M.sub.0)=.beta.'.sub.0/.beta..sub.0-.DELTA.K.sub.D0.DELTA..sub.-
X0
[0388] We this ratio the peak of first return is estimated
(.PHI..sub.D0) and from the equation .PHI..sub.D0 and .PHI..sub.0
where the azimuth of the return is calculated from the known or
estimated .PHI..sub.D0 and .PHI..sub.0. If a better estimate of the
peak of first return more samples of frequencies may be taken. The
best accuracy obtained by getting the frequency sample at the peak
of the return.
[0389] The analogous procedure would be undertaken for the second
return.
[0390] This technique is the .DELTA.C DPCA various delays plus and
if additional accuracy is required or desired the addition samples
at frequencies close to frequency processed is processed. It does
not require any channel balancing and DPCA special processing and
is very accurate.
[0391] Similarly another technique as in two channel technique to
determine azimuths is to obtain radial velocities in the two pulse
technique. Also similarly the channel balancing terms may be
obtained.
[0392] B--Similar comments apply as in the two channels at a time
since they are a duality of each other. The exchanging of .PHI.S
With .PHI..sub.As and solution thereof. The three return system is
analogous of the other three return systems related to their
related two return systems.
C--Advantages and Disadvantages of System
[0393] The aforementioned system has many advantages as the other
systems but the outstanding are as the following
[0394] 1--Channel matching is a problem but utilizing many channels
reduces the effect.
[0395] 2--Dwell time is reduced drastically due to the minimum of
only two pulses required limited by the processor to perform the
necessary functions.
[0396] 3--Returns and clutter do not compete with each other in the
resulting processing and therefore clutter and returns are
thresholded separately and returns are ideally are competing with
white noise only and make for an excellent return ratio to
noise.
[0397] 4--Very simple system-less storage-less processing-more
hardware due to RF front end and A/D converter required for every
channel.
[0398] 5--May be applied to two or more pulses to give more than
one solution and they should be very close to each other. Each
processed as two pulse system and should have same results and
correlated.
[0399] 6--The significance of the ability to process many returns
in same RDB and determining there amplitude and phases and radial
velocity gives the ability to separate clutter and other returns
such as bona fide movers, moving clutter, multi path returns, etc.
Data base of returns and the mathematical basis and knowledge aided
information would aid in categorizing these returns.
[0400] 7--If more than two pulses are implemented than the results
of each pulse should be the same or close to the same
V.sub.00--OUTPUT PULSE 1--.DELTA.C=0
V.sub.01--OUTPUT CHANNEL 2--.DELTA.C DPCA DELAY 0
V.sub.02--OUTPUT CHANNEL 2--.DELTA.C DPCA DELAY 1
V.sub.03--OUTPUT CHANNEL 2--.DELTA.C DPCA DELAY 2
V.sub.04--OUTPUT CHANNEL 2--.DELTA.C DPCA DELAY 3
X.sub.01--return equalizer between PULSE 1 and 2 for return
0-.DELTA.C-DPCA delay 0
X.sub.02--return equalizer between PULSE 1 and 2 for return
0-.DELTA.C-DPCA delay 1
X.sub.02--return equalizer between PULSE 1 and 2 for return
O-.DELTA.C-DPCA delay 2
X.sub.11--return equalizer between PULSE 1 and 2 for return
1-.DELTA.C-DPCA delay 0
X.sub.12--return equalizer between PULSE 1 and 2 for return
1-.DELTA.C-DPCA delay 1
X.sub.12--return equalizer between PULSE 1 and 2 for return
1-.DELTA.C-DPCA delay 2
W.sub.MO--RETURN 0 EQUALIZER BETWEEN PULSE 1 AND 2
W.sub.M1--RETURN 1 EQUALIZER BETWEEN PULSE 1 AND 2
A.sub.MO--AMPLITUDE 0 EQUALIZER BETWEEN PULSE 1 AND 2
A.sub.M1--AMPLITUDE I EQUALIZER BETWEEN PULSE 1 AND 2
.PSI..sub.MO--PHASE 0 EQUALIZER BETWEEN PULSE 1 AND 2
.PSI..sub.M1--PHASE 1 EQUALIZER BETWEEN PULSE 1 AND 2
W.sub.MO--RETURN 0 EQUALIZER BETWEEN PULSE 1 AND 2
W.sub.M1--RETURN 1 EQUALIZER BETWEEN PULSE 1 AND 2
A.sub.MO--AMPLITUDE 0 EQUALIZER BETWEEN PULSE 1 AND 2
A.sub.M1--AMPLITUDE 1 EQUALIZER BETWEEN PULSE 1 AND 2
.PSI..sub.MO--PHASE 0 EQUALIZER BETWEEN PULSE 1 AND 2
.PSI..sub.M1--PHASE 1 EQUALIZER BETWEEN PULSE 1 AND 2
KDO--.DELTA.C DPCA constant that makes returns equal
Ao--constant term of return o
A1--constant term of return 1
[0401] As can be observed there is a direct duality between two
channels many pulse system and the two pulse many channel system.
In the two channel many pulse system you are solving for the radial
velocity of the returns (.phi..sub.s) and calculate the azimuths
(.phi..sub.A s) and .theta..sub.s are the sum of .phi.s and DPCA
terms. All other terms are the same.
[0402] In the two pulse many channel system you are solving for the
azimuth (.phi..sub.A s) of the returns (.phi..sub.s) and calculated
the velocity and. .gamma..sub.s are the sum of .phi..sub.A s and
dpca terms.
[0403] Therefore the equations, etc may represent both systems with
this noted such as in the claims.
[0404] VI--B Three returns are very analogous to other three return
techniques
[0405] VI--C Combined techniques of section III and IV
D--Combining techniques of section III--Two pulses "N" channel
system .PHI..sub.D technique and section IIII--.DELTA.C
technique--Two pulse "N" channel system
[0406] The two techniques employ the same data and may be processed
in any manner to facilitate a solution. The following is a list of
common solutions and attributes. [0407] 1. Same solutions for all
parameters such as the following: [0408] a) .PHI..sub.D s,
.PHI..sub.A s and .PHI..sub.s and M.sub.S and X.sub.F s, X.sub.R s
and X.sub.H s [0409] b) .PHI..sub.D s have many same solutions in
the .PHI..sub.D technique [0410] c) solutions for position and
velocity of respective returns [0411] 2. (DD technique is more
effective but requires more storage and processing but requires one
less delay in data [0412] 3. Accuracy and robustness of solutions
are enhanced [0413] 4. Appearance of a very practical system
VIII--A--ONE CHANNEL SYSTEM--DELT R technique where the same as two
channel system but only employing one channel and when .PHI..sub.D
processing significant time later with the delta R technique the
change in amplitude and phase shift of the return will determine
the velocity of the return and consequently the azimuth of the
return. This system requires a relatively high resolution in range
to determine low velocity of returns.
[0414] B--One Channel or One Pulse Methodology for Detecting Ships
Over Water where the Following:
[0415] 1--Ship return much larger than water returns the velocity
and azimuth of the ship is determined if there is only one return
and range, azimuth and velocity is easily determined.
[0416] 2--Black hole and/or shadow technique to determine range,
azimuth and velocity.
[0417] 3. By delta R technique of section VIII A
[0418] 4. By one channel or one pulse techniques in the
disclosure
[0419] 5. Combination of any of the techniques that is
compatible
IX--ACCOMPANYING TECHNIQUES are illustrated for the many pulse
techniques in FIG. 6 which also applies to many channel techniques
and also illustrated in FIG. 11 employing groups of data and
interlaced data.
[0420] A1--.DELTA.I Technique with dual channel system. This
technique breaks up the received set of data into two or more
interleaved data sets and process each data set as initially
independent and the results should agree. The difference being that
there is a loss of coherent gain proportional to the number of
interlaced sets of data but that may be offset by non-coherently
integrated between sets of interlaced data. Also the bandwidth of
the filters is increased proportional to the number of interlaced
sets of data which may be an advantage or disadvantage according to
what is being processed. The processing of the interlaced data sets
as well as the full data set may get the advantage of each. In the
interlaced data there is a known relationship between each set of
data.
Comment:
[0421] 1. Interleave processing allows wider doppler bin
proportional to the number of interleaved sets of data, if that to
be effective.
[0422] 2. Same results for all interleaved data and correlate
results
[0423] 3. Amplitude and phase relationship known between
interleaved data sets.
[0424] 4. Affects on returns of larger doppler bins [0425] a)
Movers have a bandwidth of 16 hz, accordingly this will determine
how many detections per doppler bin. [0426] b) Clutter has a
bandwidth of the doppler bin. [0427] c) Affect on other returns
such as jamming, noise antenna sidelobes, other. [0428] e)
Other.
[0429] 5. It applies to all systems.
[0430] 6. The resulting solutions are increased proportional to the
number of interleaved sets of data.
[0431] 7. The doppler filter width and the ambiguous range is
increased proportional to the number of interleaved data sets. The
ambiguous velocity decreases proportional to the number of
interleaved data sets
[0432] A2--.DELTA.I Technique with .DELTA.C for single pulse system
or with dual pulse system. This technique breaks up the received
set of data into two or more interleaved data sets and process each
data set as initially independent with the .DELTA.C and/or .DELTA.C
delay technique and the results should agree. The difference being
that there is a loss of coherent gain proportional to the number of
interlaced sets of data but that may be offset by non-coherently
integrated between sets of interlaced data. Also the bandwidth of
the filters is increased proportional to the number of interlaced
sets of data which may be an advantage or disadvantage according to
what is being processed. The processing of the interlaced data sets
as well as the full data set may obtain the advantage of each. In
the interlaced data there is a known relationship between each set
of data.
Comment:
[0433] 1. Interleave processing allows wider azimuth bin
proportional to the number of interleaved sets of data, if that to
be effective.
[0434] 2. Same results for all interleaved data and correlate
results
[0435] 3. Amplitude and phase relationship between interleaved data
sets.
[0436] 4. Affects on returns of larger azimuth bins [0437] a)
Movers have a bandwidth of approximately 16 hz, accordingly this
will determine how many detections per azimuth bin. [0438] b)
Clutter has a bandwidth of the azimuth bin. [0439] c) Affect on
other returns such as jamming, noise antenna sidelobes, other.
[0440] e) Other.
[0441] 5. It Applies to Pulse Systems
[0442] 6. The resulting solutions are increased proportional to the
number of interleaved sets of data.
[0443] 7. The azimuth filter width and the ambiguous azimuth is
increased proportional to the number of interleaved data sets. The
ambiguous azimuth decreases proportional to the number of
interleaved data sets
B1. .DELTA.I+.DELTA.A Technique for dual channel system
[0444] This is similar to the .DELTA.I technique but with each
interlaced data set the receive antenna is moved approximately by
the antenna beam width divided by the number of interlaced data
sets. This technique breaks up the received set of data into two or
more interleaved data sets and process each data set as initially
independent and the results should agree. The difference being that
there is a loss of coherent gain proportional to the number of
interlaced sets of data but that may be offset by non-coherently
integrated between sets of interlaced data. Also the bandwidth of
the filters is increased proportional to the number of interlaced
sets of data which may be an advantage or disadvantage according to
what is being processed. In the interlaced data there is a known
relationship between each set of data. Due to the receive arrays
movement between each set of interlaced data set the ratio of the
amplitude of the returns between data sets is determined by receive
antenna arrays which if known will tell very accurately the returns
azimuth and must correlate with results of processing each data set
independently.
[0445] To attain curve of the ratio between apertures-vs-azimuth of
return process significant clutter only data and obtain said curve
and employ this in the above technique.
Comment: SAME AS I EXCEPT FOR THE FOLLOWING
[0446] 1. Amplitude ratio between interleaved data with
simultaneously aperture change determines the azimuth of the
return
[0447] B2. .DELTA.I+.DELTA.A Technique with .DELTA.C for dual pulse
systems. This is similar to the .DELTA.I technique but with each
interlaced data set the receive antenna is moved approximately by
the antenna b beam width divided by the number of interlaced data
sets. This technique breaks up the received set of data into two or
more interleaved data sets and process each data set as initially
independent with the .PHI..sub.D and/or .DELTA.C delay technique
and the results should agree. The difference being that there is a
loss of coherent gain proportional to the number of interlaced sets
of data but that may be offset by non-coherently integrated between
sets of interlaced data. Also the bandwidth of the filters is
increased proportional to the number of interlaced sets of data
which may be an advantage or disadvantage according to what is
being processed. In the interlaced data there is a known
relationship between each set of data. Due to the receive arrays
movement between each set of interlaced data set the ratio of the
amplitude of the returns between data sets is determined by receive
antenna arrays which if known will tell very accurately the returns
azimuth and must correlate with results of processing each data set
independently.
[0448] To attain curve of the ratio between apertures-vs-azimuth of
return process significant clutter only data and obtain said curve
and employ this in the above technique.
[0449] Comment: SAME AS I EXCEPT FOR THE FOLLOWING
[0450] 1. Amplitude ratio between interleaved data determines the
azimuth of the return
[0451] 2. For Two Pulse System
[0452] C1--.DELTA.G technique with dual channel system .PHI..sub.D
and/or .DELTA.T technique. The technique involves taking the "M"
data points and processing them in groups (two, three or more
groups). Each group is processed independently and solutions should
be very close to the same for each group and also for processing
the full set of data. To maintain gain, the full set of data is
processed. As the number of data points increases the gain
increases and the doppler bin narrows proportional to the size of
the data group. The amplitude and phase shift between groups is
dependent on the number of data points in a group. Non-coherently
processing the groups of data will gain most of the coherent gain
of the full set of data. Groups of data applications are
implemented mainly on high speed targets which may travel out of
the range gate due to their velocity.
Comment:
[0453] 1. Wider doppler bin with decreasing number of data points
in a group.
[0454] 2. Same results for all groups of data.
[0455] 3. Amplitude and phase relationship determinable between
groups.
[0456] 4. Same as 4 for delta I.
[0457] 5. The ambiguous range and velocity is the same but doppler
bin widens proportional to size of group.
[0458] C2--.DELTA.G technique with .DELTA.C for dual pulse system
.PHI..sub.D and/or .DELTA.C technique. The technique involves
taking the "N" data points and processing them in groups (two,
three or more groups). Each group is processed independently and
solutions should be very close to the same for each group and also
for processing the full set of data. To maintain gain, the full set
of data is processed. As the number of data increases the gain
increases and the azimuth bin narrows proportional to the size of
the data group. The amplitude and phase shift between groups is
dependent on the number of data in a group.
Comment:
[0459] 1. Wider azimuth bin with decreasing number of data points
in a group.
[0460] 2. Same results for all groups of data.
[0461] 3. Amplitude and phase relationship determinable between
groups.
[0462] 4. Same as 4 for delta I.
[0463] 5. The ambiguous range and velocity is the same and azimuth
bin widens proportional to size of group.
[0464] D1--.DELTA.G+.DELTA.A technique for dual channel system
.PHI..sub.D and/or .DELTA.T technique. Same as K1 but with each
group of data the antenna is moved a portion of the bandwidth of
the antenna divided by the number of groups. Each group is
initially processed independently and result close to same for each
group. The amplitude ratio between groups of data is the ratio of
the antenna curve at each group position. The antenna curves
ratio-vs-azimuth is measured with significant large clutter only
data as stated for all change in aperture data. This is performed
for all groups.
Comments:
[0465] 1. same as C1 except for amplitude ratio-vs-azimuth
[0466] D2--.DELTA.G+.DELTA.A technique dual pulse system
.PHI..sub.D and/or .DELTA.C technique. Same as K2 but with each
group of data the antenna is moved a portion of the bandwidth of
the antenna divided by the number of groups. Each group is
initially processed independently and result close to same for each
group. The amplitude ratio between groups of data is the ratio of
the antenna curve at each group position. The antenna curves
ratio-vs-azimuth is measured with significant large clutter only
data. The antenna curves ratio-vs-azimuth is measured with
significant large clutter only data as stated for all change in
aperture data. This is performed for all groups.
Comments:
[0467] 1. same as C2 except for amplitude ratio-vs-azimuth
[0468] D2--.DELTA.G+.DELTA.A technique dual pulse system
.PHI..sub.D and/or .DELTA.C Two or more groups of data within each
group of data having two or more interleaved set of data. Each
interleaved set of data within a group of data is processed
independently and the solution should be close to the same
[0469] Comments:
[0470] 1. Interleaved data within each group comments are same
delta I plus delta A comments
[0471] 2 Group data has same comments as delta G comments
[0472] 3. Amplitude and phase relationship between interleaved set
of data are determinable
[0473] 4. Amplitude and phase relationship between groups of data
are determinable
E1--.DELTA.I+.DELTA.G--
[0474] Two or more groups of data with each group of data having
two or more interleaved sets of data. Each interleaved set of data
within a group of data is processed independently and the solution
should be close to the same
[0475] Comments:
[0476] 1. Interleaved data within each group comments are same
delta I plus delta A comments
[0477] 2 Group data has same comments as delta G comments
[0478] 3. Amplitude and phase relationship between interleaved set
of data are determinable
[0479] 4. Amplitude and phase relationship between groups of data
are determinable
E2--.DELTA.I+.DELTA.G--
[0480] Two or more groups of data with each group of data having
two or more interleaved sets of data. Each interleaved set of data
within a group of data is processed independently and the solution
should be close to the same
[0481] Comments:
[0482] 1. Interleaved data within each group comments are same
delta I plus delta A comments
[0483] 2. Group data has same comments as delta G comments
[0484] 3. Amplitude and phase relationship between interleaved set
of data are determinable
[0485] 4. Amplitude and phase relationship between groups of data
are determinable
F1--.DELTA.I+.DELTA.A+.DELTA.G Technique for dual channel system
.PHI..sub.D and/or .DELTA.T
[0486] Same as .DELTA.I+.DELTA.A with the additional factor
assuming the same number of interleaved sets of data per group and
the aperture change per interleaved sets of data, then the ratio of
the output between interleaved sets of data is the same. Each
interleaved set of data within a group of data is processed
independently and the solution should be close to the same.
[0487] F2--.DELTA.I+.DELTA.A+.DELTA.G Technique dual pulse system
.PHI..sub.D and/or .DELTA.C. Same as .DELTA.I+.DELTA.A with the
additional factor assuming the same number of interleaved sets of
data per group and the aperture change per interleaved sets of
data, then the ratio of the output between interleaved sets of data
is the same. Each interleaved set of data within a group of data is
processed independently and the solution should be close to the
same.
G--Comments on all Developed Techniques
[0488] 1--If employing the basic system as two receive channels
where these two receive channels (or may be summed as one receive
channel) there is the ability to process the sum channels and the
two receive channels as independent systems. The sum system may be
processed as one channel system and the two individual channel or
pulse systems as separate system.
H--.Special Application to the Overocean Implementation
Detection of ships and location of its black hole and shadow to
determine the ships range, velocity and azimuth and ship
classification
[0489] H1--Overall detection of the ship at a particular azimuth
(proportion to phase shift of where in the radar antenna beam the
ship is detected), but when the ship has a relative radial velocity
to the radar the phase shift of the ship adds to that due to its
azimuth position relative to the boresight of the main beam of the
radar, (which has motion compensation for the boresight of the
antenna which is zero velocity) such as the following:
.PHI..sub.D1=.PHI..sub.A1+.PHI..sub.1 where .PHI..sub.D1 is the
phase shift where the ship is detected at its peak .PHI..sub.A1 is
the phase shift due to the azimuth position. .PHI..sub.1 is the
phase shift due to its radial velocity. The ship is detected at
.PHI..sub.D1, its phase shift due to its radial velocity,
.PHI..sub.1, plus that due to its azimuth position, .PHI..sub.A1,
in the main beam of the antenna. In FIG. 1 that is 1a, b, c, d and
5 is the place where the ship is detected, but the actual position
of the ship is 4. The shading of the ship shows this position. The
radar illuminates this position, but due to the ships radial
velocity it appears at 5. It leaves a lack of detection or black
hole where it was at 4. The area 3 is also a lack of detection and
this is the lined area, this is the ship blocking radar waves from
illuminating the sea behind the ship. These phenomena will assist
in the detection of the ship and the determination of its range,
azimuth and radial velocity and horizontal tangential and vertical
velocity and other ship parameters. Thus, we have a ship shaded
area where the ship is, and a lined area where the shadow of the
ship that tells us the azimuth (.PHI..sub.A1) position, when we
detect this lack of signal compared to the sea clutter next to it.
The lack of signal should be about comparable to the thermal noise
level of the radar. While the sea clutter will have a level in
general considerably higher than the thermal noise. This indicates
the azimuth position and may be correlated with the previous
determination where the azimuth, velocity and range are attained.
The area where there is a lack of detection at that azimuth is the
outline of the ship and its shadow. The area where there is a
detection of the ship is the outline of the ship without the
shadow.
[0490] In theory, if we have very fine range and doppler
resolution, this area is defined very well, but we live in the real
world and there is a limit to the resolution attained in range and
azimuth and will limit our accuracy in attaining the parameters of
the ship. FIG. 3 illustrates how the ships height profile would be
attained. D being the height of ship and E is he airborne radar and
A the height of the radar, B is the slant range of the radar to the
ship and F is the angle of the ships shadow with the sea. The
solution by simple geometry for height of the ship D.
D.apprxeq.C*sin F where sin F.apprxeq.A/(B+C) By this method
knowing "C" slant range of shadow (where lack of detection
ends)(D+C)-D=V'.sub.IN=M.sub.1e.sup.jN.PHI..sup.1 C. This method
can be performed across the width of the ship to give its outline.
These measurements are all a function of the attainable range and
doppler resolution.
[0491] 2. The aforementioned analysis may be performed with a one
antenna transmit and receive system as developed in the disclosure.
If we have only one or the ship return much greater than clutter
(ocean) return we have the following:
V.sub.01/V.sub.00=e.sup.j.PHI..sup.1
[0492] but with the two channel DPCA system with the .DELTA.T
technique we have the following:
V.sub.01/V.sub.00=e.sup.j.PHI..sup.1/W.sub.M1 where
W.sub.M1=e.sup.j(.PSI..sup.M1.sup.-K.sup.D1.sup.X.sup.1.sup.)
[0493] and this determines .PHI..sub.1 is the phase shift due to
its radial velocity.
[0494] The lack of detection that is lower than the ocean return
defines the azimuth position of the ship. It allows the measurement
of ship parameters as explained previously illustrated in FIG.
5.
[0495] 3. The aforementioned analysis may be applied for a one
transmit or a two or more receive antenna system. Each receive
antenna may be treated as independent receive system and treated
and analyzed as that so we have two or more independent looks at
the ship and the results correlated.
[0496] 4. The aforementioned analysis may be applied for a one
transmit and two receive antenna system with the two or more
receive antenna utilizing DPCA techniques to find the range, radial
velocity and azimuth independent of the shadow and black hole
technique and then correlated with other techniques. Illustrated in
FIG. 5.
[0497] All techniques or best technique for application may be
performed and correlated to obtain the best results.
[0498] 5. Applying to all systems, if a signal of the ship is
sufficient to obtain desired information with the required
accuracy:
[0499] a) Estimate of the parameters of the ship.
[0500] b) Estimate of the radial velocity, azimuth and range.
[0501] 6. Applying to all systems, if we obtain multiple looks at
the ship we will determine the unambiguous radial velocity and
tangential velocity and greater accuracy in determining the ship
parameters, range, velocity and azimuth.
[0502] Multilooks is defined as a look with data point 1 to N and
delay the data a portion of the N point such as N/4 and adding N/4
points at the end and performing the same operations. This will
result in the increased capability as stated.
[0503] When the data is delayed and reprocessed as the first set of
data the ships radial motion will be measured by the number of
range bins or part of a bin traveled in this time
(.DELTA.R/.DELTA.T) gives the true velocity of the ship and will
resolve the unambiguous velocity, if any, of the ship without
resorting to another PRF. The tangential velocity will also be
determined which could not be determined before as a measure of
(.DELTA.D/.DELTA.T) doppler bins moved in the time difference.
Hence, the total velocity of the ship is determined, not only the
radial velocity, the ratio of the radial velocity to the tangential
velocity which will give the angle the ship is pointing.
[0504] Multilooks of the ships will result in better parameter
estimation of the ship and estimation of the range, velocity and
azimuth and better estimate of the wake determination and bow wave
parameters which will aide in determining all the parameters of the
ship.
[0505] Isodop correction for the velocity of the ship, focusing the
array may be performed to enhance the accuracy of the system.
[0506] Motion compensation relative to the boresight of the antenna
is assumed.
[0507] 7. Increased range and doppler resolution-VS-decreased
spacing of doppler and range bins with same resolution applied to
all systems.
[0508] a) Increased range resolution produces smaller range bins
but with increased band width of the radar and increased storage
for the increased number of cells per given range swath. The
processing is increased due to range bin number increasing. The
number of range bins increased is independent of the dwell time
required for processing.
[0509] Increasing the doppler resolution, the number of data points
have to be increased this results in increased time on target
(ship) called dwell time and more storage and processing is
required to handle the increased number of data points. This is a
great disadvantage since it restricts the number of tasks to
perform in a limited amount of time.
[0510] There is an increase the band width of the radar and in
storage, processing and dwell time with an increase resolution of
range and doppler.
[0511] a) A decrease in the range bin spacing is performed by
increasing the number of samples, but with the same band width of
the radar. This results in an increase in the number of samples
(storage) per given range swath and also a proportional increase in
processing required with no increase in resolution of range bins,
but are more closely spaced samples of range.
[0512] A decrease in the doppler bin spacing is performed by adding
zeros to the number of data samples stored. When this is processed
as if the total number of data points includes all the zeros, the
decrease in doppler bin spacing results are proportional to the
number of zeros added. There is no additional storage, additional
zeros does not constitute additional storage. The processing
increased proportional to the additional doppler bins produced.
[0513] There is an increase in the number or range bins processed
and stored, but no increase in storage due of input data required,
but an increase in processing required, but most important no
increase in dwell time required.
[0514] c) The results are with increased resolution in range and
doppler has the disadvantage of increased bandwidth required of the
radar and increased dwell time.
[0515] On the other hand increasing the number of samples per range
bin (oversampling in range), the resolution of range is larger but
the affect of lower spacing will give the affect of increased
resolution of range without the higher bandwidth. The disadvantage
is the larger range bin; this may be ameliorated by the previous
discussion.
[0516] Adding zeros to the number of data points has the affect of
the doppler resolution is the same, but the filters are spaced
closer together. For example, if doubling the number of data points
by adding an equal number of zeros, then the spacing of the doppler
filter is halved. Since there is half the data points, the dwell
time is halved. This is analogous to over sampling in range.
[0517] The affect of closer spacing of the filters gives increased
resolution of azimuth without the increased dwell time. The
disadvantage as in over sampling in range there is a larger doppler
bin, thus may be ameliorated by previous discussion.
[0518] The trade off may be obtain doppler and range resolution as
required to detect the ship, but the over sample in range and add
zeros in doppler for the increased capability in range and
azimuth.
[0519] 8. Add ISAR processing for further classification of the
ship when the .DELTA.T parameters are processed.
[0520] 9. Additional aides in detection and measurement of ship
parameters, especially taken at different times within the same
dwell time.
[0521] a) Measurement of sea clutter all around the point where the
ship is detected.
[0522] b) Indicates the sea state conditions.
[0523] Determines the parameters of the ship, as well as radial and
tangential velocity, especially when motion compensation is
performed, as well as the array is focused and there are included
isodop corrections.
[0524] c) Around the azimuth determination of ship [0525] 1)
Another measure of the azimuth determination. [0526] 2) Another
measure of the parameters of the ship. [0527] 3) Another measure of
the radial velocity and tangential velocity. [0528] 4) Ship
direction. [0529] 5) Bow wave detection, its velocity and heading
of ship and radial and tangential velocity of the ship will give
another indication of ship parameters and sea clutter around ship.
[0530] 6) Wake determination will give another indication similar
to 5. [0531] 7) Measure sea clutter around the indication of
azimuth of ship will give additional correlation of all parameters
of the ship.
[0532] d) Sea state in general [0533] 1) Will give sea state
conditions. [0534] 2) Locations and detections of high and low
detections. (shadows of the sea state). [0535] 3) May have more
than one clutter detection per doppler bin.
[0536] 10. Problem Areas [0537] 1) High clutter sea states are a
big problem area and challenge to perform meaningful operations but
are feasible. [0538] 2) Long dwell time to perform accurate
determinations. This is the reason for decreased spacing of doppler
bins and increased sampling per range bin might ameliorate that
condition. [0539] 3) Long range makes things very difficult. [0540]
4) Performing surveillance and tracking at the same time as
classification of ships.
[0541] 11. Operate without change in time operation for the
surveillance mode.
[0542] 12. Additional techniques are to deal with the case where
sea clutter is significant in value to ship return.
[0543] 13. Two dimensional array may be employed, as well as a one
dimensional array.
[0544] 14. Combined with overland patent pending of Dual Synthetic
Aperture Radar System (DSARS) Ser. No. 10/14,156, by Thomas J.
Cataldo with overseas capability and employing the phase
corrections and phase coefficient if necessary as explained in
DSARS patent.
[0545] 15. The mode of operation depends on many factors such as
range, surveillance, tracking or spot light operation, sea state,
etc.
[0546] 16. Surveillance mode may be combined with spot image mode.
[0547] Wake and bow wave signatures of ships signatures as a
function of their velocity and direction of the ship in help in
classification of ships.
[0548] 17. Surveillance mode could be a one antenna transmit and
receive system.
[0549] 18. High sea state conditions create shadow conditions that
could be employed for better processing.
[0550] 19. Surveillance plus spot image mode may be combined to
reduce dwell time and obtain maximum information per unit time.
[0551] 20. This technique may be extended to space borne
operations
[0552] 21--With the one pulse or one channel technique an
electronic scanned array that may be rotated 360 degrees to cover
all angles.
[0553] 22--With the one pulse technique an electronic scanned array
does not require motion compensation or phase compensation for
boresight of transmitted antenna since only one pulse is
required.
Block Diagram of System
[0554] This is a simplified system indicating the basic data is
received from the radar in digital form and stored and processed in
any or combinations of the techniques described in the disclosure.
The data is spectrally processed and the detection of the ship is
performed together with the detection of the shadow and black hole
to determine the ships radial velocity, azimuth and range, as well
as the measurement of the ship parameters to classify the ship with
as much accuracy as possible.
[0555] The delay data is processed to determine radial velocity
unambiguously and to determine the horizontal and vertical
tangential velocity and the ship parameters more accurately.
I--Special Section on Detection of High Speed Targets
[0556] The detection of high speed planes and missiles is very
important in the presence of clutter. Processing in groups of data
enables the detection and measuring its velocity and azimuth
without the target passing thru range bin then and non-coherently
integrating from range to range bin. Employing groups of data keeps
the target in the range bin long enough to detect its radial
velocity and use delta R to determine its unambiguous velocity. In
this respect the range bin has to be made wide enough to be able to
have the mover a significant time in the range bin. Results may be
correlated between range bins.
[0557] Being detected in the various range bins at different times
to be able to employ the association techniques of tracking the
detections thru the range bins and doppler bins with time. This
will measure radial velocity unambiguously and tangential
velocity.
[0558] The processing by groups enables that high speed movers will
not travel thru the range bin in the time it is in the group. The
integration between groups will give a significant increase in gain
for detection.
[0559] The processing of each group together with association
processing will give the unambiguously radial velocity and the
azimuth of the mover.
J--Special Section on Foliage Penetration to Detect Movers and
Measure there Velocity and Azimuth Accurately
[0560] Foliage penetration radar has to be low in transmission
frequency enough to see thru foliage. The ground and large trees
will give a significant clutter return and wind blowing foliage a
small but significant velocity to clutter and render clutter
cancellation techniques ineffective. The USS system will separate
out all returns and identify the mover and clutter returns.
K--Special Section on Stealthy Targets
[0561] STEALTHY TARGETS PRESENT A SPECIAL CHALLENGE since they have
small radar cross sections and with the common stap systems
especially difficult because they are embedded in clutter and the
common stap systems find it very difficult to differentiate them
from clutter residue. the uss has less difficulty clutter and
target are measured differently and they don't compete with each
other. Consequently very low returns can be detected and there
velocity, azimuth and range determined.
* * * * *