CN113344039A - Multi-extension target tracking method based on space-time correlation - Google Patents

Multi-extension target tracking method based on space-time correlation Download PDF

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CN113344039A
CN113344039A CN202110547305.4A CN202110547305A CN113344039A CN 113344039 A CN113344039 A CN 113344039A CN 202110547305 A CN202110547305 A CN 202110547305A CN 113344039 A CN113344039 A CN 113344039A
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甘露
林晨
徐政五
廖红舒
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Research Institute Of Yibin University Of Electronic Science And Technology
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Abstract

The invention relates to a multi-extension target tracking method based on space-time correlation. When a target occupies multiple fractional rate units of the sensor, a single target will produce multiple measurements, i.e., an extended target. Under the background, when extended targets are crossed, a general distance-based partitioning method will classify measured values of different targets into the same measurement set, which causes the precision of the filter to be reduced and potential estimation to be wrong. The method is based on an ET-GM-PHD algorithm, adopts a space-time correlation idea, utilizes the correlation of measurement values of the extended targets at adjacent moments, and tracks the multiple extended targets on the basis of SNN division of a directed graph. The method greatly reduces the tracking error of the extended target at the intersection, and realizes accurate estimation on the number of the targets and the position of the targets. Meanwhile, the tracking process of the extended target and the point target is separated, and the calculated amount is greatly reduced.

Description

Multi-extension target tracking method based on space-time correlation
Technical Field
The invention belongs to the field of information fusion, and relates to a multi-extension target tracking method based on space-time correlation.
Background
With the development of modern sensor technology, the resolution of the sensor is higher and higher, a single target occupies multiple resolution units of the sensor, and multiple measurement information about the target is obtained at the same time, and the target type becomes an extended target. ET-GM-PHD (extended Target Gaussian Mixture PHD) is a filtering algorithm for tracking multiple extended targets under the theory of random finite set, and the method uses a Gaussian Mixture form to represent the intensity function of multiple targets so as to approximate the posterior distribution of the multiple targets. The multi-extended target method based on the random finite set avoids data association and reduces the complexity of calculation, wherein the indispensable part is to reasonably divide the measurement set at the current moment so as to find out the correct division of the measurement set. The widely used dividing method at present is distance division, and the method divides the measuring values meeting the distance threshold into the same dividing unit by utilizing the characteristic that the measuring values belonging to the same target are close to each other in space, so as to realize the division of the measuring set. However, when the target distance is close, the measurement values of different targets may fall into the same measurement set, resulting in filtering errors.
Disclosure of Invention
The invention aims to overcome the defects of the existing method, provides a multi-extension target tracking method based on space-time association, solves the problems of target state and target number estimation under the condition that the multi-extension target is closer in distance and the track is crossed, has good performance, and is not influenced by the measurement density. The method is mainly applied to the scene that a single sensor realizes the tracking of multiple extended targets in a clutter environment.
The technical scheme of the invention is as follows:
a multi-extended target tracking method based on space-time considers the relevance between measurement values of extended targets at adjacent moments, and specifically comprises the following steps:
by a single sensorCompleting the detection of the extended target, and making the measurement set obtained by the sensor at the moment k as
Figure BDA0003074018230000011
ziTo represent a single measurement in two dimensions, nkIs the number of measured values; the extended target state set in the detection area of the sensor at the moment k is
Figure BDA0003074018230000012
Wherein M iskWhich indicates the number of the extension target,
Figure BDA0003074018230000013
representing the state of motion, x, of a single extended objecti，yiThe information of the object is represented by,
Figure BDA0003074018230000014
representing object motion information.
The motion equation of the extended target is established as follows:
Xk＝FXk-1+vk
wherein the content of the first and second substances,
Figure BDA0003074018230000021
is a state transition matrix, I is an identity matrix, TsIs the sampling interval. v. ofkRepresents a covariance of
Figure BDA0003074018230000022
Process noise of σvIs the process standard deviation.
The measurement equation of the extended target is:
Zk＝HXk+wk
wherein the content of the first and second substances,
Figure BDA0003074018230000023
to observe the equation, wkRepresents a covariance of
Figure BDA0003074018230000024
Of the measured noise, σεTo measure the standard deviation of the noise.
A multi-extension target tracking method based on space-time association is shown in figure 1 and mainly comprises the following steps:
s1, when the time k is 0, the gaussian component in the initialized system is
Figure BDA0003074018230000025
Wherein w0Is the weight of the Gaussian component, m0Is the mean value of the Gaussian components, expressed as the motion state, P0For the corresponding covariance matrix, J0Is the initial number of gaussians;
s2, when k is larger than or equal to 1, traversing the Gaussian component set, performing one-step prediction according to the state transition matrix, and adding the Gaussian component of the newly generated target, wherein the steps are expressed as follows:
Figure BDA0003074018230000026
in the formula, Jk-1The number of gaussian components at time k-1,
Figure BDA0003074018230000027
and
Figure BDA0003074018230000028
respectively, parameters of the newly generated target Gaussian components, JBRepresenting the number of new target gaussian components;
s3, selecting components with weight more than 0.5 in the Gaussian components:
Figure BDA0003074018230000029
in the formula JcIs the number of gaussian components; and selects the position component thereof
Figure BDA00030740182300000210
Constructing a wave gate, and setting a distance threshold as tau; traverse the entire measurement set ZkForming measurement sets for measurement values falling into the wave gates
Figure BDA00030740182300000211
N represents the number of metrology sets;
s4, calculating a measurement set
Figure BDA00030740182300000212
Union of
Figure BDA00030740182300000213
Clustering by adopting a K-means + + algorithm to obtain L clustering centers
Figure BDA00030740182300000214
Clustering centers by adopting GM-PHD algorithm of point targets
Figure BDA00030740182300000215
Updating the Gaussian component G to obtain an updated Gaussian component:
Figure BDA00030740182300000216
in the formula
Figure BDA00030740182300000217
Is the number of gaussian components;
s5, calculating a k time measurement set ZkAnd collections
Figure BDA00030740182300000218
Difference set of
Figure BDA00030740182300000219
Clustering set by DBSCAN clustering algorithm
Figure BDA0003074018230000031
Preprocessing, if a clustering unit exists at the moment, turning to S6; otherwise, go to S7;
s6, for the clustering unit generated in S5, calculating the union of the clustering units
Figure BDA0003074018230000032
Carry out one by utilizing a directed graph SNN clustering methodStep processing, the clustering number of the step processing is K e to Kl,Ku]In which K islFor the number of clusters in the DBSCAN algorithm,
Figure BDA0003074018230000033
n is a set
Figure BDA0003074018230000034
The number of the measured values, beta, is the measurement rate of the extended target;
s61 construction set
Figure BDA0003074018230000035
Similarity matrix W of directed kNN adjacency matrixn×nSelecting k as 8 in the algorithm; the elements in W are:
Figure BDA0003074018230000036
wherein z issIs ziTo (1) a
Figure BDA0003074018230000037
A nearest neighbor point of zjTo (1) a
Figure BDA0003074018230000038
A nearest neighbor point, NiDenotes ziK nearest neighbors, N, in a kNN graphjDenotes zjK nearest neighbors, z, in a kNN graphi、zjAnd zsRespectively being vertexes in the kNN graph; n is a radical ofi∩NjDenotes ziAnd zjThe shared closest point of approach between, defined as:
Figure BDA0003074018230000039
in the formula, zijIs a virtual vertex, representing a vertex ziAnd zjAre the closest points to each other.
S62 matrix W andcluster number range [ K ]l,Ku]Clustering by adopting a spectral clustering method to form a clustering unit; the spectral clustering comprises the following steps:
(1) calculating an unnormalized laplacian matrix L from the similarity matrix W,
Figure BDA00030740182300000310
in the formula, D is a diagonal matrix and is a degree matrix of the kNN diagram.
(2) Computing a normalized Laplace matrix Ls＝D-1/2LD-1/2；
(3) Calculating the matrix LsCharacteristic value λ ofiAnd a feature vector ui；
(4) Selecting eigenvectors corresponding to K minimum eigenvalues to form a matrix U;
(5) and normalizing the matrix U to obtain a matrix Y, taking each row of the matrix Y as a new data point of a K-dimensional space, and clustering by using a K-means + + algorithm.
S7, on the basis of the S6 division result, updating the Gaussian component G by utilizing an ET-GM-PHD algorithm, and obtaining the updated Gaussian component as follows:
Figure BDA0003074018230000041
Figure BDA0003074018230000042
is the number of gaussian components.
S8, for Gaussian component
Figure BDA0003074018230000043
Pruning and merging are carried out, the Gaussian components with the weight smaller than T are deleted, and the Gaussian components with the distance smaller than mu between the merged Gaussian components are deleted.
And S9, selecting the Gaussian component with the weight greater than 0.5 as a filtering result of the target, and realizing target tracking.
The invention has the beneficial effects that: the method reduces the calculation amount of filtering, and can effectively process the target position estimation and the target number estimation of the extended target at the intersection. The extended target tracking process is converted into the form of extended target tracking and point target tracking, the operation efficiency is improved, meanwhile, the filtering algorithm has better robustness, and the interference of clutter on the estimation result is reduced.
Drawings
FIG. 1 is a flow chart of the present invention as applied to multi-extended target tracking;
FIG. 2 shows the flight path estimation, the real flight path and the measured value in the embodiment 1;
FIG. 3 OSPA error comparison under example 1;
FIG. 4 comparison of the number of targets estimated in example 1;
FIG. 5 run time comparison under example 1;
FIG. 6 shows the flight path estimation, the real flight path, and the measured value in embodiment 2;
FIG. 7 OSPA error comparison under example 2;
FIG. 8 target number estimation in example 2;
FIG. 9 run time comparison under example 2;
Detailed Description
The simulation parameters are set as follows: target survival probability of Ps0.99, with a probability of detection of PDWhen the number of the extended target measurement is 0.99, the number of the extended target measurement follows Poisson distribution with the expected value of 10; the clutter measurement number follows Poisson distribution with the expected value of 20; the maximum number of Gaussian components is J max100, the pruning threshold T is 10-6The merging threshold mu is 4; the distance threshold τ is 50. Covariance of process noise of
Figure BDA0003074018230000044
s v2; observing a variance of noise of
Figure BDA0003074018230000045
sεThe monitored area size is 20: [ -1000, 1000]×[-1000,1000]m。
Examples 1,
The purpose of the embodiment is to verify that the proposed method is at two extended targetsAnd the filtering performance of the target under the scene of close distance and parallel motion. The initial state of the target 1 is [ -600m, -500m,0m/s]TThe survival time is 1-100 s; the initial state of the target 2 is [ -600m, -600m,0m/s]TThe survival time is 1-100 s; the intensity function of the nascent object in this scenario is:
Figure BDA0003074018230000051
in the formula
Figure BDA0003074018230000052
Pγ,t＝diag([100,100,25,25])。
FIG. 2 is a comparison of the target state estimation and target true state of the present invention under example 1. It can be seen that the invention can obtain a better tracking result even when the extended targets are closer to each other.
FIG. 3 is a comparison of OSPA errors between the method of the present invention and the distance-and directed-graph SNN-partitioning method in example 1. It can be seen that the OSPA error of the method of the present invention is significantly minimized.
Fig. 4 is a comparison of the target number estimation of the method of the present invention and the distance-division and directed graph SNN-division method in embodiment 1. It can be seen that the target number estimation of the method of the present invention is most accurate.
Fig. 5 is a comparison of the algorithm running time of the method of the present invention and the distance partition and directed graph SNN partition method in embodiment 1, and it can be seen that the algorithm running time of the method of the present invention is the lowest.
Examples 2,
The simulation parameters were the same as in example 1. The purpose of this embodiment is to verify the filtering performance of the algorithm in case of target crossing. 2 targets exist in the scene, and the initial state of the target 1 is [250m,250m,0m/s]TThe survival time is 1-100 s; the initial state of the target 2 is [ -250m, -250m,0m/s]TThe survival time is 1-100 s; the two objects intersect at 56 s. The intensity function of the nascent object in this scenario is:
Figure BDA0003074018230000053
in the formula (I), the compound is shown in the specification,
Figure BDA0003074018230000054
Pγ,t＝diag([100,100,25,25])。
FIG. 6 is a comparison of the target state estimation and the target true state of the present invention in example 2. It can be seen that a better estimation result can be obtained even at the target track crossing time.
FIG. 7 shows the OSPA error comparison of the method of the present invention with the distance-and directed-graph SNN-partitioning method in example 2. It can be seen that the OSPA error of the method of the present invention is minimal even at extended target track crossing times.
Fig. 8 is a comparison of the target number estimation of the method of the present invention and the distance-division and directed graph SNN-division method in embodiment 2. It can be seen that the target number estimation of the method is the most accurate at the track crossing time.
Fig. 9 is a comparison of the algorithm running time of the method of the present invention and the distance partition and directed graph SNN partition method in embodiment 2, and it can be seen that the algorithm running time of the method of the present invention is the lowest.

Claims (1)

1. A space-time-based multi-extension target tracking method is characterized by comprising the following steps:
the detection of the extended target is finished by a single sensor, and the measurement set obtained by the sensor at the moment k is combined into
Figure FDA0003074018220000011
ziTo represent a single measurement in two dimensions, nkIs the number of measured values; the extended target state set in the detection area of the sensor at the moment k is
Figure FDA0003074018220000012
Wherein M iskWhich indicates the number of the extension target,
Figure FDA0003074018220000013
representing the state of motion, x, of a single extended objecti，yiThe information of the object is represented by,
Figure FDA0003074018220000014
representing target motion information;
the motion equation of the extended target is established as follows:
Xk＝FXk-1+vk
wherein the content of the first and second substances,
Figure FDA0003074018220000015
is a state transition matrix, I is an identity matrix, TsIs the sampling interval; v. ofkRepresents a covariance of
Figure FDA0003074018220000016
Process noise of σvIs the process standard deviation;
the measurement equation of the extended target is:
Zk＝HXk+wk
wherein the content of the first and second substances,
Figure FDA0003074018220000017
to observe the equation, wkRepresents a covariance of
Figure FDA0003074018220000018
Of the measured noise, σεMeasuring the standard deviation of the noise;
the method for tracking the extended target comprises the following specific steps:
s1, when the time k is 0, the gaussian component in the initialized system is
Figure FDA0003074018220000019
Wherein w0Is the weight of the Gaussian component, m0Is the mean value of the Gaussian components, expressed as the motion state, P0For the corresponding covariance matrix, J0Is the initial number of gaussians;
s2, when k is larger than or equal to 1, traversing the Gaussian component set, performing one-step prediction according to the state transition matrix, and adding the Gaussian component of the newly generated target, wherein the steps are expressed as follows:
Figure FDA00030740182200000110
in the formula, Jk-1The number of gaussian components at time k-1,
Figure FDA00030740182200000111
and
Figure FDA00030740182200000112
respectively, parameters of the newly generated target Gaussian components, JBRepresenting the number of new target gaussian components;
s3, selecting components with weight more than 0.5 in the Gaussian components:
Figure FDA00030740182200000113
in the formula JcIs the number of gaussian components; and selects the position component thereof
Figure FDA0003074018220000021
Constructing a wave gate, and setting a distance threshold as tau; traverse the entire measurement set ZkForming measurement sets for measurement values falling into the wave gates
Figure FDA0003074018220000022
N represents the number of metrology sets;
s4, calculating a measurement set
Figure FDA0003074018220000023
Union of
Figure FDA0003074018220000024
Clustering by adopting a K-means + + algorithm to obtain L clustering centers
Figure FDA0003074018220000025
Clustering centers by adopting GM-PHD algorithm of point targets
Figure FDA0003074018220000026
Updating the Gaussian component G to obtain an updated Gaussian component:
Figure FDA0003074018220000027
in the formula
Figure FDA0003074018220000028
Is the number of gaussian components;
s5, calculating a k time measurement set ZkAnd collections
Figure FDA0003074018220000029
Difference set of
Figure FDA00030740182200000210
Clustering set by DBSCAN clustering algorithm
Figure FDA00030740182200000211
Preprocessing, if a clustering unit exists at the moment, turning to S6; otherwise, go to S7;
s6, for the clustering unit generated in S5, calculating the union of the clustering units
Figure FDA00030740182200000212
Further processing by utilizing a directed graph SNN clustering method, wherein the clustering number is K-E [ K ∈l,Ku]In which K islFor the number of clusters in the DBSCAN algorithm,
Figure FDA00030740182200000213
n is a set
Figure FDA00030740182200000214
The number of the measured values, beta, is the measurement rate of the extended target;
s61 construction set
Figure FDA00030740182200000215
Similarity matrix W of directed kNN adjacency matrixn×nThe elements in W are:
Figure FDA00030740182200000216
wherein z issIs ziTo (1) a
Figure FDA00030740182200000217
A nearest neighbor point of zjTo (1) a
Figure FDA00030740182200000218
A nearest neighbor point, NiDenotes ziK nearest neighbors, N, in a kNN graphjDenotes zjK nearest neighbors, z, in a kNN graphi、zjAnd zsRespectively being vertexes in the kNN graph; n is a radical ofi∩NjDenotes ziAnd zjThe shared closest point of approach between, defined as:
Figure FDA00030740182200000219
in the formula, zijIs a virtual vertex, representing a vertex ziAnd zjAre the closest points to each other;
s62, for similarity matrix W and cluster number range [ Kl,Ku]Clustering by adopting a spectral clustering method to form a clustering unit; the spectral clustering comprises the following steps:
(1) calculating an unnormalized laplacian matrix L from the similarity matrix W,
Figure FDA0003074018220000031
in the formula, D is a diagonal matrix and represents a degree matrix of the kNN diagram;
(2) computing a normalized Laplace matrix Ls＝D-1/2LD-1/2；
(3) Calculating the matrix LsCharacteristic value λ ofiAnd a feature vector ui；
(4) Selecting eigenvectors corresponding to K minimum eigenvalues to form a matrix U;
(5) and normalizing the matrix U to obtain a matrix Y, taking each row of the matrix Y as a new data point of a K-dimensional space, and clustering by using a K-means + + algorithm.
S7, on the basis of the S6 division result, updating the Gaussian component G by utilizing an ET-GM-PHD algorithm, and obtaining the updated Gaussian component as follows:
Figure FDA0003074018220000032
Figure FDA0003074018220000033
is the number of gaussian components;
s8, for Gaussian component
Figure FDA0003074018220000034
Pruning and combining are carried out, the Gaussian components with the weight smaller than T are deleted, and the Gaussian components with the distance smaller than mu between the combined Gaussian components are deleted;
and S9, selecting the Gaussian component with the weight larger than 0.5 as the filtering result of the target.
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