CN109031229B - Probability hypothesis density method for target tracking in clutter environment - Google Patents

Probability hypothesis density method for target tracking in clutter environment Download PDF

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CN109031229B
CN109031229B CN201810692989.5A CN201810692989A CN109031229B CN 109031229 B CN109031229 B CN 109031229B CN 201810692989 A CN201810692989 A CN 201810692989A CN 109031229 B CN109031229 B CN 109031229B
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clutter
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CN109031229A (en
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解梅
苏星霖
薛铮
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University of Electronic Science and Technology of China
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/414—Discriminating targets with respect to background clutter

Abstract

The invention discloses a probability hypothesis density method for target tracking in a clutter environment, and belongs to the technical field of radars. Firstly, dividing the whole monitoring area into a plurality of clutter sub-areas by utilizing the difference of prior clutter densities according to the prior clutter map information of the monitoring area; in each tracking period, each clutter sub-region is respectively processed according to different parameters of different clutter rates; for each subarea, adopting GM-PHD assisted by echo amplitude to carry out filtering tracking; and an improved Gaussian component pruning scheme is adopted to improve the detection rate of the new target.

Description

Probability hypothesis density method for target tracking in clutter environment
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a probability hypothesis density method for target tracking in a clutter environment.
Background
In recent years, target tracking technology based on random finite sets has gained wide attention. The target tracking theory based on the random finite set respectively models all state sets and observed values obtained by each observation into set value state and set value observation, thereby avoiding complex data association process and directly utilizing the optimal Bayes technology to realize target tracking under clutter background, association and uncertain detection. There are many possible theoretical approximation filters that can be used in engineering implementation, and the gaussian probability density hypothesis (GM-PHD) algorithm used herein is one of them. The standard GM-PHD algorithm still has some disadvantages. In practical situations, due to the complexity of environments such as terrain, the background of a monitored area is not uniform in space, so that the density of clutter in the monitored area is not uniform, and the GM-PHD algorithm assumes that the clutter is uniformly distributed in the whole monitored area and tracks the clutter, which inevitably causes instability of tracking performance. For the radar in the fixed monitoring area, on the premise that the clutter density is assumed to change only in space and is basically unchanged or slowly changed in time, the clutter distribution condition of the monitoring area is obtained and a prior clutter map is formed, and then the target tracking is assisted by utilizing the prior information of the clutter map. It is also feasible to use the echo amplitudes to assist target tracking, since the echo amplitudes from the target and the echo amplitudes from the clutter have different probability density distributions. In addition, in order to deal with the problem that the new target is not in the assumed target probability region, the strategy of cutting and combining the Gaussian components can be changed, and the initial probability of the new target is improved. Based on the above description, the invention provides a GM-PHD method combining a prior clutter map, a target echo amplitude and an improved pruning strategy.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a probability hypothesis density method for target tracking in a clutter environment.
The technical problem proposed by the invention is solved as follows:
a probability hypothesis density method for target tracking in clutter environment comprises the following steps:
A. establishing a priori clutter map
Modeling a clutter map of a monitoring area as a combination of a plurality of areas with different clutter densities, and constructing clutter prior information of the monitoring area on the assumption that the clutter density in each clutter area is uniformly distributed;
B. knowledge-aided tracking, for each simulation instant
According to the GM-PHD algorithm, the posterior intensity function v is determined from the state at the time k-1 k-1 (x) Calculating a state prediction strength function v at the moment k k|k-1 (x) (ii) a Predicting intensity function v from state at time k k|k-1 (x) Calculating the posterior intensity function v of the state at the moment k k (x) (ii) a On the basis of the calculation result of the standard GM-PHD algorithm, v is modified according to the echo amplitude and clutter distribution information k (x) The weight value of each Gaussian component;
step C: gaussian pruning and state extraction, to state posterior intensity function v k (x) Adopting a pruning strategy: deleting all Gaussian components with weight values smaller than a specified threshold, if all the Gaussian component weights derived from a certain measured value are smaller than the specified threshold, keeping the component with the maximum weight derived from the measured value, and modifying the weight of the component into the specified threshold; and normalizing the weight of the Gaussian components after the pruning strategy is adopted, calculating the merging distance of the Gaussian components, and merging the Gaussian components to obtain the final estimation result of the target state.
According to the method, the whole monitoring area is divided into a plurality of clutter sub-areas by utilizing the difference of prior clutter densities according to the prior clutter map information of the monitoring area; in each tracking period, each clutter sub-region is respectively processed according to different parameters of different clutter rates; and for each sub-area, adopting the GM-PHD assisted by the echo amplitude to carry out filtering tracking, and adopting an improved Gaussian component pruning scheme to improve the detection rate of the new target.
The invention has the beneficial effects that:
the algorithm of the invention utilizes priori knowledge to assist target tracking, utilizes priori clutter information of radar monitoring areas, and adopts different parameters to track and filter areas with different clutter densities; meanwhile, the amplitude information of the radar echo signal is utilized, and a filtering updating equation is modified according to different target echoes and clutter echo distributions; in addition, the pruning rule of the Gaussian mixture probability hypothesis density algorithm is modified, and the tracking starting probability of the target is improved.
Drawings
FIG. 1 is a prior knowledge assistance diagram;
fig. 2 is a flow chart of gaussian pruning and state extraction.
Detailed Description
The invention is further described below with reference to the figures and examples.
The present embodiment provides a method for probability hypothesis density of target tracking in a clutter environment, where an auxiliary schematic diagram of prior knowledge is shown in fig. 1, and the method includes the following steps:
step A, establishing a prior clutter map
Modeling a clutter map of a monitored region as a combination of regions of different clutter densities, assuming that the clutter density within each clutter region is subject to uniform distribution, the different clutter regions having different clutter densities, i.e. V = V 1 ∪V 2 ∪...∪V M Wherein V denotes the entire detection area, V 1 ～V M Representing different clutter areas divided by different clutter densities, wherein M is the total number of the clutter areas; recording clutter prior information for each clutter region including an average false alarm count for each clutter region
Figure BDA0001711343380000021
And false alarm location distribution density
Figure BDA0001711343380000022
Step B, knowledge-aided tracking
Step B-1, predicting:
the posterior intensity function of the target state vector x at time k-1 is assumed to be of the following Gaussian mixture:
Figure BDA0001711343380000031
wherein, J k-1 J =1, 2.. J. k-1 ，
Figure BDA0001711343380000032
And
Figure BDA0001711343380000033
respectively the weight, mean and covariance matrix of the jth Gaussian component at the time k-1,
Figure BDA0001711343380000034
represents a mean value of
Figure BDA0001711343380000035
Covariance matrix
Figure BDA0001711343380000036
A gaussian distribution of;
the state prediction strength function at the time k is as follows:
Figure BDA0001711343380000037
wherein p is S In order to target the probability of survival,
Figure BDA0001711343380000038
and
Figure BDA0001711343380000039
respectively the mean and covariance matrices of the calculated jth predicted strength gaussian component at time k,
Figure BDA00017113433800000310
the method comprises the following steps of (1) taking a motion prediction matrix of a target, Q a process noise covariance matrix, and superscript T as a transposition; j is a unit of γ，k For the number of new target gaussian components at time k, h =1,2 γ，k ；
Figure BDA00017113433800000311
Figure BDA00017113433800000312
And
Figure BDA00017113433800000313
respectively is the weight, the mean value and the covariance matrix of the h-th Gaussian component of the new target intensity function at the moment k,
Figure BDA00017113433800000314
represents a mean value of
Figure BDA00017113433800000315
The covariance matrix is
Figure BDA00017113433800000316
A gaussian distribution of (d);
step B-2, updating:
predicting the state by a strength function v k|k-1 (x) The rewrite is:
Figure BDA00017113433800000317
wherein, J k|k-1 Predict the number of gaussian components of the intensity function for the state, l =1,2 k|k-1 ；
Figure BDA00017113433800000318
And
Figure BDA00017113433800000319
respectively the weight, mean and covariance matrix of the ith gaussian component,
Figure BDA00017113433800000320
represents a mean value of
Figure BDA00017113433800000321
The covariance matrix is
Figure BDA00017113433800000322
(ii) a gaussian distribution of;
the gaussian posterior intensity formula updated at time k is:
Figure BDA00017113433800000323
wherein p is D Is a target detection probability, m z For efficient number of measurements, n =1,2 z ，
Figure BDA00017113433800000324
z n Is a measure of the return of the radar,
Figure BDA0001711343380000041
h is a target measurement matrix, R is a measurement noise covariance matrix,
Figure BDA0001711343380000042
represents a mean value of
Figure BDA0001711343380000043
Covariance matrix of
Figure BDA0001711343380000044
A gaussian distribution of (d); weight of
Figure BDA0001711343380000045
The calculation formula of (a) is as follows:
Figure BDA0001711343380000046
wherein λ is k As a measured value z n Average false alarm number of clutter area, c k As a measured value z n Distribution density of false alarm positions of the clutter region, a n As a measured value z n The amplitude of the echo of (a) is,
Figure BDA0001711343380000047
a false alarm amplitude likelihood function representing a detection threshold of tau,
Figure BDA0001711343380000048
representing a target amplitude likelihood function with a detection threshold of tau,
Figure BDA0001711343380000049
represents a mean value of
Figure BDA00017113433800000410
The covariance matrix is
Figure BDA00017113433800000411
(ii) a gaussian distribution of;
step C, to Gaussian posterior intensity v k (x) Gaussian pruning and state extraction are performed, the flow chart of which is shown in fig. 2:
step C-1, deleting weighted value
Figure BDA00017113433800000412
Less than a predetermined threshold epsilon 1 All gaussian components of (a);
if the value z is measured n All derived Gaussian component weight values are less than epsilon 1 Then the component with the largest weight is retained and its weight value is modified to epsilon 1 ；
Step C-2, rewriting the Gaussian component after the step C-1 into the following form:
Figure BDA00017113433800000413
wherein, J k|k The number of gaussian components after gaussian pruning at the time k,
Figure BDA00017113433800000414
and
Figure BDA00017113433800000415
respectively the weight, mean and covariance matrix of the u-th gaussian component,
Figure BDA00017113433800000416
represents a mean value of
Figure BDA00017113433800000417
The covariance matrix is
Figure BDA00017113433800000418
A gaussian distribution of (d);
step C-3. Calculate v k|k (x) Combined distance of gaussian components:
Figure BDA00017113433800000419
wherein v =1,2 k|k ，w＝1，2，...，J k|k And v ≠ w;
if d is vw Less than a merging threshold epsilon 2 The corresponding two gaussian components are combined into a single gaussian component, denoted as (w) vw ，m vw ，P vw ) And has:
Figure BDA00017113433800000420
Figure BDA0001711343380000051
Figure BDA0001711343380000052
step C-4, rewriting the Gaussian component after the step C-3 into the following form:
Figure BDA0001711343380000053
wherein, J k R =1,2.., J, the number of combined gaussian components k ，
Figure BDA0001711343380000054
And
Figure BDA0001711343380000055
respectively the weight, mean and covariance matrix of the r-th gaussian component,
Figure BDA0001711343380000056
represents a mean value of
Figure BDA0001711343380000057
The covariance matrix is
Figure BDA0001711343380000058
(ii) a gaussian distribution of;
extraction of v k|k (x) The weight being greater than a threshold epsilon 3 As a final estimation result of the target state:
Figure BDA0001711343380000059

Claims (1)

1. a probability hypothesis density method for target tracking in clutter environment is characterized by comprising the following steps:
A. establishing a priori clutter map
Modeling a clutter map of a monitoring area as a combination of a plurality of areas with different clutter densities, and constructing clutter prior information of the monitoring area on the assumption that the clutter density in each clutter area is uniformly distributed;
the specific process of the step A is as follows:
modeling a clutter map of a monitored region as a combination of regions of different clutter densities, assuming that the clutter density within each clutter region is subject to uniform distribution, the different clutter regions having different clutter densities, i.e. V = V 1 ∪V 2 ∪...∪V M Wherein V represents the entire detection region, V 1 ～V M Representing different clutter areas divided by different clutter densities, wherein M is the total number of the clutter areas; recording clutter prior information for each clutter region, including the average of each clutter regionNumber of average false alarms
Figure FDA0003631520530000011
And false alarm location distribution density
Figure FDA0003631520530000012
B. Knowledge-aided tracking, for each simulation instant
According to the GM-PHD algorithm, from the state posterior intensity function v at the time k-1 k-1 (x) Calculating a state prediction strength function v at the moment k k|k-1 (x) (ii) a Predicting the intensity function v from the state at the time k k|k-1 (x) Calculating the posterior intensity function v of the state at the moment k k (x) (ii) a On the basis of the calculation result of the standard GM-PHD algorithm, v is modified according to the echo amplitude and clutter distribution information k (x) The weight value of each Gaussian component;
the specific process of the step B is as follows:
step B-1, predicting:
the posterior intensity function of the target state vector x at time k-1 is assumed to be of the following mixed gaussian form:
Figure FDA0003631520530000013
wherein, J k-1 J =1, 2.. J. k-1 ，
Figure FDA0003631520530000014
And
Figure FDA0003631520530000015
respectively the weight, mean and covariance matrix of the jth Gaussian component at the time k-1,
Figure FDA0003631520530000016
represents a mean value of
Figure FDA0003631520530000017
Covariance matrix
Figure FDA0003631520530000018
A gaussian distribution of;
the state prediction strength function at the time k is as follows:
Figure FDA0003631520530000019
wherein p is S In order to target the probability of survival,
Figure FDA00036315205300000110
and
Figure FDA00036315205300000111
respectively the mean and covariance matrices of the calculated jth predicted strength gaussian component at time k,
Figure FDA0003631520530000021
f is a motion prediction matrix of the target, Q is a process noise covariance matrix, and superscript T represents transposition; j. the design is a square γ,k For the number of new target gaussian components at time k, h =1,2 γ,k ；
Figure FDA0003631520530000022
Figure FDA0003631520530000023
And
Figure FDA0003631520530000024
respectively is the weight, the mean value and the covariance matrix of the h-th Gaussian component of the new target intensity function at the moment k,
Figure FDA0003631520530000025
represents a mean value of
Figure FDA0003631520530000026
The covariance matrix is
Figure FDA0003631520530000027
(ii) a gaussian distribution of;
step B-2, updating:
predicting the state by a strength function v k|k-1 (x) The rewrite is:
Figure FDA0003631520530000028
wherein, J k|k-1 Predict the number of gaussian components of the intensity function for the state, l =1,2 k|k-1 ；
Figure FDA0003631520530000029
And
Figure FDA00036315205300000210
respectively the weight, mean and covariance matrix of the ith gaussian component,
Figure FDA00036315205300000211
represents a mean value of
Figure FDA00036315205300000212
Covariance matrix of
Figure FDA00036315205300000213
A gaussian distribution of (d);
the gaussian posterior intensity formula updated at time k is:
Figure FDA00036315205300000214
wherein p is D Is the target detection probability, m z For an effective number of measurements, n =1,2,. Multidot.m z ，
Figure FDA00036315205300000215
z n Is a measure of the return of the radar,
Figure FDA00036315205300000216
h is a target measurement matrix, R is a measurement noise covariance matrix,
Figure FDA00036315205300000217
Figure FDA00036315205300000218
represents a mean value of
Figure FDA00036315205300000219
The covariance matrix is
Figure FDA00036315205300000220
A gaussian distribution of (d); weight of
Figure FDA00036315205300000221
The calculation formula of (a) is as follows:
Figure FDA00036315205300000222
wherein λ is k As a measured value z n Average false alarm number of clutter area, c k As a measured value z n Distribution density of false alarm positions of clutter areas, a n As a measured value z n The amplitude of the echo of (a) is,
Figure FDA00036315205300000223
a false alarm amplitude likelihood function representing a detection threshold t,
Figure FDA00036315205300000224
representing a target amplitude likelihood function with a detection threshold of tau,
Figure FDA00036315205300000225
represents a mean value of
Figure FDA00036315205300000226
Covariance matrix of
Figure FDA00036315205300000227
(ii) a gaussian distribution of;
step C: gaussian pruning and state extraction, to state posterior intensity function v k (x) Adopting a pruning strategy: deleting all Gaussian components with weight values smaller than a specified threshold, if all the Gaussian component weights derived from a certain measured value are smaller than the specified threshold, keeping the component with the maximum weight derived from the measured value, and modifying the weight of the component into the specified threshold; normalizing the weight of the Gaussian components after the pruning strategy is adopted, calculating the merging distance of the Gaussian components, and merging the Gaussian components to obtain a final estimation result of the target state;
the specific process of the step C is as follows:
step C-1, deleting weighted value
Figure FDA0003631520530000031
Less than a prescribed threshold value epsilon 1 All gaussian components of (a);
if the measured value z is n All derived Gaussian component weight values are less than epsilon 1 Then the component with the largest weight is retained and its weight value is modified to epsilon 1 ；
Step C-2, rewriting the Gaussian component after the step C-1 into the following form:
Figure FDA0003631520530000032
wherein, J k|k The number of gaussian components after gaussian pruning at the time k,
Figure FDA0003631520530000033
and
Figure FDA0003631520530000034
respectively the weight, mean and covariance matrix of the u-th gaussian component,
Figure FDA0003631520530000035
represents a mean value of
Figure FDA0003631520530000036
Covariance matrix of
Figure FDA0003631520530000037
A gaussian distribution of (d);
step C-3. Calculate v k|k (x) Combined distance of gaussian components:
Figure FDA0003631520530000038
wherein v =1,2 k|k ，w＝1,2,...,J k|k And v ≠ w;
if d is vw Less than a merging threshold epsilon 2 The corresponding two gaussian components are combined into a single gaussian component, denoted as (w) vw ,m vw ,P vw ) And has the following:
Figure FDA0003631520530000039
Figure FDA00036315205300000310
Figure FDA00036315205300000311
step C-4, rewriting the Gaussian component after the step C-3 into the following form:
Figure FDA00036315205300000312
wherein, J k R =1, 2.., J, the number of combined gaussian components k ，
Figure FDA00036315205300000313
And
Figure FDA00036315205300000314
respectively the weight, mean and covariance matrix of the r-th gaussian component,
Figure FDA0003631520530000041
represents a mean value of
Figure FDA0003631520530000042
Covariance matrix of
Figure FDA0003631520530000043
(ii) a gaussian distribution of;
extraction of v k|k (x) The weight being greater than a threshold epsilon 3 As the final estimation result of the target state:
Figure FDA0003631520530000044
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