U.S. patent application number 12/110808 was filed with the patent office on 2009-01-15 for method and apparatus for all-polarization direction finding.
This patent application is currently assigned to L-3 Communications Integrated Systems, L.P.. Invention is credited to Dennis J. Close, Mark L. Kargel, Steven P. Stanners, Steven D. Thornton.
Application Number | 20090015479 12/110808 |
Document ID | / |
Family ID | 39687278 |
Filed Date | 2009-01-15 |
United States Patent
Application |
20090015479 |
Kind Code |
A1 |
Thornton; Steven D. ; et
al. |
January 15, 2009 |
METHOD AND APPARATUS FOR ALL-POLARIZATION DIRECTION FINDING
Abstract
Embodiments of the present invention provide a method and
apparatus for all-polarization direction finding. The method and
apparatus generally include acquiring measurements at least
partially corresponding to an emitted signal and generated
utilizing a blind signal extraction algorithm, forming an
all-polarization cost function utilizing the acquired measurements,
and determining an angle of arrival for the emitted signal
utilizing the formed all-polarization cost function. Such a
configuration enables angles of arrivals to be easily determined
for signals having any polarization without using a multiple signal
classification (MUSIC) algorithm.
Inventors: |
Thornton; Steven D.;
(Rockwall, TX) ; Close; Dennis J.; (Heath, TX)
; Kargel; Mark L.; (Rockwall, TX) ; Stanners;
Steven P.; (Rowlett, TX) |
Correspondence
Address: |
HOVEY WILLIAMS LLP
10801 Mastin Blvd., Suite 1000
Overland Park
KS
66210
US
|
Assignee: |
L-3 Communications Integrated
Systems, L.P.
Greenville
TX
|
Family ID: |
39687278 |
Appl. No.: |
12/110808 |
Filed: |
April 28, 2008 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
11368155 |
Mar 3, 2006 |
7414582 |
|
|
12110808 |
|
|
|
|
Current U.S.
Class: |
342/417 |
Current CPC
Class: |
G01S 3/74 20130101; H01Q
3/267 20130101 |
Class at
Publication: |
342/417 |
International
Class: |
G01S 5/02 20060101
G01S005/02 |
Claims
1. A method of determining an angle of arrival for an emitted
signal having any polarization, the method comprising: acquiring
measurements at least partially corresponding to the emitted signal
and generated utilizing a blind signal extraction algorithm;
forming an all-polarization cost function utilizing the acquired
measurements; and determining the angle of arrival for the emitted
signal utilizing the formed all-polarization cost function.
2. The method of claim 1, wherein the measurements include a weight
vector.
3. The method of claim 2, wherein the measurements include
calibration measurements comprising a matrix having vertical and
horizontal array calibration vectors.
4. The method of claim 2, wherein the all-polarization cost
function is formed to include calibration normalization.
5. The method of claim 1, wherein the angle of arrival is
determined by acquiring a maximum of the all-polarization cost
function.
6. The method of claim 1, wherein the angle of arrival is
determined by acquiring a minimum of the all-polarization cost
function.
7. The method of claim 1, wherein the cost function is operable to
be utilized by a signal specific direction finding algorithm.
8. The method of claim 7, wherein the signal specific direction
finding algorithm corresponds to a Maximum Likelihood Direction
Finding (MLDF) algorithm.
9. A computer program for determining an angle of arrival for an
emitted signal having any polarization, the computer program stored
on a computer-readable medium for operating a computing element and
comprising: a code segment operable to acquire measurements at
least partially corresponding to the emitted signal and generated
utilizing a blind signal extraction algorithm; a code segment
operable to form an all-polarization cost function utilizing the
acquired measurements; and a code segment operable to determine the
angle of arrival for the emitted signal utilizing the formed
all-polarization cost function.
10. The computer program of claim 9, wherein the measurements
include a weight vector.
11. The computer program of claim 10, wherein the measurements
include calibration measurements comprising a matrix having
vertical and horizontal array calibration vectors.
12. The computer program of claim 9, wherein the code segment forms
the all-polarization cost function to include calibration
normalization.
13. The computer program of claim 9, wherein the code segment
determines the angle of arrival by acquiring a minimum of the
all-polarization cost function.
14. The computer program of claim 9, wherein the cost function is
operable to be utilized by a signal specific direction finding
algorithm.
15. The computer program of claim 14, wherein the signal specific
direction finding algorithm corresponds to a Maximum Likelihood
Direction Finding (MLDF) algorithm.
16. A computing element operable to determine an angle of arrival
for an emitted signal having any polarization, the computing
element comprising: a memory operable to store measurements at
least partially corresponding to the emitted signal and generated
utilizing a blind signal extraction algorithm; and a processor
coupled with the memory and operable to-- form an all-polarization
cost function utilizing the stored measurements; and determine the
angle of arrival for the emitted signal utilizing the formed
all-polarization cost function.
17. The computing element of claim 16, wherein the acquired
measurements include a weight vector
18. The computing element of claim 17, wherein the stored
measurements include calibration measurements comprising a matrix
having vertical and horizontal array calibration vectors.
19. The computing element of claim 17, wherein the processor forms
the all-polarization cost function to include calibration
normalization.
20. The computing element of claim 16, wherein the processor
determines the angle of arrival by acquiring a minimum of the
all-polarization cost function.
21. The computing element of claim 16, wherein the cost function is
operable to be utilized by a signal specific direction finding
algorithm.
22. The computing element of claim 21, wherein the signal specific
direction finding algorithm corresponds to a Maximum Likelihood
Direction Finding (MLDF) algorithm.
Description
RELATED APPLICATION
[0001] The present application is a continuation patent application
and claims priority benefit, with regard to all common subject
matter, of earlier-filed U.S. non-provisional patent applications
titled "METHOD AND APPARATUS FOR ALL-POLARIZATION DIRECTION
FINDING", Ser. No. 11/368,155, filed Mar. 3, 2006. The identified
earlier-filed application is hereby incorporated by reference in
its entirety into the present application.
BACKGROUND
[0002] 1. Field
[0003] The present invention relates to signal tracking. More
particularly, the invention relates to a method and apparatus for
all-polarization direction finding that utilizes signal
measurements provided by a blind signal extraction algorithm.
[0004] 2. Related Art
[0005] The ability to determine the source geolocation of emitted
signals is becoming increasingly important as the use of wireless
communications devices becomes commonplace throughout the world.
For example, the U.S. Federal Communications Commission Enhanced
911 (E911) rules will eventually require cellular telephone
carriers to identify the geolocations, i.e. the physical source
locations, of subscribers who place calls to 911. Additionally,
wireless communication device users often desire to acquire
accurate geolocations for navigation purposes, such as to generate
a route between a current location and a destination. Further,
military and law enforcement agencies often desire to locate
sources of emitted signals for tracking and targeting purposes.
[0006] Methods and devices have been developed that enable signal
geolocations to be determined. Some of these methods include
utilizing Global Position System (GPS) elements that must be
coupled with signal emitters to determine geolocations, thereby
increasing system cost and complexity. Other methods include
utilizing one or more collector elements, such as antennas, to
generate signal measurements and compute geolocations utilizing the
generated signal measurements.
[0007] Although utilizing signal measurements enables geolocations
to be determined without physically interfacing with signal
emitters, such methods often require, utilize, or present
information concerning the angle of arrival (AOA) of emitted
signals. Unfortunately, developed methods of calculating AOA
require signals to be exclusively vertically or horizontally
polarized or require the use of algorithms such as the multiple
signal classification (MUSIC) algorithm. As signals are often not
exclusively vertically or horizontally polarized and the MUSIC
algorithm requires knowledge of how many signals are in the
environment and is generally inoperable to utilize measurements
provided by blind signal extraction algorithms, signal tracking
methods are often inhibited when faced with diversely polarized
signals.
SUMMARY
[0008] The present invention solves the above-described problems
and provides a distinct advance in the art of signal tracking. More
particularly, the invention provides a method and apparatus for
all-polarization direction finding that utilizes signal
measurements provided by a blind signal extraction algorithm. Such
a configuration enables angles of arrivals to be easily calculated
for signals having any polarization without using a MUSIC
algorithm.
[0009] In one embodiment, the present invention provides a method
of determining an angle of arrival for an emitted signal having any
polarization. The method generally includes acquiring measurements
at least partially corresponding to the emitted signal and
generated utilizing a blind signal extraction algorithm, forming an
all-polarization cost function utilizing the acquired measurements,
and determining the angle of arrival for the emitted signal
utilizing the formed all-polarization cost function.
[0010] In another embodiment, the present invention provides a
computer-readable medium encoded with a computer program for
determining an angle of arrival for an emitted signal having any
polarization. The computer program is stored on a computer-readable
medium for operating a computing element and generally includes a
code segment operable to acquire measurements at least partially
corresponding to the emitted signal and generated utilizing a blind
signal extraction algorithm, a code segment operable to form an
all-polarization cost function utilizing the acquired measurements,
and a code segment operable to determine the angle of arrival for
the emitted signal utilizing the formed all-polarization cost
function.
[0011] In another embodiment, the present invention provides a
computing element operable to determine an angle of arrival for an
emitted signal having any polarization. The computing element
generally includes a memory and a processor coupled with the
memory. The memory is operable to store measurements at least
partially corresponding to the emitted signal and generated
utilizing a blind signal extraction algorithm. The processor is
operable to form an all-polarization cost function utilizing stored
measurements and determine the angle of arrival for the emitted
signal utilizing the formed all-polarization cost function.
[0012] Other aspects and advantages of the present invention will
be apparent from the following detailed description of the
preferred embodiments and the accompanying drawing figures.
BRIEF DESCRIPTION OF THE DRAWING FIGURES
[0013] A preferred embodiment of the present invention is described
in detail below with reference to the attached drawing figures,
wherein:
[0014] FIG. 1 is a block diagram of some of the elements operable
to be utilized by various embodiments of the present invention;
[0015] FIG. 2 is a schematic view of various angles formed between
a moving collector and a signal-emitting target;
[0016] FIG. 3 is a flow chart showing some of the steps operable to
be performed by the present invention;
[0017] FIG. 4 is a spectrum graph showing an output of an
all-polarization MLDF cost function employing calibration
normalization, the graph having an x axis representing angle of
arrival and a y axis representing magnitude;
[0018] FIG. 5 is a spectrum graph showing an output of an
all-polarization MLDF cost function lacking calibration
normalization; the graph having an x axis representing angle of
arrival and a y axis representing magnitude;
[0019] FIG. 6 is an error graph showing Maximum Likelihood
Direction Finding (MLDF) error corresponding to the
all-polarization cost function of FIG. 4; and
[0020] FIG. 7 is an error graph showing Maximum Likelihood
Direction Finding (MLDF) error corresponding to the
all-polarization cost function of FIG. 5.
[0021] The drawing figures do not limit the present invention to
the specific embodiments disclosed and described herein. The
drawings are not necessarily to scale, emphasis instead being
placed upon clearly illustrating the principles of the
invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0022] The following detailed description of the invention
references the accompanying drawings that illustrate specific
embodiments in which the invention can be practiced. The
embodiments are intended to describe aspects of the invention in
sufficient detail to enable those skilled in the art to practice
the invention. Other embodiments can be utilized and changes can be
made without departing from the scope of the present invention. The
following detailed description is, therefore, not to be taken in a
limiting sense. The scope of the present invention is defined only
by the appended claims, along with the full scope of equivalents to
which such claims are entitled.
[0023] Methods consistent with the present teachings are especially
well-suited for implementation by a computing element 10, as
illustrated in FIG. 1. The computing element 10 may be a part of a
communications network 12 that enables various devices to exchange
information and data. The computing element 10 may include a
processor 14 coupled with a memory 16 to perform the various
functions described herein. As should be appreciated, the processor
14 and memory 16 may be integral or discrete and comprise various
conventional devices, such as microcontrollers, microprocessors,
programmable logic devices, etc. Further, the computing element 10
may include additional devices, such as a display for indicating
processed information, such as a geolocation or angle of arrival,
or additional processing and memory elements. Further, the
computing element 10 may comprise a plurality of computing elements
or a network of computing elements such that one or more portions
of the invention may be implemented utilizing a first computing
element and one or more other portions of the invention may be
implemented utilizing a second computing element.
[0024] The present invention can be implemented in hardware,
software, firmware, or combinations thereof. In a preferred
embodiment, however, the invention is implemented with a computer
program. The computer program and equipment described herein are
merely examples of a program and equipment that may be used to
implement the present invention and may be replaced with other
software and computer equipment without departing from the scope of
the present teachings. It will also be appreciated that the
principles of the present invention are useful independently of a
particular implementation, and that one or more of the steps
described herein may be implemented without the assistance of the
computing element 10.
[0025] Computer programs consistent with the present teachings can
be stored in or on a computer-readable medium residing on or
accessible by the computing element 10, such as the memory 16, for
instructing the computing element 10 to implement the method of the
present invention as described herein. The computer program
preferably comprises an ordered listing of executable instructions
for implementing logical functions in the computing element 10 and
other computing devices coupled with the computing element 10. The
computer program can be embodied in any computer-readable medium
for use by or in connection with an instruction execution system,
apparatus, or device, such as a computer-based system,
processor-containing system, or other system that can fetch the
instructions from the instruction execution system, apparatus, or
device, and execute the instructions.
[0026] The ordered listing of executable instructions comprising
the computer program of the present invention will hereinafter be
referred to simply as "the program" or "the computer program." It
will be understood by persons of ordinary skill in the art that the
program may comprise a single list of executable instructions or
two or more separate lists, and may be stored on a single
computer-readable medium or multiple distinct media.
[0027] In the context of this application, a "computer-readable
medium", including the memory 16, can be any means that can
contain, store, communicate, propagate or transport the program for
use by or in connection with the instruction execution system,
apparatus, or device. The computer-readable medium can be, for
example, but not limited to, an electronic, magnetic, optical,
electromagnetic, infrared, or semi-conductor system, apparatus,
device, or propagation medium. More specific, although not
inclusive, examples of the computer-readable medium would include
the following: an electrical connection having one or more wires, a
portable computer diskette, a random access memory (RAM), a
read-only memory (ROM), an erasable, programmable, read-only memory
(EPROM or Flash memory), an optical fiber, and a portable compact
disc (CD) or a digital video disc (DVD). The computer-readable
medium could even be paper or another suitable medium upon which
the program is printed, as the program can be electronically
captured, via for instance, optical scanning of the paper or other
medium, then compiled, interpreted, or otherwise processed in a
suitable manner, if necessary, and then stored in a computer
memory.
[0028] As shown in FIG. 1, the computing element 10 is preferably
directly or indirectly coupled with one or more collector elements
18 to enable function of the present invention as described herein.
It should be appreciated the computing element 10 and the collector
elements 18 may be integral such as where one or more of the
collector elements 18 are operable to independently perform signal
tracking as described herein. Thus, the computing element 10 and
collector elements 18 need not necessarily be coupled through the
communications network 12 with other devices or collector elements
to enable operation of the present invention.
[0029] The collector elements 18 may include any devices or
elements that are operable to detect and/or otherwise receive an
emitted electromagnetic signal. Thus, the collector elements 18 may
include stationary and non-stationary antennas, unidirectional and
omni-directional antennas, electrical elements operable to relay a
signal, etc. In various embodiments the collector elements 18 may
comprise a plurality of communication towers, such as
cellular-phone towers, associated via the communications network
12. Thus, the present invention is not limited to the utilization
of only one type or configuration of collector elements 18.
[0030] A flowchart of steps that may be utilized by the present
invention to determine an angle of arrival is illustrated in FIG.
3. Some of the blocks of the flow chart may represent a module
segment or portion of code of the computer program of the present
invention which comprises one or more executable instructions for
implementing the specified logical function or functions. In some
alternative implementations, the functions noted in the various
blocks may occur out of the order depicted in FIG. 3. For example,
two blocks shown in succession in FIG. 3 may in fact be executed
substantially concurrently, or the blocks may sometimes be executed
in the reverse order depending upon the functionality.
[0031] In step 100, measurements at least partially corresponding
to an emitted signal are acquired. The present invention may
acquire the measurements utilizing various methods, including
utilizing one or more of the collector elements 18 to detect and/or
receive the signal, retrieving the measurements through the
communications network 12 from one or more of the collector
elements 18 and/or computing elements, retrieving the measurements
from the memory 16, etc. Thus, the present invention is not
required to directly measure the emitted signal to acquire the
measurements.
[0032] Preferably, the measurements corresponding to the emitted
signal are at least partially generated by the computing element
10, or by other devices accessible through the communications
network 12, utilizing a blind signal extraction algorithm. The
blind signal extraction algorithm generally produces signal
measurements that can be used by one or more signal specific
direction finding (DF) algorithms, such as a Maximum Likelihood
Direction Finding (MLDF) algorithm. As is known in the art, MLDF
algorithms advantageously utilize blind signal extraction
algorithms to determine an angle of arrival (AOA) for emitted
signals.
[0033] The measurements corresponding to the emitted signal may be
generated with any blind signal extraction algorithm operable to be
utilized by MLDF algorithms or any other signal specific DF
algorithm. Thus, the blind signal extract algorithm may correspond
to a spectral self-coherence restoral (SCORE) algorithm if the
emitted signal is spectrally self-coherent at known values of
frequency separation, a multi-target constant modulus algorithm
(MT-CMA) if the emitted signal has a sufficiently low modulus
variation, a DMP algorithm, a 2D RAKE algorithm, combinations and
variations thereof, etc.
[0034] In various embodiments, the measurements corresponding to
the emitted signal include a weight vector w to facilitate
determination of the cost function in step 102. Both w and {right
arrow over (w)} are utilized interchangeably herein to represent
the weight vector w. The weight vector w may be conventionally
generated by the blind signal extraction algorithm for utilization
in direction finding. For instance, the blind signal extraction
algorithm may generate the weight vector w by maximizing the
signal-to-interference-noise-ration (SINR) of the emitted signal.
The weight vector w preferably corresponds to weight vectors
utilized in signal specific DF algorithms, such as ML-like copy/DF
MLDF algorithms.
[0035] In various embodiments, the measurements may also include
calibration measurements. The calibration measurements preferably
include at least one array calibration vector a to facilitate
formation of the cost function in step 102 and determination of the
AOA in step 104. Both a and {right arrow over (a)} are utilized
interchangeably herein to represent the array calibration vector a.
The array calibration vector a is preferably a function of azimuth
(.theta.) and depression angle (.phi.) such that the array
calibration vector a may be represented as a(.theta., .phi.).
[0036] Preferably, the calibration measurements include two
diversely polarized array calibration vectors, a.sub.h and a.sub.v,
respectively corresponding to a horizontal calibration vector and a
vertical calibration vector. As should be appreciated, the present
invention is not limited to horizontal and vertical polarizations,
as right-circular, left-circular, and other signal polarizations
may be employed utilizing the calibration vectors. The array
calibration vectors may be formed in a generally conventionally
manner by obtaining calibration data from the collector elements 18
and from a known or control source location.
[0037] The obtained calibration data may be processed by the
processor 12 by taking the dominant eigenvector of the covariance
data. The normalized eigenvector then may represent one of the
array calibration vectors, such as a.sub.h. Calibration data may be
received and processed for all desired azimuth and depression angle
orientations to form both vertical, horizontal, right-circular,
left-circular, etc., array calibration vectors. As should be
appreciated by those skilled in the art, the present invention may
employ any method of forming array calibration vectors, and need
not be limited to the particular method discussed above.
[0038] The two array calibration vectors may be formed into a
matrix, A(.theta., .phi.), to facilitate usage of the vectors by
the cost function in step 102 as is described in more detail below.
A(.theta., .phi.) may be given by:
A(.theta., .phi.)=[{right arrow over (a)}.sub.v(.theta.,
.phi.){right arrow over (a)}.sub.h(.theta., .phi.)].sub.(n.times.2)
(1)
[0039] In step 102, an all-polarization cost function is formed
utilizing the measurements acquired in step 100. The
all-polarization cost function is not dependent on a particular
signal polarization and may be utilized in step 104 to calculate
the AOA of an emitted signal having any polarization. For example,
the cost function may be utilized to calculate the AOA of signals
having vertical, horizontal, right-circular, and left-circular
polarizations. Thus, the all-polarization cost function may be
similar to conventional signal specific cost functions, such as a
MLDF cost function, with the exception that the all-polarization
cost function of the present invention is not limited to a single
polarization.
[0040] As is known in the art, a single polarization MLDF cost
function .rho. may be given by the following equation:
.rho. mldf ( .theta. , .phi. ) = a -> * ( .theta. , .phi. ) Rxx
- 1 a -> ( .theta. , .phi. ) w -> * a -> ( .theta. , .phi.
) a -> * ( .theta. , .phi. ) w -> ( 2 ) ##EQU00001##
[0041] wherein a is an array calibration vector, Rxx is a
time-average data auto correlation matrix, w is a weight vector,
.theta. is azimuth, and .phi. is depression angle.
[0042] Utilizing the weight vector and matrix of horizontal and
vertical array calibration vectors acquired in step 100, the
present invention is operable to from an all-polarization MLDF cost
function given by the following equation:
.rho. ap_mldf ( .theta. , .phi. ) = det ( [ A * ( .theta. , .phi. )
Rxx - 1 A ( .theta. , .phi. ) ] 2 .times. 2 ) ( w -> * A (
.theta. , .phi. ) A * ( .theta. , .phi. ) w -> ) ( 1 .times. 1 )
( 3 ) ##EQU00002##
wherein A is the matrix of horizontal and vertical array
calibration vectors acquired in step 100, w is the weight vector
acquired in step 100, Rxx is a time-average data auto correlation
matrix, .theta. is azimuth, and .phi. is depression angle. The
denominator of equation (3) generally corresponds to a beam (gain)
pattern for a particular weight set and the numerator generally
corresponds to a Capon spectrum.
[0043] The all-polarization MLDF cost function may alternatively be
given by:
.rho. ap_mldf ( .theta. , .phi. ) = ( w -> * A ( .theta. , .phi.
) A * ( .theta. , .phi. ) w -> ) ( 1 .times. 1 ) det ( [ A * (
.theta. , .phi. ) Rxx - 1 A ( .theta. , .phi. ) ] 2 .times. 2 ) ( 4
) ##EQU00003##
[0044] wherein A is the matrix of horizontal and vertical array
calibration vectors acquired in step 100, w is the weight vector
acquired in step 100, Rxx is a time-average data auto correlation
matrix, .theta. is azimuth, and .phi. is depression angle. Thus,
equation (4) is generally the inverse of equation (3).
[0045] The time-average data auto correlation matrix Rxx utilized
in equations (3) and (4) is generally conventional and is given by
the equation:
Rij = Xj * Xi N ( 5 ) ##EQU00004##
[0046] wherein i and j are sensor indexes, N is the number of time
samples collected, and * is a multiplier corresponding to a
Hermitian operator for complex value multiplication.
[0047] The all-polarization cost function given by equations (3) or
(4) is configured for use with signals having any polarization, and
is not limited to vertically polarized signals as equation is (2),
due to the all-polarization cost function's utilization of
measurements, including the matrix of horizontal and vertical array
calibration vectors, corresponding to various polarizations. For
instance, the cost functions provided herein may be employed by any
signal specific DF algorithm, blind signal extract algorithm, etc.,
and need not be limited to MLDF-type configurations.
[0048] As should be appreciated by those skilled in the art, the
present invention is not limited to the two cost functions given
above by equations (3) and (4), as the present invention may
utilize any all-polarization cost function formed utilizing signal
measurements generated by a blind signal extraction algorithm. For
example, equations (3) and (4) may be modified to utilize
calibration vectors corresponding to right-circular and
left-circular polarizations, or any other polarization, and are not
limited to the horizontal and vertical polarizations expressly
utilized above. Thus, variations and modifications of equations (3)
and (4) may be employed without departing from the scope of the
present invention.
[0049] In various embodiments it may be desirable to utilize an
all-polarization cost function that includes calibration
normalization to further facilitate accurate AOA determination.
All-polarization calibration normalized cost functions may be given
by the following equations:
.rho. ap_mldf ( .theta. , .phi. ) = det ( [ A ( .theta. , .phi. ) *
A ( .theta. , .phi. ) ] det ( [ A * ( .theta. , .phi. ) Rxx - 1 A (
.theta. , .phi. ) ] 2 .times. 2 ) ( w -> * A ( .theta. , .phi. )
A * ( .theta. , .phi. ) w -> ) ( 1 .times. 1 ) ( 6 ) .rho.
ap_mldf ( .theta. , .phi. ) = ( w -> * A ( .theta. , .phi. ) A *
( .theta. , .phi. ) w -> ) ( 1 .times. 1 ) det ( [ A ( .theta. ,
.phi. ) * A ( .theta. , .phi. ) ] ) det ( [ A * ( .theta. , .phi. )
Rxx - 1 A ( .theta. , .phi. ) ] 2 .times. 2 ) ( 7 )
##EQU00005##
[0050] wherein equation (6) is similar to the cost function
provided by equation (3) but includes the calibration normalizing
term det([A(.theta., .phi.)*A(.theta., .phi.)] in its numerator and
equation (7) is similar to the cost function provided by equation
(4) but includes the calibration normalizing term det([A(.theta.,
.phi.)*A(.theta., .phi.)] in its denominator.
[0051] Utilization of the cost functions provided by equations (6)
or (7) limits skewing and inadvertent scaling caused by differences
in the normalization of the individual calibration spaces of the
array calibration vectors a.sub.h and a.sub.v. These differences in
normalization of the array calibration vectors may skew results in
all-pole configurations due to utilization of the matrix A if
calibration normalization is not utilized.
[0052] FIGS. 4-7 illustrate the functionality of the calibration
normalized cost functions in comparison to the all-polarization
cost function given by equations (3) and (4). For instance, FIG. 4
illustrates a sample output of the cost function given by equation
(7), having calibration normalization, while FIG. 5 illustrates a
sample output of the cost function given by equation (4), lacking
calibration normalization. As is readily apparent, ambiguous or
false maximums are reduced by the calibration normalization of
equation (7), thereby facilitating the AOA determination in step
104. Similarly, FIG. 6 illustrates MLDF error for the sample output
of equation (7) while FIG. 7 illustrates MLDF error for the sample
output of equation (4).
[0053] In step 104, the angle of arrival (AOA) of the emitted
signal is determined utilizing the cost function or functions
formed in step 102. As shown in FIG. 2, AOA refers to the angle
formed between the source of the emitted signal and the collector
element relative to the collector element. As should be
appreciated, the cost function may be utilized to determine a
direction of arrival (DOA) instead of the AOA by providing a
reference point for the AOA calculation.
[0054] The AOA of the emitted signal is preferably determined by
calculating a minimum of the all-polarization cost function formed
in step 102 and given by equation (6) or (3). The denominator of
the all-polarization cost function is a measure of the projection
of the weight vector w onto the calibration matrix A. The
denominator will be maximized when the weight vector w is closest
to the calibration matrix A, and thus contributes to the minimum of
the cost function. In the numerator of the cost function,
Rxx.sup.-1 is similar to known EnE Nterms in MUSIC cost functions.
Since all eigenvalues of Rxx are positive and the eigenvalues
associated with the noise subspace are the smallest ones, the noise
eigenvalues and vectors will be largest component of Rxx.sup.-1.
Thus, the numerator will be minimized when the calibration matrix A
is orthogonal to the noise subspace.
[0055] Thus, the minimum of the cost function formed in step 102
and given by equation (6) or (3) generally corresponds to the AOA
of the emitted signal. In alternative embodiments where equation
(7) or (4) is utilized as the cost function, the maximum of the
cost function is acquired to determine the AOA of the emitted
signal. As existing cost function search and optimization
algorithms function best on roughly parabolic surfaces, and the
minimum of equations (6) and (3) corresponds to a roughly parabolic
surface, utilization of the cost function provided by equation (6)
or (3) is generally preferable over utilization of the cost
function provided by equations (7) or (4). However, any of the cost
functions described herein and variations thereof may be employed
by the present invention to determine AOA by finding any
combination of maximums or minimums.
[0056] Determination of the AOA is further facilitated by the cost
function as ambiguities at angles not corresponding to the AOA are
suppressed by the beam pattern which is formed from vector matrix A
and the weight vector w and calibration normalization which is
utilized by equations (6) and (7). Such suppression of ambiguous
angles enables rapid determination of minimums and maximums of the
cost function employed by the present invention utilizing various
optimization and search methods provided in the art.
[0057] In various embodiments it may be desirable to interpolate
portions of the cost function or results acquired utilizing the
cost function to ensure accurate and reliable AOA determinations.
For instance, a calibration or interpolation model may be utilized
to form the array calibration vectors and/or the array calibration
matrix. The calibration and interpolation models enable the cost
function to provide a continuous function of .theta. and .phi. even
though measurements exist only at discrete azimuths and depression
angles. The calibration model may be formed in a generally
conventional manner, such as by utilizing a calibration model
similar to those utilized in single-polarization MLDF algorithms or
MUSIC algorithms.
[0058] The AOA determined utilized the cost function of step 102
may be retained with the memory 16 for later use by the computing
element 10, transmitted to the communications network 12 for
utilized by devices coupled with the communications network 12,
provided to a user utilizing visual or audio elements, transmitted
to the source of the emitted signal to facilitate location
determination, provided to computer programs or devices coupled
with the computing element 10, combinations thereof, etc.
Similarly, the cost function provided in step 102 may be utilized
by any signal specific DF algorithms to efficiently determine
AOA.
[0059] Although the invention has been described with reference to
the preferred embodiment illustrated in the attached drawing
figures, it is noted that equivalents may be employed and
substitutions made herein without departing from the scope of the
invention as recited in the claims. For example, each of the
various equations provided herein may be replaced or substituted
with innumerable variations and general equivalents.
* * * * *