U.S. patent number RE42,546 [Application Number 11/318,398] was granted by the patent office on 2011-07-12 for method and system for target localization.
This patent grant is currently assigned to Nevada Asset Liquidators, LLC. Invention is credited to Jeffrey Bulow, Douglas M. Peters.
United States Patent |
RE42,546 |
Bulow , et al. |
July 12, 2011 |
**Please see images for:
( Certificate of Correction ) ** |
Method and system for target localization
Abstract
.[.The present inventions comprise a.]. .Iadd.A .Iaddend.method
of estimating a minimum range for a target with respect to a first
point of interest, independent of actual.[.,.]. range to the
target, comprising obtaining three bearing data points; using the
three bearing data points to determine a speed contribution
V.sub.os .Iadd.cos (.theta..sub..beta.) .Iaddend.of a first point
of interest to a distance from a relative velocity vector over a
time frame comprising t.sub.0 to t.sub.0'; determining an angle
.theta..sub..beta. as defined by the bearing relative to ownship's
heading at the point in time of closest approach to a second point
of interest; and calculating a minimum range using a predetermined
formula.
Inventors: |
Bulow; Jeffrey (Syracuse,
NY), Peters; Douglas M. (Pelham, NH) |
Assignee: |
Nevada Asset Liquidators, LLC
(Las Vegas, NV)
|
Family
ID: |
29731676 |
Appl.
No.: |
11/318,398 |
Filed: |
December 22, 2005 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
|
Reissue of: |
10108236 |
Mar 27, 2002 |
6668218 |
Dec 23, 2003 |
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Current U.S.
Class: |
701/21; 701/36;
367/99; 180/168; 701/98; 340/436; 701/301; 342/455; 701/27;
701/300; 701/1; 701/472 |
Current CPC
Class: |
G01S
3/8086 (20130101) |
Current International
Class: |
B60L
15/00 (20060101) |
Field of
Search: |
;701/1,21,27,36,98,214,301,300 ;180/168 ;340/346 ;342/455
;367/99 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Wei et al., Estimation of vector miss distnace based on source
localization, 2004, IEEE, p. 604-609. cited by examiner .
Price et al., Discarding armture and barrel optimiztion or a cannon
caliber electomagnetic laucher system, 1994, IEEE, p. 225230. cited
by examiner .
Zielinski et al., Integrated launch package performance in the
cannon-caliber launcher, 1997, IEEE, p. 163-168. cited by examiner
.
Shukla et al., A powerfulkinematic model for proportionalnavigation
of guided weapons against maneuvering targets, 1989, IEEE, p.
194-208. cited by examiner .
Albus, J.S.; "4-D/RCS, A reference model architecture for demo
III;" 1997; Internet;
http://www.isd.mel.nist.gov/documents/library/isd.sub.--pub.htm- l;
pp. 1-95. cited by other.
|
Primary Examiner: Tran; Khoi
Assistant Examiner: Sriraman; Nikhil
Claims
What is claimed is:
1. A method of estimating a minimum range .Iadd.from an ownship
.Iaddend.to a target .Iadd.at a closest point of approach (CPA)
between the target and the ownship.Iaddend., comprising: .[.a..].
.Iadd.a bearing detector .Iaddend.obtaining at least three bearing
data points of the target with respect to .[.an.]. .Iadd.the
.Iaddend.ownship.Iadd., wherein each of said bearing data points
includes a bearing angle and a corresponding time of
acquisition.Iaddend.; .[.b. using the three bearing data points to
determine a speed contribution V.sub.os of a first point of
interest to a distance from a relative velocity vector over a time
frame comprising an initial time t.sub.o to a predetermined time
t.sub.i;.]. .[.c..]. .Iadd.a computer system .Iaddend.determining
an angle .theta..sub..beta..[.as defined as.]..Iadd., where
.theta..sub..beta. is .Iaddend.the bearing relative to the
ownship's heading at the .[.point in .]. time .Iadd.(t.sub..beta.)
.Iaddend.of .Iadd.the .Iaddend.closest .Iadd.point of
.Iaddend.approach .[.to a second point of interest.].; and .[.d..].
.Iadd.the computer system .Iaddend.calculating a minimum range Min
R.sub.CPA using the formula.Iadd.: .Iaddend. Min
R.sub.CPA=V.sub.OS(t.sub..beta.-t.sub.i)cos(.theta..sub..beta.-.theta..su-
b.i).sub..theta..sub.i.sub.|=0; .Iadd.using the calculated minimum
range for at least one of: targeting a weapon with respect to the
target, navigating the ownship;.Iaddend. .[.e..]. wherein
.[.t.sub..beta. is the time at which .theta..sub..beta. was
mreaured and.]. .theta..sub.i is a bearing angle .[.to the target
relative to the ownship.]. .Iadd.corresponding to a first of said
at least three bearing data points obtained .Iaddend.at time
t.sub.i.Iadd., and V.sub.os is the speed of the ownship during said
obtaining said at least three bearing data points.Iaddend..
2. The method of claim 1, further comprising generating a
representation of the probability of the location of the target
using the calculated minimum range.
3. The method of claim 1.Iadd., .Iaddend.wherein the calculated
minimum range is .Iadd.further .Iaddend.used for .[.at least one of
targeting a weapon with respect to the second point of interest,
navigation of the ownship,.]. estimating a passing range between
the ownship and the .[.second point of interest.]. target.[., and
avoidance of the second point of interest.]..
4. The method of claim 1.Iadd., .Iaddend.wherein the .Iadd.at least
three bearing .Iaddend.data points are obtained passively.
5. The method of claim 1, further comprising: .[.f..]. obtaining
.Iadd.a .Iaddend.fourth .Iadd.bearing .Iaddend.data point .[.of the
second point with respect to an ownship.].; .[.g..]. calculating a
further set of minimum ranges using the formula .[.of step (d).].
.Iadd.for Min R.sub.CPA.Iaddend.; and .[.h..]. repeating .[.steps
(e) and (f).]. .Iadd.obtaining bearing data points and performing
corresponding calculations of Min R.sub.CPA .Iaddend.to determine a
maneuvering of the .[.second point of interest.]. .Iadd.target
.Iaddend.over time.
6. The method of claim 1, further comprising: .[.f..]. obtaining an
additional plurality of .Iadd.bearing .Iaddend.data points of the
.[.second point.]. .Iadd.target .Iaddend.with respect to .[.an.].
.Iadd.the .Iaddend.ownship; .[.g..]. calculating a further set of
minimum ranges using the formula .[.of step (d).]. .Iadd.for Min
R.sub.CPA.Iaddend.; and .[.h..]. determining a deviation of a
calculated minimum range from others of the calculated minimum
ranges.
7. A method for estimating a minimum range Min R.sub.CPA to a
contact .Iadd.from an ownship.Iaddend., independent of actual
contact range, comprising: a. .Iadd.a bearing detector
.Iaddend.passively obtaining at least three bearing data points of
the contact relative to .[.an.]. .Iadd.the .Iaddend.ownship; b.
.Iadd.a computer system .Iaddend.determining an angle
.theta..sub..beta. defining the bearing .Iadd.to the contact
.Iaddend.relative to .[.a heading of.]. the ownship at the point in
time of closest approach to .[.a second point of interest.].
.Iadd.the contact.Iaddend.; c. .Iadd.the computer system
.Iaddend.calculating .[.a.]. .Iadd.the .Iaddend.minimum range at
.[.CPA.]. .Iadd.a closest point of approach (CPA) .Iaddend.between
the ownship and the .[.target.]. .Iadd.contact .Iaddend.using the
formula Min
R.sub.CPA=V.sub.os(t.sub..beta.-t.sub.i)cos(.theta..sub..beta.-.theta-
..sub.i).sub..theta..sub.i.sub.|=0; and .[.d. generating a
representation of the probability of the location of the target
.]..Iadd.contact .Iaddend. .[.located at the minimum range;.].
.Iadd.d. using the calculated minimum range to alter a heading of
the ownship;.Iaddend. e. wherein t.sub..beta. is the time .[.at
which.]. .Iadd.corresponding to .Iaddend..theta..sub..beta..[.was
measured.]., .theta..sub.i is a bearing angle to the contact
relative to the ownship at time t.sub.i; and V.sub.os is a speed
.[.contribution.]. of .[.a first point of interest to a distance
from a relative velocity vector over a time frame comprising an
initial time t.sub.0 to a predetermined time t.sub.i.]. .Iadd.the
ownship during said passively obtaining said at least three bearing
data points.Iaddend..
8. The method of claim 7, further comprising: f. obtaining a fourth
data point; g. using the fourth data point to calculate an angle to
bearing at CPA relative to the heading of the ownship; h.
calculating a time of CPA for all combinations of the three of four
bearing data points; and i. determining noise in the system by
comparing a deviation in at least one of the bearing at CPA,
relative to the heading of the ownship and the time of CPA for each
potential solution, to a predetermined value.
9. The method of claim 8, wherein the step of determining noise in
the system further comprises determining the mean and standard
deviations in the bearing calculations at CPA.
10. The method of claim 7 further comprising: f. obtaining an
estimate of a current minimum range at a time t.sub.i, the estimate
comprising: i. calculating a current minimum range R.sub.(current
minimum) by dividing .Iadd.Min .Iaddend.R.sub.CPA by the cosine of
(.theta..sub..beta.-.theta..sub.i) where .theta..sub.0 is a bearing
relative to the ownship when .theta.=0, and .theta..sub.i is a
bearing relative to the ownship at time t.sub.i; and ii. generating
a representation of the probability of the location of the
contact.
11. The method of claim 7, further comprising: f. obtaining
.[.said.]. additional .Iadd.bearing .Iaddend.data points of the
.[.second point of interest.]. .Iadd.contact .Iaddend.with respect
to said ownship; g. using the additional .Iadd.bearing
.Iaddend.data points to refine the system noise estimate by
calculating the mean and standard deviation of the bearings at CPA;
h. using the additional .Iadd.bearing .Iaddend.data points to
refine the mean bearing at CPA with respect to ownship's heading;
i. determining a trend of change in the mean value of bearing at
CPA with respect to ownship's heading; j. using the trend of change
in the mean value of bearing at CPA with respect to ownship's
heading to determine change in .Iadd.a .Iaddend.relative velocity
vector between said ownship and said .[.target.].
.Iadd.contact.Iaddend..
12. A system for calculating an estimated minimum range
.[.estimate.]. R.sub.CPA from a source to a target, comprising: a.
a bearing detector capable of passively obtaining a bearing to the
target from the source; b. a computer having a processor and
memory; and c. range calculation software executing in the
computer; d. wherein i. the memory stores at least three bearing
data points obtained from the bearing detector; ii. the range
calculation software uses the stored three bearing data points to
determine a speed .[.contribution.]. V.sub.os of the .[.target to a
distance from a relative velocity vector over.]. .Iadd.source
during .Iaddend.a time .[.from t.sub.0 to t.sub.0'.]. .Iadd.when
said at least three bearing data points are obtained.Iaddend.; iii.
the range calculation software determines an angle
.theta..sub..beta. defined by the bearing .Iadd.to the target
.Iaddend.relative to .[.a heading of.]. the source at the point in
time of closest approach .[.to.]. .Iadd.between the source and
.Iaddend.the target; iv. the range calculation software calculates
a minimum range from the source to the target.[.and as Min
R.sub.CPA=V.sub.OS(t.sub..beta.-t.sub.i)cos(.theta..sub..beta..theta..sub-
.i).sub..theta.i|=0; and.]..Iadd., wherein said minimum range is
based in part on V.sub.os, .theta..sub..beta., and the point in
time of closest approach; and.Iaddend. .[.v. the range calculation
software generates a representation of the probability of the
location of a target..]. .Iadd.wherein the system is configured to
use the calculated minimum range to alter a heading of the
source;.Iaddend. .Iadd.wherein the source and the target are
physical objects..Iaddend.
13. The system of claim 12 further comprising an output device
capable of reproducing a representation of at least one of the
calculated minimum range output and the probability of the location
of the target.
.Iadd.14. A method, comprising: a. a bearing detector obtaining at
least three bearing data points of a target with respect to a
vehicle; b. a computer system determining an angle
.theta..sub..beta., wherein .theta..sub..beta. is defined as the
bearing of the target relative to the vehicle's heading at the time
of closest approach to the target; c. the computer system
estimating a minimum range from the vehicle to the target using
said obtained three bearing data points, said bearing angle
.theta..sub..beta. and a speed of the vehicle during said
obtaining; and d. using said estimated minimum range to alter a
heading of the vehicle..Iaddend.
.Iadd.15. The method of claim 1, further comprising using said
calculated minimum range at the closest point of approach to
estimate a minimum range at time t.sub.i..Iaddend.
.Iadd.16. The method of claim 15, wherein said minimum range at
said time t.sub.i is equal to Min R.sub.CPA divided by
cos(.theta..sub.0-.theta..sub.i), wherein .theta..sub.0 is a
bearing angle at time t.sub.0 and .theta..sub.i is a bearing angle
at said time t.sub.i..Iaddend.
.Iadd.17. The method of claim 1, wherein .theta..sub..beta. is
calculated according to the following formula:
.theta..beta..function..function..theta..times..DELTA..function..theta..t-
imes..DELTA..function..theta..times..DELTA..function..theta..times..functi-
on..theta..times..DELTA..function..theta..times..function..theta..times..D-
ELTA..function..theta..times..function..theta..times..DELTA.
##EQU00005## wherein .theta..sub.j and .theta..sub.k are bearing
angles respectively corresponding to second and third ones of said
at least three bearing data points, wherein .theta..sub.j and
.theta..sub.k are obtained at times t.sub.j and t.sub.k
respectively, and wherein .DELTA.t.sub.j,k, .DELTA.t.sub.k,i,
.DELTA.t.sub.i,j are the differences between times t.sub.j and
t.sub.k; t.sub.k and t.sub.i; and t.sub.i and t.sub.j,
respectively..Iaddend.
.Iadd.18. The method of claim 7, further comprising using said
calculated minimum range at the closest point of approach to
estimate a minimum range at time t.sub.i..Iaddend.
.Iadd.19. The method of claim 18, wherein said minimum range at
said time t.sub.i is equal to Min R.sub.CPA divided by
cos(.theta..sub.0-.theta..sub.i), wherein .theta..sub.0 is a
bearing angle at time t.sub.0 and .theta..sub.i is a bearing angle
at said time t.sub.i..Iaddend.
.Iadd.20. The method of claim 7, wherein .theta..sub..beta. is
calculated according to the following formula:
.theta..beta..function..function..theta..times..DELTA..function..theta..t-
imes..DELTA..function..theta..times..DELTA..function..theta..times..functi-
on..theta..times..DELTA..function..theta..times..function..theta..times..D-
ELTA..function..theta..times..function..theta..times..DELTA.
##EQU00006## wherein .theta..sub.j and .theta..sub.k are bearing
angles respectively corresponding to second and third ones of said
at least three bearing data points, wherein .theta..sub.j and
.theta..sub.k are obtained at times t.sub.j and t.sub.k
respectively, and wherein .DELTA.t.sub.j,k, .DELTA.t.sub.k,i,
.DELTA.t.sub.i,j are the differences between times t.sub.j and
t.sub.k; t.sub.k and t.sub.i; and t.sub.i and t.sub.j,
respectively..Iaddend.
.Iadd.21. A method for tracking a second point of interest relative
to a first point of interest, said method comprising: a computer
system receiving information indicative of at least three bearing
data points of said second point of interest relative to said first
point of interest, wherein each of the at least three bearing data
points includes a bearing angle and a corresponding acquisition
time, wherein each acquisition time is different; the computer
system estimating a minimum range of said second point of interest
relative to said first point of interest, wherein said estimating
uses one or more equations, wherein said one or more equations have
a closed-form solution, and wherein at least one of said one or
more equations is based in part upon three of said at least three
bearing data points; and altering a heading of the first point of
interest based at least in part on the estimated minimum range;
wherein the first and second points of interest are physical
objects..Iaddend.
.Iadd.22. The method of claim 21, wherein at least one of said one
or more equations is also based in part on a speed of said first
point of interest..Iaddend.
.Iadd.23. The method of claim 22, wherein said estimated minimum
range corresponds to a closest point of approach (CPA) between the
first and second points of interest..Iaddend.
.Iadd.24. The method of claim 23, further comprising using said
estimated minimum range corresponding to said CPA to estimate a
minimum range at a time t.sub.i..Iaddend.
.Iadd.25. The method of claim 24, wherein said minimum range at
said time t.sub.i is equal to said minimum range corresponding to
said CPA divided by cos(.theta..sub.0-.theta..sub.i), wherein
.theta..sub.0 is a bearing angle at a time t.sub.0 and
.theta..sub.i is a bearing angle at said time t.sub.i..Iaddend.
.Iadd.26. The method of claim 23, wherein said estimating said
minimum range includes estimating a bearing angle
.theta..sub..beta. at the CPA..Iaddend.
.Iadd.27. The method of claim 26, wherein said estimating
.theta..sub..beta. is based in part upon said at least three
bearing data points..Iaddend.
.Iadd.28. The method of claim 26, wherein .theta..sub..beta. is
calculated using the following equation:
.theta..beta..function..function..theta..times..DELTA..function..theta..t-
imes..DELTA..function..theta..times..DELTA..function..theta..times..functi-
on..theta..times..DELTA..function..theta..times..function..theta..times..D-
ELTA..function..theta..times..function..theta..times..DELTA.
##EQU00007## wherein .theta..sub.j and .theta..sub.k are bearing
angles respectively corresponding to second and third ones of said
at least three bearing data points, wherein .theta..sub.j and
.theta..sub.k are obtained at times t.sub.j and t.sub.k
respectively, and wherein .DELTA.t.sub.j,k, .DELTA.t.sub.k,i,
.DELTA.t.sub.i,j are the differences between times t.sub.j and
t.sub.k; t.sub.k and t.sub.i; and t.sub.i and t.sub.j,
respectively..Iaddend.
.Iadd.29. The method of claim 23, wherein the estimation of said
minimum range is based upon a time t.sub..beta. corresponding to
the CPA..Iaddend.
.Iadd.30. The method of claim 21, wherein said minimum range (Min
R.sub.CPA) corresponds to a closest point of approach (CPA) between
the first and second points of interest, and wherein Min R.sub.CPA
is calculated according to the formula Min
R.sub.CPA=V.sub.os(t.sub..beta.-t.sub.i)cos(.theta..sub..beta.-.theta..su-
b.i).sub..theta.i|=0, and wherein V.sub.os is a speed of said first
point of interest, .theta..sub.i is a bearing angle between the
first point of interest and the second point of interest at time
t.sub.i, and .theta..sub..beta. is a bearing angle between the
first point of interest and the second point of interest at time
t.sub..beta., wherein t.sub..beta. is an estimated time
corresponding to the CPA..Iaddend.
.Iadd.31. The method of claim 21, wherein said at least three
bearing data points include four or more bearing data points, the
method further comprising estimating a minimum range corresponding
to each three data point-combination of the four or more bearing
data points..Iaddend.
.Iadd.32. The method of claim 31, further comprising performing a
statistical analysis on each of said estimated minimum
ranges..Iaddend.
.Iadd.33. The method of claim 32, wherein said statistical analysis
includes calculating a mean minimum range..Iaddend.
.Iadd.34. The method of claim 32, wherein said statistical analysis
includes calculating a standard deviation of said estimated minimum
range..Iaddend.
.Iadd.35. The method of claim 21, wherein said receiving includes
receiving four or more bearing data points, the method further
comprising using the received four or more data points to detect
the presence of noise..Iaddend.
.Iadd.36. The method of claim 21, wherein said receiving includes
receiving five or more bearing data points, the method further
comprising using the received five or more data points to detect
maneuvering of said second point of interest..Iaddend.
.Iadd.37. The method of claim 21, wherein said first point of
interest is a water vessel..Iaddend.
.Iadd.38. The method of claim 21, wherein said second point of
interest is a water vessel..Iaddend.
.Iadd.39. The method of claim 21, wherein said first point of
interest is in motion, and said second point of interest is
stationary..Iaddend.
.Iadd.40. The method of claim 21, wherein the one or more equations
include the following mathematical operations: addition,
subtraction, multiplication, division, cosine, tangent, inverse
tangent..Iaddend.
.Iadd.41. The method of claim 21, further comprising using said
estimated minimum range to launch a weapon at said second point of
interest..Iaddend.
.Iadd.42. A method for tracking a second point of interest relative
to a first point of interest, said method comprising: a computer
system receiving information indicative of at least three bearing
data points, wherein each of said at least three bearing data
points includes a bearing angle and a corresponding acquisition
time, wherein each bearing angle is measured between a heading of
said first point of interest and the second point of interest at
said corresponding acquisition time, wherein each said
corresponding acquisition time is different; the computer system
estimating a minimum range of said second point of interest
relative to said first point of interest, wherein said estimating
is performed in a single iteration through a set of one or more
equations, wherein said set of equations are based in part upon
three of said at least three bearing data points; and altering a
heading of the first point of interest based at least in part on
the estimated minimum range; wherein the first and second points of
interest are physical objects..Iaddend.
.Iadd.43. The method of claim 42, wherein said set of equations are
based in part upon a speed of the first point of
interest..Iaddend.
.Iadd.44. The method of claim 42, wherein said at least three
bearing data points is a number (N) of bearing data points greater
than or equal to four, said method further comprising performing a
number (C) of minimum range calculations for each three data
point-combination of said N bearing data points, where
C=N!/((N-3)!*3!), wherein each of said C minimum range calculations
is performed in a single iteration through said set of
equations..Iaddend.
.Iadd.45. The method of claim 42, further comprising computing a
mean minimum range from said C minimum range
calculations..Iaddend.
.Iadd.46. The method of claim 42, further comprising computing a
standard deviation of said C minimum range
calculations..Iaddend.
.Iadd.47. The method of claim 42, wherein either or both of said
first and second points of interest are water vessels..Iaddend.
.Iadd.48. The method of claim 42, wherein said set of equations is
based in part upon an angle between a heading of said first point
of interest and said second point of interest at a closest point of
approach between said first and second points of
interest..Iaddend.
.Iadd.49. The method of claim 42, further comprising using said
estimated minimum range to alter a heading of said first point of
interest..Iaddend.
.Iadd.50. The method of claim 42, further comprising using said
estimated minimum range to launch a weapon at said second point of
interest..Iaddend.
.Iadd.51. The method of claim 42, wherein said minimum range
corresponds to a closest point of approach between said first and
second point of interest..Iaddend.
.Iadd.52. The method of claim 42, further comprising using said
minimum range at said closest point of approach to calculate a
minimum range at a different time..Iaddend.
.Iadd.53. A system, comprising: a processor; and a memory coupled
to the processor, wherein the memory is configured to store program
instructions executable by the processor to: receive at least three
bearing data points of a second point of interest relative to a
first point of interest, wherein each of the at least three bearing
data points includes a bearing angle and a corresponding
acquisition time, wherein each bearing angle is an angle between a
heading of said first point of interest and a second point of
interest at said corresponding acquisition time, wherein each
acquisition time is different, and wherein said first and second
points of interest are physical objects; and estimate a minimum
range of said second point of interest relative to said first point
of interest, wherein said estimation uses one or more equations,
wherein said one or more equations have a closed-form solution, and
wherein at least one of said one or more equations is based in part
upon three of said at least three bearing data points; wherein said
system is further configured to use said estimated minimum range to
alter a heading of said first point of interest..Iaddend.
.Iadd.54. The system of claim 53, further comprising one or more
bearing detectors configured to obtain bearing data
points..Iaddend.
.Iadd.55. The system of claim 54, wherein said bearing detectors
are configured to obtain said bearing data points
passively..Iaddend.
.Iadd.56. The system of claim 53, wherein the one or more equations
include the following mathematical operations: addition,
subtraction, multiplication, division, cosine, tangent, inverse
tangent..Iaddend.
.Iadd.57. The system of claim 53, wherein said system is further
configured to use said estimated minimum range to target said
second point of interest using a weapons system configured to
target said second point of interest..Iaddend.
.Iadd.58. The system of claim 53, wherein said estimated minimum
range corresponds to a closest point of approach (CPA) between said
first and second points of interest, and wherein said system is
further configured to use said estimated minimum range in order to
estimate a minimum range at a time other than a time corresponding
to said CPA..Iaddend.
.Iadd.59. A system, comprising: a processor; and a memory coupled
to the processor, wherein the memory is configured to store program
instructions executable by the processor to: receive at least three
bearing data points of a second point of interest relative to a
first point of interest, wherein said data points are acquired at
different times, and wherein said first and second points of
interest are physical objects; and estimate a minimum range of said
second point of interest relative to said first point of interest,
wherein said estimating is performed in a single iteration through
a set of one or more equations, wherein said set of equations are
based in part upon three of said at least three bearing data
points; wherein said system is further configured to use said
estimated minimum range to target said second point of interest
with a weapons system..Iaddend.
.Iadd.60. The system of claim 59, wherein each of the at least
three bearing data points includes a bearing angle and a
corresponding acquisition time..Iaddend.
.Iadd.61. The system of claim 59, further comprising one or more
bearing detectors configured to obtain bearing data
points..Iaddend.
.Iadd.62. The system of claim 59, wherein the number of said at
least three bearing data points is a number (N) greater than or
equal to four, said method further comprising performing a number
(C) of minimum range calculations for each three data
point-combination of said N bearing data points, where
C=N!/((N-3)!*3!), wherein each of said C minimum range calculations
is performed in a single iteration through said set of
equations..Iaddend.
.Iadd.63. The system of claim 59, wherein said system is further
configured to use said estimated minimum range to alter a heading
of said first point of interest..Iaddend.
.Iadd.64. A non-transitory computer readable medium comprising
program instructions, wherein the instructions are
computer-executable to: receive at least three bearing data points
of a second point of interest relative to a first point of
interest, wherein each of the at least three bearing data points
includes a bearing angle and a corresponding acquisition time,
wherein each acquisition time is different; estimate a minimum
range of said second point of interest relative to said first point
of interest, wherein said estimation uses one or more equations,
wherein said one or more equations have a closed-form solution, and
wherein said one or more equations are based in part upon three of
said at least three bearing data points; and use said estimated
minimum range to alter a heading of said first point of interest;
wherein said first and second points of interest are physical
objects..Iaddend.
.Iadd.65. The non-transitory computer readable medium of claim 64,
wherein the one or more equations include the following
mathematical operations: addition, subtraction, multiplication,
division, cosine, tangent, inverse tangent..Iaddend.
.Iadd.66. A non-transitory computer readable medium comprising
program instructions, wherein the instructions are computer
executable to: receive at least three bearing data points of a
second point of interest relative to a first point of interest,
wherein each of said data points corresponds to different points in
time, and wherein said first and second points of interest are
physical objects; calculate an estimation of a minimum range of
said second point of interest relative to said first point of
interest, wherein said estimation is performed in a single
iteration through one or more equations, wherein said one or more
equations depend in part upon three of said at least three bearing
data points; and use said estimated minimum range to target said
second point of interest with a weapons system..Iaddend.
.Iadd.67. A method, comprising: a computer system receiving
information indicative of at least three bearing data points,
wherein each of the at least three bearing data points includes a
bearing angle and a corresponding acquisition time, wherein each
bearing angle is measured between a heading of a first point of
interest and a second point of interest, and wherein each
acquisition time is different; the computer system estimating a
minimum range of said second point of interest relative to said
first point of interest, wherein said estimating is based on one or
more equations having a closed-form solution, and wherein said one
or more equations are based in part upon three of said at least
three bearing data points; and using said estimated minimum range
to change a heading of said first point of interest; wherein said
first point of interest and said second point of interest are
physical objects, and wherein said first point of interest is a
vehicle..Iaddend.
.Iadd.68. The method of claim 67, wherein said first point of
interest is an automobile..Iaddend.
.Iadd.69. The method of claim 67, wherein said first point of
interest is a water vessel..Iaddend.
.Iadd.70. The method of claim 67, wherein said first point of
interest is an aircraft..Iaddend.
.Iadd.71. The method of claim 67, wherein said estimation of said
minimum range is based in part upon a bearing angle
.theta..sub..beta. that corresponds to a closest point of approach
(CPA) between said first and second points of
interest..Iaddend.
.Iadd.72. The method of claim 67, wherein said bearing angle
.theta..sub..beta. at the CPA is calculated according to the
following formula:
.theta..beta..function..function..theta..times..DELTA..function.-
.theta..times..DELTA..function..theta..times..DELTA..function..theta..time-
s..function..theta..times..DELTA..function..theta..times..function..theta.-
.times..DELTA..function..theta..times..function..theta..times..DELTA.
##EQU00008## wherein .theta..sub.j and .theta..sub.k are bearing
angles respectively corresponding to second and third ones of said
at least three bearing data points, wherein .theta..sub.j and
.theta..sub.k are obtained at times t.sub.j and t.sub.k
respectively, and wherein .DELTA.t.sub.j,k, .DELTA.t.sub.k,i,
.DELTA.t.sub.i,j are the differences between times t.sub.j and
t.sub.k; t.sub.k and t.sub.i; and t.sub.i and t.sub.j,
respectively..Iaddend.
.Iadd.73. The method of claim 67, wherein said estimated minimum
range corresponds to a closest point of approach (CPA) between said
first and second points of interest, and wherein said method
further comprises using said estimated minimum range at said CPA to
estimate a minimum range at a time t.sub.i..Iaddend.
.Iadd.74. The method of claim 73, wherein said minimum range at
said time t.sub.i is equal to said minimum range at said CPA
divided by cos(.theta..sub.0-.theta..sub.i), wherein .theta..sub.0
is a bearing angle at time t.sub.0 and .theta..sub.i is a bearing
angle at said time t.sub.i..Iaddend.
.Iadd.75. A method, comprising: a computer system receiving
information indicative of at least three bearing data points,
wherein each of the at least three bearing data points includes a
bearing angle and a corresponding acquisition time, wherein each
bearing angle is measured between a heading of a first point of
interest and a second point of interest, and wherein each
acquisition time is different, and wherein said first and second
points of interest are physical objects; the computer system
estimating a minimum range of said second point of interest
relative to said first point of interest, wherein said estimating
is based on one or more equations having a closed-form solution,
and wherein said one or more equations are based in part upon three
of said at least three bearing data points; and targeting said
second point of interest using a weapons system, wherein said
targeting is based in part upon said estimated minimum
range..Iaddend.
.Iadd.76. The method of claim 75, wherein said first point of
interest is a water vessel..Iaddend.
.Iadd.77. The method of claim 75, wherein said estimation of said
minimum range is based in part upon a bearing angle
.theta..sub..beta. that corresponds to a closest point of approach
(CPA) between said first and second points of
interest..Iaddend.
.Iadd.78. The method of claim 77, wherein said bearing angle
.theta..sub..beta. at the CPA is calculated according to the
following formula:
.theta..beta..function..function..theta..times..DELTA..function.-
.theta..times..DELTA..function..theta..times..DELTA..function..theta..time-
s..function..theta..times..DELTA..function..theta..times..function..theta.-
.times..DELTA..function..theta..times..function..theta..times..DELTA.
##EQU00009## wherein .theta..sub.j and .theta..sub.k are bearing
angles respectively corresponding to second and third ones of said
at least three bearing data points, wherein .theta..sub.j and
.theta..sub.k are obtained at times t.sub.j and t.sub.k
respectively, and wherein .DELTA.t.sub.j,k, .DELTA.t.sub.k,i,
.DELTA.t.sub.i,j are the differences between times t.sub.j and
t.sub.k; t.sub.k and t.sub.i; and t.sub.i and t.sub.j,
respectively..Iaddend.
.Iadd.79. The method of claim 75, wherein said estimated minimum
range corresponds to a closest point of approach (CPA) between said
first and second points of interest, and wherein said method
further comprises using said estimated minimum range at said CPA to
estimate a minimum range at a time t.sub.i..Iaddend.
.Iadd.80. The method of claim 75, wherein said minimum range at
said time t.sub.i is equal to said minimum range at said CPA
divided by cos(.theta..sub.0-.theta..sub.i), wherein .theta..sub.0
is a bearing angle at time t.sub.0 and .theta..sub.i is a bearing
angle at said time t.sub.i..Iaddend.
.Iadd.81. The method of claim 14, wherein the vehicle is an
aircraft, a water vessel, or an automobile..Iaddend.
.Iadd.82. The method of claim 67, wherein the second point of
interest is another vehicle..Iaddend.
.Iadd.83. The method of claim 67, wherein the second point of
interest is a stationary object..Iaddend.
Description
FIELD OF THE INVENTION
The present inventions relate to localization of an object or
target of interest.
DESCRIPTION OF THE RELATED ART
It is often desirable to track one object from another object to
determine if the tracked object will intercept the tracking object,
or at what point in time will the tracked object be at it closest
approach to the tracking object, sometimes referred to in the art
as "Target Motion Analysis." For example, a vessel afloat in the
presence of subsea or partially submerged obstacles would need to
know where those obstacles are in order to avoid hitting those
obstacles. By way of example and not limitation, such systems have
been proposed in the art to avoid collisions with other vessels,
collisions with such as icebergs, and collisions with submerged
objects sufficient to cause damage such as ledges, seamounts, or
reefs.
Some of the prior art has proposed using statistically based
tracking methods. For example, U.S. Pat. No. 5,732,043 to Nguyen et
al. for "Optimized Deterministic Bearings Only Target Motion
Analysis Technique" teaches using four target bearings to optimize
a target track solution.
In other art, U.S. Pat. No. 6,199,471 issued to Perruzzi, et al.
for a "Method And System For Determining The Probable Location Of A
Contact" teaches a method and a system for determining a weapon
firing strategy for an evading target. Perruzzi '471 comprises the
steps of sensing the motion of the target, analyzing the motion of
the target, providing a weapon employment decision aid, determining
the evasion region for the target using the weapon employment
decision aid and the analyzed motion, visually displaying the
evasion region, feeding operator knowledge about evading target,
and generating a representation of the probability of the location
of the evading target.
U.S. Pat. No. 5,867,256 to Van Rheeden for "Passive Range
Estimation Using Image Size Measurements" teaches a range
estimation system and method which comprises a data base containing
data for identification of certain targets and data for estimating
the initial range to each of the targets as a function of the
observed dimensions of the targets. A sensor (1) observes a scene
containing a target a plurality of spaced apart times while the
sensor is moving relative to the target to provide data from each
observation of the scene relating to the dimensions of the target
within the scene. The remaining range to the target is estimated
from the observed dimensions of the target from the range traveled
since a prior estimation of range and from a prior estimation of
the remaining range to the target. The sensor (1) provides
electrical signals representing the observed scene (3) and can be a
visible light or infrared sensor. A computer (9) is used to
identify the target from the data base, estimate the initial range
to the target and estimate the remaining range from the range
traveled between successive observations of the scene and the
change of dimensions of the target in the observed scene.
As noted in the prior art, there are a number of situations where
it is desirable to estimate the range to an object of interest or
target (e.g. aircraft without the aid of instrument landing
systems, automobiles that would be aware of the distance between
vehicles to avoid collisions, and missile-based warfare). As also
known in the art, active techniques to measure range, such as
radar, ladar and sonar, have drawbacks, primarily in military
applications, including easy detection by the target under attack.
This is true, for example, in submarine warfare where one vessel
may want to use sonar to determine the position and velocity of an
enemy ship. In such situations, it is advantageous to estimate
range to the target passively.
For passive tracking situations, in order to react quickly,
tracking methods would preferably fix a boundary on the range to
the tracked object quickly while using a minimum amount of data,
preferably passive data. Further, it is preferable to calculate the
bearing of the tracked object with respect to the tracking object
at a point of closest approach, along with calculating a time to
that closest approach, independent of other position data.
The AN/SQQ-89(V) UFCS (Navy) surface ship ASW Fire Control System
currently uses the Manual Adaptive Target Estimator (MATE) and
Maximum Likelihood Estimator (MLE) algorithms to determine target
position. These algorithms require substantially more data than the
present inventions to obtain their results. The MATE algorithm
requires operator based estimates, and systematic manual
manipulation of the data to arrive at a position, course and speed
estimate of the target. The MLE algorithm also requires limited
operator input to arrive at a statistically based estimate of
position, course and speed of the target. Both of these algorithms
require a substantial amount of data, approximately fifteen to
twenty data points, to arrive at a stable solution.
BRIEF DESCRIPTION OF THE DRAWINGS
These and other features, aspects, and advantages of the present
inventions will become more fully apparent from the following
description, appended claims, and accompanying drawings in
which:
FIG. 1 is an exemplary Cartesian plot of a target, an ownship, and
various vectors related to the two, in a geographic reference
frame; and
FIG. 2 is an exemplary Cartesian plot of a target, an ownship, and
various vectors related to the two, in a reference frame relative
to an ownship's position;
FIG. 3 is an exemplary Cartesian plot showing determination of
target maneuvers and noise in the system; and
FIG. 4 is a schematic representation of an exemplary system.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring to FIG. 1, an exemplary Cartesian plot of a target, an
ownship, and various vectors related to the two in a geographic
reference frame, the present inventions comprise a method of
providing bounds for approximations for tracking an object such as
target 2 with respect to a first object such as ownship 1. The
present inventions comprise methods for creating calculations
useful for bounding tracking sensor localization using a
substantially minimum amount of data, in a preferred embodiment
especially using passively obtained data as that term is understood
by those of ordinary skill in the target detection arts. The
methods comprise calculating relative bearing at a closet point of
approach ("CPA") and time of CPA independently of other position
data, estimating target motion analysis ("TMA") solution noise, and
detecting contact maneuvers.
In a preferred embodiment, the methods of the present inventions
may be used to conduct passive TMA using symmetries associated with
two different views of a problem to be solved, e.g. two reference
frames and two points of interest. A first of these frames,
geographic frame of reference 100, is shown in FIG. 1 and second
frame of reference, relative frame of reference 200, is shown in
FIG. 2.
As used herein, the "points of interest" include a first physical
object such as ownship 1, and a second, target 2, such as second
vessel. As further used herein, "ownship" means a first reference
point that is not a target, i.e. the vessel making the
calculations. Each of these points of interest may be in motion or
stationary, and, if in motion, may be in motion in different planes
with respect to each other. "Target motion analysis" or TMA means
that the course and speed for target 2, which may initially be
unknown, are resolved as well as the range to and bearing of target
2 at or for a predetermined time frame with respect to ownship 1.
In a preferred embodiment of the present inventions, bearing at
CPA, time of CPA, a minimum range to the target with associated
course and speed for the minimum range only as a limiting
condition, and an initial estimate of the target's true range,
course and speed may be determined.
The methods of the present inventions are not limited to surface or
subsea water vessels. By way of example and not limitation, target
2 may be another vessel, an iceberg, a submerged object such as a
ledge or reef, or the like, assuming that target 2 emits a signal
that can be detected by a passive sensor for the passive solution.
Further, the methods of the present inventions may be used with
partially or fully submerged features such as rocks or debris,
floating materials, stationary materials, and the like, or
combinations thereof, especially if the presence of such features
may be determined, but a measurement of range to the feature may be
lacking in the detection device that detects the feature. However,
it is expressly understood that active as well as passive data may
be used in the present inventions' methods, in which case any
single active signal may be used to determine a range value which
can then be used in conjunction with passive data to fully resolve
range, bearing, course and speed.
In general, the present inventions' methods comprise obtaining at
least three bearing and time data points for a first estimate, e.g.
at time points t.sub.1, t.sub.2, t.sub.3, t.sub.4. These data are
used to isolate a passive TMA estimate based on a single leg of
time tagged, bearings only data, i.e. no maneuvering of the first
point of interest such as ownship 1 is required to obtain a passive
estimate. Further, the present inventions' methods comprise a
closed form expression for an estimate that may be resolved in a
single iteration as opposed to prior art methods such as those
using first order statistical solutions.
The present inventions' methods utilize velocity vectors of the two
items of interest, i.e. vector 13 and estimated vector 30. These
velocity vectors, when arranged to determine their vector
difference, form one side 52, 53 of a parallelogram as well as a
diagonal of that parallelogram, shown as darkened portion 51 of
vector 13. For the parallelogram to remain a parallelogram when
angles of vertices of the parallelogram change, the perpendicular
distances to respective opposite sides of the parallelogram change
in a predetermined fashion, i.e. as the angles of the parallelogram
whose diagonal remains at substantially the same orientation to
ownship 1's constant course, change from .pi./2, the corresponding
length of the diagonal must increase by an amount equal to the
relative velocity of ownship 1 and target 2 multiplied by the new
elapsed time value for the second course crossing minus t.sub.0,
such that perpendicular distance to opposing sides increases by an
amount proportional to twice the range at CPA. Additionally, the
greater the difference between values of adjacent vertices, the
smaller the perpendicular distance to opposing sides.
Further, successive time-lagged bearing lines, e.g. lines 11 and
12, form a parabola, shown as solution parabola 15, in geometric
reference frame 100 for substantially all geometries involving two
points of interest 1,2, where each of the points of interest 1,2
maintains a substantially constant respective course and speed over
a time period used for obtaining bearing measurements. Solution
parabola 15 is formed by recognizing that each of the bearing lines
11,12,13,20,30 in geographic reference frame 100 are tangent to
solution parabola 15 at a predetermined, unique point. If the
bearing lines of a data set belonging to one target are tangent to
solution parabola 15 at various points along solution parabola 15,
and if the angles of the parallelogram vertices change such that
the angle of course incidence deviates from the value at which the
relative velocity vector bisects the angle of course incidence and
the courses represented by two of the parallelogram sides are
constrained to remain tangent to the parallelogram, the
perpendicular distance to opposing sides always increases. This
increase may only be accomplished by increasing the parallelogram
perimeter.
Accordingly, solution parabola 15 will be fixed in geographic
reference frame 100, and each data set to be gathered will generate
one and one only solution parabola 15, although different data sets
may generate the same solution parabola 15. Further, for all
potential pairs of bearing lines 11,12,13,20,30 tangent to solution
parabola 15 when the course of ownship 1 is one of the bearing
lines and remains fixed, e.g. line 13, the value of the bearing at
the CPA, e.g. angle 50', is constant for potential ranges at CPA.
As a result, the difference vector of each potential velocity
vector pair, i.e. velocity vector for target 2 and velocity vector
of ownship 1, remains parallel for all geometries involving those
two points of interest where each point of interest 1, 2 maintains
its respective course and speed at a constant value during the time
of measurements and calculation. This allows calculation of bearing
at CPA, time of CPA, and minimum range at CPA, with data comprising
a single leg of passive, time tagged bearings. Further, this allows
estimates of TMA solutions based on minimum range and preferred
range estimates with data comprising a single leg of passive, time
tagged bearings.
Referring now to FIG. 2, to help ensure that solution parabola 15
is fixed at the correct location in geographic reference frame 100,
the presently preferred embodiment of the present inventions'
methods requires fixing an ownship 1 at rest reference frame 200
with respect to geographic reference frame 100. In the preferred
embodiment, this may be accomplished by requiring that the location
of ownship 1 at an initial time t.sub.0 is the same point in the
two reference frames, e.g. 10, and that the bearing value BRG.sub.0
is equal to zero (as used herein "BRG" means bearing).
In the case where the incident angle of the mutual courses of
target 2 and ownship 1 is greater than .pi./2, an additional step
may be required to reflect the original bearing line data, e.g. 13,
around a preferred bearing line in the original data set indicated
by the axis of original solution parabola 15 to generate revised
parabola 15 for a set of pseudo-data that reflects the course of
target 2 in a reference frame for which the incident angles of
courses is less than .pi./2. This situation will also require
extrapolating the course of ownship 1 into a predetermined future
time point and reversing the course such that the ownship arrives
at the same point at the time ownship 1 crosses the course of
target 2.
Referring additionally to FIG. 1, ownship 1 is located initially at
point 10. In the preferred embodiment, a first step to calculation
of solution parabola 15 is to obtain three bearing data points,
e.g. at times t.sub.1,t.sub.2,t.sub.3,or t.sub.4, wherein the times
t.sub.1,t.sub.2,t.sub.3, or t.sub.4 at which the bearing data
points were obtained are also obtained. Bearing data is collected
in a fixed ownship reference frame such as frame 100. At a minimum,
three bearing-time data points are obtained that are relative
bearings with respect to point 10.
Bearing data may then be translated to a moving ownship reference
frame 200. Two sets of data may form vectors, one set representing
target 2, e.g. 30, and the other set representing ownship 1, e.g.
13, which may then cross each other at different times. By way of
example and not limitation, vectors 30 and 13 may cross when target
2 appears at 0.degree. relative bearing or 180.degree. known
bearing, or when ownship 1 appears at 0.degree. relative to the
course of target 2 or when ownship 1 appears at 180.degree. unknown
to the course of target 2.
As will be understood, a large, potentially infinite number of
potential solution points may exist based on passive bearing data.
Accordingly, the present inventions' method selects at least one
potential solution point, e.g. bearing line 20, to indicate a range
at CPA. In a preferred embodiment, bearing line 20 may be selected
manually by examining target geometry. In alternative embodiments,
bearing line 20 may be selected automatically such as by using
artificial intelligence methods, heuristics, or the like, or a
combination thereof.
Referring back to FIG. 1, once the initial three bearing data are
obtained, a first estimate may be computed for relative bearing at
CPA, as well as a time of CPA, by the following formulae:
tan(.theta..sub..beta.-.theta..sub.i)/=V.sub.REL(t.sub..beta.-t.sub.i)/R.-
sub.CPA|.theta..sub.i=0 (1)
t.sub..beta.=R.sub.CPA[tan(.theta..sub..beta.-.theta..sub.i)/V.sub.REL]+t-
.sub.i|.theta..sub.i=0 (2)
.theta..beta..function..function..theta..times..DELTA..times..times..func-
tion..theta..times..DELTA..times..times..function..theta..times..DELTA..ti-
mes..times..function..theta..times..function..theta..times..DELTA..times..-
times..function..theta..times..function..theta..times..DELTA..times..times-
..function..theta..times..function..theta..times..DELTA..times..times.
##EQU00001## In these equations (1), (2), and (3),
.theta..sub..beta. is as defined in equation (3) and
representatively shown as angle 50 in FIG. 1; .theta..sub.i is the
bearing angle to the target 2 relative to ownship 1 at time t.sub.i
and representatively shown as angle 50' in FIG. 1; t.sub..beta. is
the time at which .theta..sub..beta. was measured; t.sub.i is the
time at which .theta..sub.i was measured; .DELTA.t is the
difference between two time measurements, e.g. .DELTA.t.sub.j,k is
the difference between time t.sub.j and time t.sub.k; V.sub.REL is
the difference velocity between target 2 and ownship 1; and
R.sub.CPA is the range to target 2 at CPA.
The formulae of the present inventions' methods may then be used to
calculate a bearing fan to determine bearing data at a
predetermined time in the future, independent of other position
data. A bearing fan is a group of bearing data spaced at
predetermined points in time that predicts where in bearing space
target 2 will be at some point in future time, assuming that target
2 and ownship 1 maintain their current course and speed. By way of
example and not limitation, the present inventions may be used to
generate both relative and true bearings and time at CPA, where the
time at relative bearing equals zero degrees (0.degree.) or one
hundred eighty degrees (180.degree.).
The formulae also provide an early estimate of minimum target
ranges for any bearing, independent of other position data.
Further, the formulae may be useful in many other ways, by way of
example and not limitation for providing parameters useful for
early target maneuver detectors or Open/Close determinations as
well as estimates of a ratio of relative speed to range at CPA.
The present inventions' methods may further be used to provide a
real-time measure of the effect of noise on potential solutions. In
a preferred embodiment, this real-time measure begins with a fourth
data point, e.g. data point t.sub.4.
Having selected a potential solution point, e.g. bearing line 20,
the direction of the relative velocity vector 60 can be
determined.
Referring now to FIG. 4, in a preferred embodiment, data obtained
for the calculations defined herein are preferably manipulated by
computer 200 which has been programmed to carry out the functions
set forth in this description and typically accessible to ownship 1
such as by being onboard ownship 1. Computer 200 may comprise any
suitable computer known in the art. Computer 200 further comprises
a processor, memory, and output device (not shown in the figures)
as well as range calculation software executing within computer
200. Output device 210 may comprise a display device 210, a hard
copy device 212, or the like, or a combination thereof.
Data sets comprising passive bearing data may be gathered such as
by using one or more sensors (shown as 230 in FIG. 4 for
illustration) deployed within or near ownship 1 and capable of
passively obtaining a bearing to target 2 from a desired location
such as ownship 1 and providing measurements related to target 2
and ownship 1. Sensors 230 may comprise any suitable sensors known
in the art such as passive acoustic sensors. The data may be
passively obtained by numerous means as will be familiar to those
of ordinary skill in the passive data acquisition arts. Once
gathered, these data may be stored for later processing in the
memory of computer 200 or in a passive bearing data collection
device (not shown in the figures) that is addressably in
communication with the computer. The analysis performed may occur
within the computer or a portion of the computer which has been
programmed to analyze the data received by the sensors.
Using the range calculation software, the computer may retrieve at
least three of the stored bearing data points obtained from the
bearing detector, such as from the computer's memory. The range
calculation software may then use the three retrieved bearing data
points to determine a speed contribution V.sub.os
.Iadd.cos(.theta..sub..beta.) .Iaddend.of a first point of interest
to a distance from a relative velocity vector over a time from
t.sub.0 to t.sub.0' in accordance with the teachings of the present
inventions. By way of example and not limitation, in accordance
with the teachings of the present inventions the range calculation
software may determine an angle .theta..sub..beta. defined by the
bearing of target 2 relative to a heading of ownship 1 at the point
in time of closest approach to a second point of interest and then
calculates a minimum range from the source to the target as Min
R.sub.CPA=V.sub.os(t.sub..beta.-t.sub.i)cos(.theta..sub..beta.-.theta..su-
b.i).sub..theta..sub.i.sub.|=0; and
The range calculation software may then generate a representation
of the probability of the location of target 1 and present that
information such as on the output device.
In the operation of an exemplary embodiment, referring to FIG. 1
and FIG. 2, it is first noted that the following expression holds
for linear motion when an object moving in a straight line with a
velocity of V.sub.R, e.g. target 2, passes a stationary observer,
e.g. ownship 1, at a distance of R.sub.CPA where R.sub.CPA is the
distance at closest approach to the stationary observer:
tan(.theta..sub.i-.theta..sub.0)=(t.sub.i-t.sub.0)(V.sub.R/R.sub.CPA)
(4) As used in equation (4), .theta..sub.0 is the angle between
ownship 1's heading and target 2 at an initial time t.sub.0;
.theta..sub.i is the angle between ownship 1's heading and target 2
at time t.sub.i; t.sub.i is the time of bearing reading
.theta..sub.i; and t.sub.0 is the time of bearing reading
.theta..sub.0. Further, the ratio V.sub.R/R.sub.CPA is a calculated
value, and therefore V.sub.R may be estimated based on an estimated
value of R.sub.CPA. Alternatively, R.sub.CPA may be estimated based
on an estimated value of V.sub.R.
Additionally, it is noted that relative velocity vector 60 is
perpendicular to the relative bearing line 20 at CPA in fixed
ownship reference frame 100, allowing for calculation of a minimum
range estimate at CPA R.sub.CPA that is substantially independent
of actual contact range. By way of example and not limitation,
although at this point the "correct" solution may be unknown, a
minimum range estimate calculation is possible because a point when
CPA occurs is known as is the point at which target 2 is detected
at relative bearing equals .theta..sub..beta.. The minimum range
estimate for the distance at which ownship 1 is closest to target
2, R.sub.CPA, shown in FIG. 1 at 51, may be calculated by: Min
R.sub.CPA=V.sub.os(t.sub..beta.-t.sub.0)cos(.theta..sub..beta.-.theta..su-
b.0) (5) In equation (5), t.sub..beta. is the time at which
.theta..sub..beta. was measured; t.sub.0 is the time of bearing
reading .theta..sub.0; V.sub.os is magnitude of the velocity of
ownship; and .theta..sub.0 is the angle between ownship 1's heading
and target 2 at a time t.sub.i=0.
If an actual solution is selected, a right triangle may be formed
by using ownship vector 51 multiplied by the .DELTA.t.sub.CPA as
the hypotenuse 32 of that triangle. Accordingly, the contact's
range at CPA may be determined using hypotenuse 32, the relative
bearing at CPA, and the relative velocity vector as follows:
R.sub.CPA.sub.est=V.sub.OS*.DELTA.t.sub.CC*cos(.theta..sub..beta.)
(6) where .DELTA.t.sub.CC is the difference between course
crossings, course crossings being defined as the time when ownship
1 crosses the target 2's course and to and the other components
have the definitions given above.
Accordingly, using these estimates, the following calculations can
then be made. For bearing BRG at CPA, independent of actual contact
range,
.theta..beta..function..function..theta..times..DELTA..times..times..func-
tion..theta..times..DELTA..times..times..function..theta..times..DELTA..ti-
mes..times..function..theta..times..function..theta..times..DELTA..times..-
times..function..theta..times..function..theta..times..DELTA..times..times-
..function..theta..times..function..theta..times..DELTA..times..times.
##EQU00002## In equation (7), .theta..sub.i is the angle between
ownship 1's heading and target 2 at time t.sub.i; .theta..sub.j is
the angle between ownship 1's heading and target 2 at time t.sub.j;
.theta..sub.k is the angle between ownship 1's heading and target 2
at time t.sub.k; and .DELTA.t.sub..alpha.,.beta. is the time
difference between measurements .theta..sub..alpha.,
.theta..sub..beta. respectively, i.e., where .alpha. and .beta. are
generic indices which are respectively pair-wise, i.e. (j,k),
(k,i), and (i,j).
For the ratio of relative speed to the range at CPA,
.function..theta..beta..function..theta..function..theta..beta..times..fu-
nction..theta..function..theta..beta..function..theta..function..theta..be-
ta..times..function..theta..DELTA..times..times. ##EQU00003## In
equation (8), .theta..sub..beta. is the BRG at CPA; .theta..sub.i
is the angle between ownship 1's heading and target 2 at time
t.sub.i; .theta..sub.j is the angle between ownship 1's heading and
target 2 at time t.sub.j; and .DELTA.t.sub.i,j is the time
difference between measurements .theta..sub.i and
.theta..sub.j.
For the time of CPA independent of actual contact range,
.beta..function..function..theta..beta..theta..times..theta.
##EQU00004## In equation (9), .theta..sub..beta. is the angle
between ownship 1's heading and target 2 at CPA; .theta..sub.i is
the angle between ownship 1's heading and target 2 at time t.sub.i;
t.sub.i is the time of bearing reading .theta..sub.i; and
t.sub..beta. is the time of bearing reading .theta..sub..beta.,
time at which CPA occurs.
For an estimate of the minimum range at CPA, independent of actual
contact range,
MinR.sub.CPA=V.sub.os(t.sub..beta.-t.sub.i)cos(.theta..sub..beta.-.theta.-
.sub.i).sub..theta..sub.i.sub.|=0 (10) In equation (10),
.theta..sub..beta. is the angle between ownship 1's heading and
target 2 at CPA; .theta..sub.i is the angle between ownship 1's
heading and target 2 at time t.sub.i; V.sub.os is a magnitude of
ownship's velocity; t.sub.i is time of bearing reading
.theta..sub.i; and t.sub..beta. is the is the time at which
.theta..sub..beta. was measured.
Using these formulae, an estimate of minimum range at a
predetermined time may therefore calculated by: Min R.sub.est=Min.
R.sub.CPA/cos(.theta..sub..beta.-.theta..sub.j)|.theta..sub.j=current
bearing measure (11) where the terms in equation (11) are defined
above.
Further, from an estimate of R.sub.CPA(Minimum) an estimate of the
current minimum range at any time t.sub.i make be found using the
following formula:
R.sub.(CURRENTMINIMUM)=R.sub.CPA(MINIMUM)/cos(.theta..sub.0-.theta..sub.i-
) (14)
In an exemplary embodiment, the above may be used to base target
open-close on measurements calculated at the time of the
decision.
Referring now to FIG. 3, a Cartesian graph of target maneuvers and
noise, if more than three points are used, a series of subsequent
measurements may be used to determine maneuvering of target 2. By
way of example and not limitation, a set of five or more usable
bearing points may be obtained as a set of calculated points
C.sub.1, C.sub.2, and C.sub.3 in accordance with the teachings of
the present inventions during times {t.sub.1,t.sub.2,t.sub.3},
{t.sub.2,t.sub.3,t.sub.4}, and {t.sub.3,t.sub.4,t.sub.5} (these
time points are not shown in FIG. 3). Points C.sub.1, C.sub.2, and
C.sub.3 may be extrapolated to indicate that target 2 (shown as the
dark circles in FIG. 3) is maneuvering in a non-linear fashion.
Additionally, the estimates may be used to determine noise or a
range of noise in the readings. By way of example and not
limitation, a set of five or more usable bearing points may be
interpreted as a set of calculated points P.sub.1, P.sub.2, and
P.sub.3 obtained in accordance with the teachings of the present
inventions during times {t.sub.6,t.sub.7,t.sub.8},
{t.sub.7,t.sub.8,t.sub.9}, and {t.sub.8,t.sub.9,t.sub.10} (these
time points are not shown in FIG. 3). However, P.sub.2 can be seen
to have deviated from a predicted point P.sub.2', indicating that
noise is present in the system. In a currently envisioned
embodiment, trends over time may therefore use these deviations to
estimate the amount and effects of noise present in the system. If
an assumption is made that any set of four points represents a
stable, noise-free solution, analysis of deviation from a predicted
point may be made with four points. In such an analysis, a fifth
point may then be obtained and used to determine if the deviation
is random or the result of a deterministic event, e.g. a
maneuvering of target 2. Thus, a minimum set of points required to
detect the possible presence of noise is four, and the minimum set
of points required to detect the possible presence of maneuvering
of target 2 is five.
Referring back to FIG. 2, in a reference frame 200 relative to a
position of ownship 1, three bearing/time measurements are taken,
an angle to bearing at CPA relative to a heading of ownship 1 is
calculated, and the time of CPA is calculated. Based on the
teachings of these inventions that target 2 and ownship 1 remain on
a constant course and speed over a period of time required to
collect bearing measurements, a fourth data point may be obtained.
When taken with any of the other two of the three bearing data
points, the fourth data point should yield the same solution, i.e.,
the angle to bearing at CPA relative to the heading of ownship 1,
and the time of CPA will be constant for all combinations of the
three of four bearing data points. A deviation in the bearing at
CPA relative to the heading of ownship 1 and the time of CPA
represents noise in the system which can be detected by this method
of calculating the angle to bearing at CPA for each potential
solution.
Prior art methods look at each bearing measurement as a unique
point in "the" solution set and do not consider triplet-wise
combinations of points as potential solutions to the angle at CPA,
each one as valid as the other, if the bearing measurements are
independent. Therefore, with the present inventions, with four data
points, four potential solutions may be investigated; with five
independent points, ten potential solutions may be investigated;
and with six independent points, twenty potential solutions may be
investigated. This is quickly recognized as the number of possible
combinations of n items taken three at a time. A statistical
analysis of the potential solutions may then yield trends and/or
the mean and standard deviation of bearings at CPA. The mean of the
bearing at CPA and the mean time of CPA are more accurate solutions
of the bearing at CPA and time of CPA than any one potential
solution based on a triplet of bearing measurements.
Thus, the present inventions may allow creating twenty solutions
with only six data points rather than waiting for twenty data
points. Likewise, four points may be sufficient to determine that
there is noise in system and calculating four bearing angle
solutions at CPA provides a first order estimate of the magnitude
of the noise and a first order estimate of the mean bearing at CPA
and mean time of CPA.
It is also noted that in the preferred embodiment, bearing rate
curve inflection points are always plus or minus around 30.degree.
of the BRG at CPA.
It will be understood that various changes in the details,
materials, and arrangements of the parts which have been described
and illustrated above in order to explain the nature of this
inventions may be made by those skilled in the art without
departing from the principle and scope of the inventions as recited
in the following claims.
* * * * *
References