U.S. patent application number 09/815408 was filed with the patent office on 2002-01-31 for enhanced determination of position-dependent signal characteristics of a wireless transmitter.
Invention is credited to Maloney, John E., Pack, Kenneth D..
Application Number | 20020011952 09/815408 |
Document ID | / |
Family ID | 26908605 |
Filed Date | 2002-01-31 |
United States Patent
Application |
20020011952 |
Kind Code |
A1 |
Pack, Kenneth D. ; et
al. |
January 31, 2002 |
Enhanced determination of position-dependent signal characteristics
of a wireless transmitter
Abstract
A method and system for determining with enhanced accuracy a
line of bearing and related signal characteristics of a mobile
wireless transceiver in a cellular-telephone communications system
is presented. Three or more conventionally configured antenna
elements are used to provide a high resolution line of bearing
estimate through disambiguation of positional parameters associated
with inter-element signal characteristics derived from signal
products. The high resolution line of bearing estimate can then be
used to determine the location of the transmitter.
Inventors: |
Pack, Kenneth D.; (Fairfax,
VA) ; Maloney, John E.; (Springfield, VA) |
Correspondence
Address: |
Michael D. Stein
WOODCOCK WASHBURN KURTZ
MACKIEWICZ & NORRIS LLP
One Liberty Place - 46th Floor
Philadelphia
PA
19103
US
|
Family ID: |
26908605 |
Appl. No.: |
09/815408 |
Filed: |
March 22, 2001 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60214013 |
Jun 26, 2000 |
|
|
|
Current U.S.
Class: |
342/442 ;
342/450 |
Current CPC
Class: |
G01S 3/48 20130101 |
Class at
Publication: |
342/442 ;
342/450 |
International
Class: |
G01S 005/04; G01S
003/02 |
Claims
What is claimed is:
1. A method for measuring position-dependent characteristics of
mobile radio signals from a mobile transmitter, the method
comprising the steps of receiving the transmitted signals at an
antenna configuration having multiple phase-synchronized receiving
elements; performing disambiguation processing for the extraction
of position dependent characteristics of the signals; and
evaluating the characteristic parameters indicative of the
transmitter's position.
2. The method of claim 1, wherein said antenna configuration has
three or more elements.
3. The method of claim 2, wherein said antenna elements comprise at
least one pair of elements whose inter-element separation is a
large quantity of half wavelengths of the signals.
4. The method of claim 2, wherein said antenna elements comprise at
least two pairs of elements whose inter-element separations differ
by a small quantity of half wavelengths of the signals.
5. The method of claim 1, wherein said disambiguation processing
includes the extraction of signal characteristics having reduced
ambiguity for resolving the selection of the accurate positional
interpretation of extracted ambiguous characteristics.
6. The method of claim 1, wherein said disambiguation processing
includes formation of differences of inter-element signal phase
differences.
7. The method of claim 1, wherein said disambiguation processing
includes formation of higher-order signal products.
8. The method of claim 1, wherein said evaluated characteristic
parameters indicative of the transmitter's position include angle
of arrival.
9. The method of claim 1, wherein said evaluated characteristic
parameters directly quantify the transmitter's position.
10. An apparatus for measuring position-dependent characteristics
of mobile radio communications signals from a mobile transmitter,
comprising: an antenna configuration having multiple elements for
receiving the transmitted signals; phase-synchronized elemental
signal receivers for extracting the signals to be processed; a
signal processing unit that performs disambiguation processing for
the extraction of position-dependent characteristics of the
signals; and a processing unit that evaluates the characteristic
parameters indicative of the transmitter's position.
11. An apparatus as in claim 10, wherein said antenna configuration
has three or more elements.
12. An apparatus as in claim 11, wherein said antenna elements
comprise at least one pair of elements whose inter-element
separation is a large quantity of half wavelengths of the
signals.
13. An apparatus as in claim 11, wherein said antenna elements
comprise at least two pairs of elements whose inter-element
separations differ by a small quantity of half wavelengths of the
signals.
14. An apparatus as in claim 10, wherein said disambiguation
processing includes the extraction of signal characteristics having
reduced ambiguity for resolving the selection of the accurate
positional interpretation of extracted ambiguous
characteristics.
15. An apparatus as in claim 10, wherein said disambiguation
processing includes formation of differences of inter-element
signal phase differences.
16. An apparatus as in claim 10, wherein said disambiguation
processing includes formation of higher-order signal products.
17. An apparatus as in claim 10, wherein said evaluated
characteristic parameters indicative of the transmitter's position
include angle of arrival.
18. An apparatus as in claim 10, wherein said evaluated
characteristic parameters directly quantify the transmitter's
position.
Description
BACKGROUND OF THE INVENTION
[0001] The present invention relates to a method and system for
determining with enhanced accuracy the direction or other
location-related signal characteristics of a mobile radio
transmitter, such as a cellular telephone, a personal digital
assistant, a two-way pager, or other wireless communications
device. Location-related services, such as 911 emergency system
services, require timely and accurate information. One method for
locating a mobile transmitter is to determine the transmitter's
directional bearings relative to two or more known locations, and
to estimate the transmitter's location based on where the lines of
bearing intersect. Prior directional location approaches have been
thwarted by the multifold directional ambiguities that are
attendant to the use of standard communications antennas in the
signal measurements process, and hence have employed augmentations
to the conventional antennas. The present invention enables the
straightforward usage of the conventional antenna configurations in
extracting the location-related signal characteristics to support
accurate location determination.
SUMMARY OF THE INVENTION
[0002] The present invention provides a system, apparatus, and
method for measuring position-dependent characteristics of mobile
radio signals from a mobile transmitter, including: receiving the
transmitted signals at an antenna configuration having multiple
phase-synchronized receiving elements, performing disambiguation
processing for the extraction of position-dependent characteristics
of the signals, and evaluating the characteristic parameters
indicative of the transmitter's position. The antenna configuration
of the present invention may have three or more elements. These
antenna elements may comprise at least one pair of elements whose
inter-element separation is a large quantity of half wavelengths of
the signals, and/or may comprise at least two pairs of elements
whose inter-element separations differ by a small quantity of half
wavelengths of the signals. The disambiguation processing may
include the extraction of signal characteristics having reduced
ambiguity for resolving the selection of the accurate positional
interpretation of extracted ambiguous characteristics. Further, the
disambiguation processing may include formation of differences of
inter-element signal phase differences or of higher-order signal
products. The evaluated characteristic parameters indicative of the
transmitter's position may include angle of arrival and/or may
directly quantify the transmitter's position.
[0003] In addressing the location-determination ambiguities
mentioned above, a significant objective of the present invention
is the innovative application of antenna configurations with
elements structured and exploited to mitigate or avoid the highly
ambiguous positional relations that can occur when standard
communications antennas are used to sense signal characteristics
indicative of transmitter positions. With such ambiguities thus
addressed, a further objective of the present invention is to
enable the fall exploitation of the potential
location-determination accuracy achievable through the use of such
antenna configurations.
BRIEF DESCRIPTION OF THE DRAWINGS
[0004] FIG. 1. depicts the geometric relations that exist with the
arrival from relative directional angle ".alpha." of a signal plane
wave at the positions of two antenna elements that are separated by
a fixed distance "d."
[0005] FIG. 2. shows a graphical comparison of phase difference
relations for signals from antenna elements spaced one half
wavelength apart and spaced ten wavelengths apart.
[0006] FIG. 3. depicts the geometric relations that exist with the
arrival of a signal plane wave at the positions of three antenna
elements.
[0007] FIG. 4. shows signal and data processing functional flow for
an exemplary embodiment of a three-element antenna system.
[0008] FIG. 5. is a block diagram showing the process flow for the
disambiguated characterization and angle-of-arrival extraction
using equivalent analytic signals.
DETAILED DESCRIPTION
[0009] The present invention is an extension of the Direction
Finding Localization System and the Communications Localization
System described in U.S. Pat. Nos. 4,728,959 and 5,959,580. More
specifically, the present invention uses differences of phase
differences or similarly derived signal characteristic
measurements, e.g., of second order products of signal covariances
or products, to disambiguate and estimate the signal angle of
arrival or other position-sensitive parameters. Prior directional
location determination approaches typically encounter difficulties
due to the multifold directional ambiguities that are attendant to
the use of standard communications antennas in the signal
measurement process. Hence, the approaches have typically employed
augmentations of the conventional antennas or additions of separate
antennas. The present invention enables the straightforward usage
of the conventional antenna configurations in extracting the
location-related signal characteristics to support accurate
location determination. An embodiment of the invention can output
the disambiguated angle of arrival or position-related parametric
estimate, and can use such an estimate, derived from the
appropriate processing of a disambiguating antenna element
configuration, to resolve ambiguities from widely spaced antenna
elements to achieve a more accurate angle of arrival or other
position-related parametric estimate.
[0010] Line of bearing or directional location determination
systems can relate the relative phase of the signal received at two
or more antenna elements to the angle of arrival of the signal or
directly to a quantification of parameters representing the
position or location of the signal transmitter. FIG. 1 shows a
plane wave signal 101 arriving at two antenna elements 102 and 103
separated by a distance d 104. The plane wave is arriving from the
upper right hand corner of the figure, at an angle a 105 with
respect to the line 106 connecting the two antenna elements. The
line 107 perpendicular to the plane wave's direction of propagation
represents a wavefront of constant phase across the plane wave. In
FIG. 1, the wave has to travel a distance d-cos(a) 108 further to
the left antenna element than to the right element. In the time it
takes the isophase wavefront to travel from the right to the left
antenna element, the phase of the elemental signal's carrier
frequency at the right element advances by .PHI. radians.
[0011] As represented in FIG. 1, the relationship between the
relative phase, .PHI., and the signal's angle of arrival, .alpha.,
is:
.PHI.=(2.pi./.lambda.)d cos(.alpha.) (equation 1)
[0012] where
[0013] .lambda.=c/f; wavelength of signal
[0014] f=frequency of signal
[0015] c=speed of light
[0016] d=distance between the antenna elements
[0017] .alpha.=signal's angle of arrival
[0018] With most real world systems, this relationship is
complicated by the interaction of the antenna elements with each
other and by nearby reflectors, including a backplane or other
wave-focussing structures, and multipath propagation. Accurate
phase to angle of arrival conversion can be accomplished by
tabulating measurements of the relative phase for different angles
or modeling the interaction and modifying the above equation.
Depending on the desired system accuracy, the above equation may be
accurate enough.
[0019] When the distance or separation between the two receiving
antenna elements is less than half a wavelength, i.e.,
d<.lambda./2, then signals arriving from direction a can
generate a unique relative phase response .PHI.. However, the
inter-element phase relations are ambiguous to additive multiples
of one "cycle," i.e., 2 .pi.c radians (or 360 degrees). Thus, when
the distance between elements is larger than half of the signal's
wavelength, multiple angles can generate the same relative phase
response. For example, if d=.lambda., then the above relation
becomes:
.PHI.=2 .pi. cos(.alpha.)
[0020] In this case, the relative phase differences for signals
arriving at 0 and 180 degrees (0 and .pi. radians) cannot be
differentiated from that for those arriving at 90 degrees (.pi./2
radians). In all three cases, with due account for the ambiguous
additive multiples of one cycle (2 .pi. radians), the ambiguous
relative phase difference is zero degrees or radians. The larger
the separation between the two antennas, the more ambiguous the
angle of arrival is for any given measured phase difference. FIG. 2
illustrates how ambiguous the phase difference measurement can be
when the antenna elements are separated by ten wavelengths,
represented by the dotted line 201, compared to when the antenna
elements are separated by half a wavelength, represented by the
continuous line 202. FIG. 2 also illustrates that, when the
ambiguity can be resolved or disambiguated, phase measurement
errors associated with the elements separated by ten wavelengths
map to smaller angle of arrival errors than identical phase
measurement errors associated with the half wavelength separated
antenna elements.
[0021] Cellular telephone networks use a network of fixed base
stations, each station servicing a geographic cell. Some cells are
serviced by a single monopole antenna. In this case, the antenna is
connected to a transmitter and a receiver. However, often cells are
subdivided into sectors. Each sector may be serviced by three
directional antenna elements located at the base station. Typically
the antenna elements for each sector are aligned in a straight
line, orientated approximately in the same, common, sector-centered
direction, and separated from each other by multiple wavelengths.
The outer most antenna elements are often used to receive signals
from cellular phones, and the middle antenna element is used to
transmit signals to the cellular phones and is typically positioned
in the central region between the two, end, receiving elements. In
typical urban and suburban environments, the separation of the two
receiving elements is ten to twelve wavelengths, to support
enhanced performance through diversity reception.
[0022] Since the typical, "conventional," cellular-antenna elements
are separated by a large multiple of wavelengths, line of bearing
or position determination systems based on equation 1 cannot use
the existing sectored antennas unless the system can resolve or
disambiguate the ambiguities arising from multiple wavelength
spacing.
[0023] The ambiguity can be resolved by installing an additional
pair of antenna elements separated by one half wavelength. In this
case, the two added elements are independent of the existing
cellular antenna elements. If the resulting accuracy is good enough
for the system requirements, then no further processing or
adjustment is required. If higher angular accuracy is desired, then
the estimate and bearing error based on the additional antenna
element pair provide bounds for mapping the relative phase
measurement from the widely spaced cellular antenna elements to the
disambiguated, more accurate angle of arrival.
[0024] A second method for resolving the ambiguity involves
installing an added antenna element a half wavelength away from
either end antenna element. In this case, the antenna elements
separated by a half wavelength can be processed using the same
technique as described above for processing an additional pair of
antenna elements separated by a half wavelength.
[0025] A third method involves moving the middle antenna element to
a position within a half wavelength from either end and
reconfiguring the middle antenna element so that it connects to
both a transmitter and a receiver, as is done with some monopole
antennas.
[0026] The three methods described above use at least one pair of
antenna elements separated by approximately a half wavelength. A
bearing estimate based on half wavelength separated antenna
elements can be made using an apparatus based on U.S. Pat. No.
4,728,959, entitled "Direction Finding Localization System," and
U.S. Pat. No. 5,959,580, entitled "Communications Localization
System," both of which are incorporated herein by reference.
[0027] An alternative approach, described below, enables the
derivation of disambiguated signal characteristics without the
necessary use of antenna configurations that have elements spaced
by approximately a half wavelength. The basics of this approach can
be seen in a detailed examination of the phase and element
separation relations. The geometric relations of this approach are
depicted in FIG. 3. The radio signal 301 arrives at antenna
elements "i" 302, "j" 303, and "k" 304 from the direction a 305
relative to the baseline 306 between elements "i" and "j." The
phase difference between the elemental signals received through
antenna elements "i" and "j" can be approximated by equation 2; the
exact relationship depends on the degree of interaction between
each antenna element and neighboring reflectors:
.PHI..sub.ij=(2 .pi./.lambda.)d.sub.ij.cos(.alpha.) (equation
2)
[0028] where
[0029] .PHI..sub.ij=phase difference between antenna elements i and
j
[0030] .lambda.=signal wavelength
[0031] d=distance between the antenna elements i and j
[0032] .alpha.=signal's angle of arrival
[0033] Similarly, the phase difference between antenna elements "j"
and "k" is given by
.PHI..sub.jk=(2 .pi./.lambda.)d.sub.jk.cos(.alpha.)
[0034] When the antenna elements are sufficiently aligned in a
straight line, such as may be the three antenna elements servicing
the same sector on a sectored antenna tower, the difference of the
phase differences, .DELTA..sub.ijk, may be represented and related
to the signal source location by equations 3a, 3b, and 3c.
.DELTA..sub.ijk=.PHI..sub.ij-.PHI..sub.jk (equation 3a)
.DELTA..sub.ijk=(2 .pi./.lambda.)d.sub.ij.cos(.alpha.)-(2
.pi./.lambda.)d.sub.jk.cos(.alpha.) (equation 3b)
.DELTA..sub.ijk=(2 .pi./.lambda.).(d.sub.ij-djk).cos(.alpha.)
(equation 3c)
[0035] For clarity, as shown in FIG. 3, element "j" is assumed to
be between "i" and "k." If the elements are not colinear, but
rather the baseline 307 between elements "j" and "k" is offset by
the angle .beta. 308 relative to the baseline between elements "i"
and "j," then the difference of phase differences relation can be
expressed as
.DELTA..sub.ijk=(2
.pi./.lambda.).[(d.sub.ij-d.sub.jk.cos(.beta.)).cos(.al-
pha.)-d.sub.jk.sin(.beta.).sin(.alpha.)] (equation 3d)
[0036] This minimal added complexity, in equation 3d, is trivially
accommodated with appropriate adaptations of the calculations that
are applied with the expression of equation 3c, and generally is
not explicitly addressed in most of the elucidating descriptions
herein.
[0037] When the difference .vertline.d.sub.ij-d.sub.jk.vertline. in
the antenna element separations is less than half a wavelength,
then all differences of phase difference measurements can map
unambiguously to associated angles of arrival. When the difference
in the antenna element separations is between a half wavelength and
a full wavelength, then some differences of phase difference
measurements will map unambiguously to angles of arrival, and other
differences of phase difference measurements will each map to two
possible angles of arrival. In this case, the theoretical break
point, bp, between ambiguous and unambiguous differences of phase
difference measurements is:
bp=360.(1-.vertline.dij-djk.vertline./.lambda.) degrees (equation
4)
[0038] When the magnitude of a difference of phase difference
measurements, .DELTA..sub.ijk, is less than the break point, bp,
the difference can be related to a unique angle of arrival.
[0039] FIG. 4 shows a system for determining the relative direction
of a wireless transmitter using three antenna elements. The system
consists of antenna elements, filters, mixers, digital signal
acquisition units, and a computer or digital signal processor. The
data flow through the system can be illustrated by reviewing how
data from 401 antenna element 1 are processed. The system can be
expanded to use additional antenna elements by adding additional
filters, mixers, and digital acquisition components. For example,
the processing for such additional elements could be implemented
with the analysis of the elemental signals in triplets, as with the
relations specifically described herein.
[0040] The elemental radio signal received at 401 antenna element 1
is supplied to bandpass filter 402 to filter out or sufficiently
attenuate signals that are not of interest. When the antenna
element serves as a transmitter as well as a receiver, the bandpass
filter filters out unwanted transmitted signals and passes received
signals of interest. The signal line from local oscillator 408
supplies mixer 403, which bandshifts the radio signal to an
intermediate frequency. The same signal from local oscillator 408
bandshifts the radio signals from each antenna element thus
maintaining the phase relationship of the signals received at all
the antenna elements. Additional filters 404 and mixers 405 may be
added provided the mixers use a common local oscillator 409 to
maintain the phase relationship of the signals received at all the
antenna elements.
[0041] After the signal has passed the final mixer, filter 406
filters the signal in preparation for digital signal acquisition
407. Each digital signal acquisition unit converts an analog signal
to a digitized signal and stores the resultant data samples in a
computer 411, digital signal processor, or device capable of
performing arithmetic and logical operations on the digitized data.
Maintaining the phase relationship of the received signals, the
digital signal acquisition units are synchronized using a common
local oscillator 410.
[0042] Within computer 411, the data stream from each antenna
element may be further filtered. If the processed signal is from an
analog cellular phone, the phase of the signal at each instant in
time can be determined by converting the signal to its
frequency-shifted, equivalent, "analytic" form (hereinafter, the
analytic signal) and then taking the arctangent of the real and
imaginary (i.e., "quadrature") components of the signal. A
description of analytic signals can be found in "Theory and
Application of Digital Signal Processing," page 72, by Lawrence
Rabiner and Benard Gold (Prentice-Hall, Englewood Cliffs, N.J.,
1975), or in "Discrete-Time Signal Processing," page 683, by Alan
V. Oppenheim and Ronald W. Schafer (Prentice-Hall, Englewood
Cliffs, N.J., 1989), both of which texts are incorporated herein by
reference. If the phone supports a digital technology, such as time
division multiple access (TDMA) or code division multiple access
(CDMA), and broadcasts in a digital mode, then the computer can
also extract the phone generated digital signal data from the data
stream before or after converting the signal to its analytic
form.
[0043] Computer 411 calculates the inter-element complex signal
products, covariances, covariance products, phase differences,
difference of phase differences, angles of arrival, and/or error
estimates. This information is transferred to a localization
process in a processor 412 that can combine information from two or
more systems or information from one system together with
collateral, location-sensitive data to determine the transmitter's
location. Example systems for combining such measured signal
characteristic information with other relevant position-indicative
information are described in U.S. Pat. No. 4,728,959, entitled
"Direction Finding Localization System," and U.S. Pat. No.
5,959,580, entitled "Communications Localization System," both of
which patents are incorporated herein by reference.
[0044] FIG. 5 shows a block diagram depicting how the angle of
arrival can be extracted from the analytic signal. The processes of
blocks 501, 502, and 503 convert to equivalent analytic form the
digitized signal from the digital signal acquisition component 407,
shown in FIG. 4. The process of block 504 produces inter-element
signal products, covariances, and/or products of products or
covariances, as needed. From these signal-related products, the
process of block 504 extracts or derives signal characteristic
measurements, such as the phase differences and difference of phase
differences from the analytic signals. There are several techniques
for calculating the difference of the phase differences, as shown
in the following examples.
[0045] The first technique is to calculate the derived phase
difference from the instantaneous phase of the analytic signals.
For example, the instantaneous phases, .PHI..sub.I(t) and
.PHI..sub.j(t), can be obtained at each moment in time "t" for the
signals received with antenna elements "i" and "j." Each analytic
signal sample z;(t) at time "t" can be represented by a complex
number, having real and imaginary components or having magnitude
and phase components. The instantaneous phase of the analytic
signal can be calculated using:
.PHI..sub.i(t)=atan2(IM(z.sub.i(t))), RE(z.sub.1(t))) (equation
5)
[0046] where
[0047] atan2( ) calculates the dual-component arctangent valid over
the range -.pi. to +.pi. (or 0 to 2 .pi.) 2 .pi. radians=360
degrees)
[0048] IM( ) extracts the imaginary component of the analytic
signal
[0049] RE( ) extracts the real component of the analytic signal
[0050] Then the instantaneous phase difference .PHI..sub.ij(t)
between antenna elements "i" and "j" can be determined by the
subtraction:
.PHI..sub.ij(t)=.PHI..sub.i(t)-.PHI..sub.j(t) (equation 6)
[0051] The phase differences can be temporally averaged or
integrated to create a more accurate or stable estimate. Such an
averaged, integrated, filtered or smoothed estimate can be obtained
with the application of appropriate models or weighting for the
contributions to the "average." For example, the desired parametric
estimate may be the simple, constant- or equi-weighted average,
provided the averaging period or interval is short enough that the
transmitting phone does not appreciably move with respect to the
antennas during the interval. For more extended integrations or
filtering, including Kalman filtering, appropriate
parameterizations may account for relational signal changes that
can be anticipated due to transmitter motion over the duration of
the integration interval. For example, such filtering could even
include multiple motion models representing different transmitter
speeds or other forms of rates of change, with the ultimate results
attained through joint probabilistic combination approaches.
[0052] The process of evaluation for .PHI..sub.ij(t) should bound
it between -180 and +180 degrees. In this bounding process, called
"phase unwrapping," if the preliminary value of .PHI..sub.ij(t) is
greater than 180 degrees, then 360 degrees are subtracted from
.PHI..sub.ij(t), and if the preliminary value of .PHI..sub.ij(t) is
less than -180 degrees, then 360 degrees are added to
.PHI..sub.ij(t) Similarly the phase difference .PHI..sub.jk(t)
between antenna elements "j" and "k" can be determined by:
.PHI..sub.jk(t)=.PHI..sub.j(t)-.PHI..sub.k(t) (equation 6a)
[0053] The difference of the phase differences then can be produced
by the subtraction:
.DELTA..sub.ijk=.PHI..sub.ij(t)-.PHI..sub.jk(t) (equation 3a)
[0054] This difference should also be limited to the range between
-180 and +180 degrees. As with the individual differences above,
the difference of phase differences can be averaged to create a
more accurate estimate.
[0055] A second technique, that avoids the (-180, +180 degree)
boundary problem, is to compute the difference of phase differences
using the analytic signals z.sub.i(t), z.sub.j(t), z.sub.k(t)
associated with antennas "i", "j", and "k". The instantaneous phase
difference .PHI..sub.ij(t) between the analytic signals obtained
with antenna elements "i" and "j" can be determined from the
"conjugate product" of the analytic signal samples, i.e., the
product of signal z.sub.i(t) with the complex conjugate of signal
z.sub.j(t):
.PHI..sub.ij(t)=atan2(IM(z.sub.i(t).z*.sub.j(t)),
RE(z.sub.i(t).z*.sub.j(t- ))) (equation 7)
[0056] where z*.sub.j(t) is the complex conjugate of z.sub.j(t).
The complex conjugate z* of a complex number z has the magnitude of
the complex number z, but the phase is the negative of that of the
complex number z. As with the phase differences above, the
stability of the conjugate products can be enhanced through
temporal averaging or integration to form the complex "covariance"
of the signals, e.g., of z.sub.i(t) and z.sub.j(t). Under stable
conditions, this "averaged" covariance represents an estimate of
the "expectation value" of the conjugate product. As described,
this covariance and the instantaneous conjugate products, from
which it derives, are equivalently related to the averaged or
instantaneous phase differences through the arctangent relation.
Then, as in the previous technique, any difference formed from the
subtraction of phase differences derived from the conjugate
products and any summation involved in the integration of phase
differences should be phase unwrapped.
[0057] The difference of the phase differences, .DELTA..sub.ijk(t),
for antennas i, j, and k can be alternatively obtained from:
.DELTA..sub.ijk(t)=atan2(IM(z.sub.i(t).z*.sub.j(t).z.sub.k(t)),
RE(z.sub.i(t).z*.sub.j(t).z.sub.k(t))) (equation 8)
[0058] In this relation, the higher-order (i.e., the fourth-order)
product of the elemental signal components is inherently and
equivalently imbued with the position-dependent characteristics
represented in the difference of the phase differences discussed
previously. As in the previous technique, the difference of phase
differences extracted in this fashion can be temporally averaged or
integrated to create a more accurate estimate, with due attention
to phase unwrapping. Alternatively, again avoiding the need for and
complexities of intermediate phase unwrapping, the tri-signal,
higher-order, complex products of the paired-signal conjugate
products can be temporally averaged together before the arctangent
is calculated.
[0059] A third technique uses the Fourier Transform of the signal
data from each antenna element to derive the equivalent narrow-band
analytic signal "frequency" components, and calculates the phase of
each frequency component of the signal (reference Rabiner &
Gold, Chapter 6, or Oppenheimer & Schafer, Chapter 8). In this
technique, the narrow-band complex spectra components
Z.sub.i((.omega.) for angular frequency .omega.(=2 .pi.f) over the
desired spectral domain can be manipulated in the manners analogous
to the processes involving the full-band analytic signal z.sub.i(t)
for time sample t, described in the above discussions.
[0060] Block 505 shows that after the difference of the phase
differences has been calculated, the computer can convert the
difference of the phase differences to an angle of arrival. The
angle of arrival calculation can be done several different ways.
The following three techniques exemplify the conversion.
[0061] The first technique ignores the presumably negligible
interactions of the antenna elements and uses the approximate
relation of equation 3c:
.DELTA..sub.ijk=(d.sub.ij-djk).(2 .pi./.lambda.).cos(.alpha.)
(equation 3c)
[0062] The inverse function for equation 3c, yielding the angle of
arrival, is:
.alpha.=acos(.DELTA..sub.ijk..lambda./(2 .pi..(d.sub.ij-d.sub.jk))
(equation 9a)
[0063] Of course, the equivalent inverse for the non-colinear form
in equation 3d can be implemented with iterative accommodation for
the transcendental functions. For example, the inverse can be
iteratively evaluated by beginning with an initial value of zero
for the cosine, cos(.alpha..sup.(0))=0, and then iterating to
convergence before inverting: 1 cos ( ( n + 1 ) ) = ijk / 2 + d jk
sin ( ) 1 - ( cos ( ( n ) ) ) 2 d ij - d jk cos ( )
(equation9b)
[0064] Alternatively, in standard form, the general inversion for
equation 3d is expressed as
.alpha.=acos(.DELTA..sub.ijk..lambda./(2
.pi..d.sub.ijk))-.gamma..sub.ijk (equation 9c.1)
[0065] where
d.sub.ijk={square root}{square root over
((d.sub.ij-d.sub.jk.cos(.beta.)).-
sup.2+(d.sub.jk.sin(.beta.)).sup.2)} (equation 9c.2)
.gamma..sub.ijk=atan2(d.sub.jk.sin(.beta.),
d.sub.ij-d.sub.jk.cos(.beta.) (equation 9c.3)
[0066] A second technique establishes a database of measurements or
calibrations of the characteristic differences of the phase
differences or associated complex product-based equivalents for a
transmitter at known angles or other position-related parametric
values with respect to the antennas. The data are compiled into a
table of experimentally or empirically derived measurements with
minimized. ambiguities versus signal angles of arrival or
transmitter positions. When signals from a transmitter at an
unknown location are received and processed, the derived difference
of phase differences or other complex-product based equivalent is
compared against the tabulated database. The two table entries
closest to the measured value bound the angle of arrival or
position relation; a refined angle of arrival or parameterized
position estimate is made by interpolating between the two table
entries.
[0067] A third technique, based upon a modification of equation 3c,
uses the inverse of this modified equation to convert measurements
to appropriate associated angles of arrival. The modified equation
could be based on either modeling the interaction between the
antenna elements and their neighborhood, or doing a parametric or
polynomial fit to a table built using the second technique.
[0068] Block 506 is an optional block for generating a second angle
of arrival estimate using just the measurements of the phase
differences or equivalent signal products. The rationale for using
such measurements can be seen in the functional inverses of
equations 1 and 3c.
.alpha.=acos((.PHI..sub.ij(t)-.PHI..sub.jk(t))..lambda./(2
.pi..(d.sub.ij-d.sub.jk)) (equation 10a)
.alpha.=acos((.PHI..sub.ij(t)..lambda./(2 .pi..d.sub.ij)) (equation
10b)
[0069] The position-determination accuracy benefits in the use of
disambiguated measurements obtained with antenna configurations
with conventional element spacings or separations can be seen in
the associated angle-of-arrival relations. The angle of arrival
error associated with the angle of arrival determined from the
difference of the phase differences depends upon the difference of
the separation between antenna elements "i" and "j" and the
separation between antenna elements "j" and "k". Since the
separations between the antenna elements of either pair may be
significantly larger than the difference of the separations, the
angle of arrival errors associated with the angles of arrival
determined from the phase differences of related signal products
may be significantly less than the angle of arrival errors
associated with the differences of phase differences or related
higher-order signal products. Thus, as described herein, with the
usages of such "higher order" measurements or other disambiguating
measurements in the disambiguation of "standard" measurements, the
enhanced accuracies of the extracted signal characterizations can
be exploited in the derivations or position-dependent parameters
with correspondingly enhanced accuracy.
[0070] The conversion of phase difference or signal product to
angle of arrival or other position-related parametric description
can be accomplished by techniques analogous to the techniques used
for converting a difference of phase differences to an angle of
arrival. The preferred technique is to measure or derive the signal
characteristics, such as the phase differences, for a transmitter
at known angles or positions with respect to the antennas. The
measurements are compiled into a table or database of measured
signal characteristics, such as phase differences, versus angles of
arrival or other position-descriptive parameters.
[0071] Subsequently, elemental phase relations may be measured for
signals from a transmitter at an unknown location, and these
measurements may be evaluated in association with the previously
established table or database for determination of the appropriate
positional parameters. For example, the signals can be received
with an antenna configured with three or more elements, and then
the tabulated phase relations can be evaluated to extract for each
measured phase difference the two tabulated phase differences
closest to the measured phase difference. The tabulated values that
are selected are those having the appropriate difference or
characteristic closer to the measured difference of phase
differences or other measured characteristic having reduced
ambiguity. The angle of arrival can then be determined by
interpolating between these two measurements.
[0072] Illustration of this procedure is attained with reference to
FIG. 2.
[0073] Assume the dotted line representing the phase difference
when the antenna separation is ten wavelengths is converted to a
table. Assume the table was built by making a measurement with the
test transmitter moved in front of the antenna elements from an
angle of arrival of 0 degrees, to an angle of arrival of 180
degrees in 1 degree increments. When signals from a transmitter at
an unknown location are received, an initial angle of arrival
estimate can be made based on the difference of phase differences.
As an example interpolation algorithm or procedure, if the angle of
arrival estimate for the initial unambiguous differential phase is
118 degrees and the paired-element phase difference-measurement is
-7.2 degrees for the ambiguous phase relation of the elements with
large spatial separation, then the table search would begin at 118
degrees for an angle of arrival. At 118, the phase difference for
the example is 108. The search algorithm checks higher angle of
arrival entries until reaching a phase difference less than -7.2
degrees. This table entry (angle=121, phase difference=-54) and the
preceding table entry (angle=120, phase difference=0) are saved as
a candidate match. The algorithm then searches for lower angles of
arrival until first finding where the phase difference changes from
being positive to being negative, and then finding the next phase
difference that is greater than -7.2 degrees. This table entry
(angle=113, phase difference=33.3) and the previous entry
(angle=114, phase difference=-24.) are saved as a candidate match.
The two candidate matches are compared and whichever is closer to
the initial estimate is retained. Finally, the angle of arrival is
computed by interpolating between the two retained table entries.
In this case, using a linear interpolator, the angle of arrival
(AOA) would be estimated at
AOA=[(-7.2-0)/(-54-0)].(121-120)+120=120.133 degrees
[0074] After the disambiguated angles of arrival or related signal
characteristic measurements have been estimated, the measurement
data are passed to the localization system 412, which combines the
data with measurements from multiple systems or with collateral
position-dependent information to determine the transmitter's
location. The processes and methods for evaluation of the estimated
location representation from the signal-related measurements and
any associated information are not the subject of the present
invention. Such techniques may include least-squares evaluations,
probability-based likelihood function analyses, rule-based
heuristic procedures, and other appropriate standard processing
technologies known to those skilled in the arts.
[0075] The principles, preferred embodiments and modes of operation
of the present invention have been set forth in the foregoing
specification, from which it should now be readily apparent that a
person of ordinary skill in the art may implement appropriate data
processing routines. The embodiments disclosed herein should be
interpreted as illustrating the present invention and not as
restricting it. The foregoing disclosure is not intended to limit
the range of equivalent structure available to a person of ordinary
skill in the art in any way, but rather to expand the range of
equivalent structures in ways not previously envisioned. Numerous
variations and changes can be made to the foregoing illustrative
embodiments without departing from the scope and spirit of the
present invention as set forth in the appended claims.
* * * * *