CN112328959A - Multi-target tracking method based on adaptive extended Kalman probability hypothesis density filter - Google Patents

Multi-target tracking method based on adaptive extended Kalman probability hypothesis density filter Download PDF

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CN112328959A
CN112328959A CN202011097165.7A CN202011097165A CN112328959A CN 112328959 A CN112328959 A CN 112328959A CN 202011097165 A CN202011097165 A CN 202011097165A CN 112328959 A CN112328959 A CN 112328959A
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齐滨
梁国龙
张博宇
付进
张光普
邹男
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Abstract

The invention discloses a multi-target tracking method based on an adaptive extended Kalman probability hypothesis density filter, and belongs to the technical field of multi-target tracking. Firstly, initializing the intensity of a new target by using a two-point difference algorithm, and then eliminating the wrong intensity of the new target by using a target maximum speed constraint algorithm. In addition, in order to eliminate the interference of the clutter measurement values, the live target measurement values and the new target measurement values are respectively extracted from the measurement value set by using an improved measurement value classification algorithm, and then the live target and the new target are respectively updated by using the live target measurement values and the new target measurement values, so that the accuracy of the algorithm is improved. The invention solves the problem that the EK-PHD filter cannot track the target under the condition that the strength of the newborn target is unknown.

Description

Multi-target tracking method based on adaptive extended Kalman probability hypothesis density filter
Technical Field
The invention relates to a multi-target tracking method based on an adaptive extended Kalman probability hypothesis density filter, and belongs to the technical field of multi-target tracking.
Background
With the development of modern information science and technology, the multi-target tracking technology has wide application and plays an important role in the fields of vision, radar and sonar tracking, vehicle tracking and the like. In a multi-target tracking scene, not only the state of targets can change along with the change of time, but also the number of the targets can change along with the appearance and disappearance of the targets, so that the multi-target tracking problem is always a hotspot and difficult problem for the research of experts and scholars at home and abroad. The traditional method for solving the multi-target Tracking problem is a Data Association technology, which includes a Multiple Hypothesis Tracking (MHT) algorithm and a Joint Probability Data Association (JPDA) algorithm. However, these algorithms not only face the uncertainty problem of data association, but the amount of computation also increases as the number of targets and measurements increases.
In order to solve the problem of computational complexity of the traditional multi-target tracking algorithm, Mahler proposes a Probability Hypothesis Density (PHD) filter based on a Random Finite Set (RFS) theory. The PHD filter transmits first-order statistical moments of the target state instead of posterior probability density of multiple targets, so that the combination problem caused by data association is avoided while the space computation complexity of a single target state is reduced. The iterative process of the PHD filter can be implemented by means of Gaussian Mixture, i.e. Gaussian Mixture probability hypothesis density filter (GM-PHD). Since the state model and the measurement model of the GM-PHD hypothesis target are both linear gaussian models, when the state model or the measurement model is nonlinear, the nonlinear state model or the measurement model may be approximated by an Extended Kalman Filter (EKF) to obtain an Extended Kalman probabilistic hypothesis density Filter (EK-PHD), and thus the EK-PHD Filter may be regarded as an extension of the GM-PHD Filter. Although the EK-PHD filter can avoid the problem of computational complexity caused by data association, the new target strength is usually used as a priori known information to participate in the iterative process of the EK-PHD filter, but in an actual tracking environment, the new target strength is usually unknown, which brings a certain limit to the application of the EK-PHD filter in actual engineering. Aiming at the problem that an EK-PHD filter cannot track a target under the condition that the intensity of a newborn target is unknown, an improved extended Kalman probability hypothesis density filter for adaptively estimating the intensity of the newborn target is provided.
Disclosure of Invention
The invention aims to provide a multi-target tracking method based on an adaptive extended Kalman probability hypothesis density filter, which aims to solve the problem that an EK-PHD filter cannot track a target under the condition that the strength of a newborn target is unknown.
A multi-target tracking method based on an adaptive extended Kalman probability hypothesis density filter comprises the following steps:
step one, initializing a newborn intensity function v0(x)；
Step two, according to the new strength function v0(x) Predicted survival target intensity function vs,k|k-1(x) And a new target intensity function vγ,k|k-1(x)；
Step three, dividing the measurement value set, and extracting a survival target measurement value and a new target measurement value from the measurement value set;
step four, updating the intensity function predicted in the step two by respectively utilizing the survival target measured value and the new target measured value to obtain an updated survival target intensity function vs,k(x) And a new target intensity function vγ,k(x) The final updated target intensity function is vk|k(x)；
Step five, utilizing a pruning threshold TthAnd combining the updated intensity function v of the threshold U versus the step fourk|k(x) Pruning and merging to obtainTo the target intensity function vk(x)；
Step six, setting a target state extraction threshold value wthAnd from the target intensity function v of step fivek(x) The weight value of the middle extraction is more than wthAs a final tracking result.
Further, in step one, specifically, the intensity function v is initialized0(x) Expressed as:
Figure BDA0002724128380000021
wherein
Figure BDA0002724128380000022
Represents a mean value of
Figure BDA0002724128380000023
Covariance of
Figure BDA0002724128380000024
A gaussian density function of, and
Figure BDA0002724128380000025
weight of object, J0To initialize the target number.
Further, in the second step, specifically,
intensity function v for predicting survival targetss,k|k-1(x) The expression is as follows:
Figure BDA0002724128380000031
wherein
Figure BDA0002724128380000032
Represents a mean value of
Figure BDA0002724128380000033
Covariance of
Figure BDA0002724128380000034
A gaussian density function of, and
Figure BDA0002724128380000035
as a predicted survival target weight, JS，k|k-1In order to predict the number of surviving objects,
predicting an intensity function v of a nascent objectγ,k|k-1(x) The expression is as follows:
Figure BDA0002724128380000037
wherein
Figure BDA0002724128380000038
Represents a mean value of
Figure BDA0002724128380000039
Covariance of
Figure BDA00027241283800000310
A gaussian density function of, and
Figure BDA00027241283800000311
to predict the new target weight, Jγ,k|k-1Is the predicted number of new targets.
Further, in step three, specifically, for the measured value set ZkIs divided from the measured value set ZkExtracting a survival target measurement value set Zs,kAnd a new set of target measurements Zγ,k。
Further, in step four, specifically, the survival target measurement value set Z extracted in step three is useds,kFor predicted survival target intensity function vs,k|k-1(x) Updating, the updated surviving objective intensity function vs,k(x) Expressed as:
Figure BDA00027241283800000312
wherein p isD,kThe probability of detection is indicated and,
Figure BDA00027241283800000313
represents the updated survival target weight value of the current system,
Figure BDA00027241283800000314
represents the updated mean value of the surviving objects,
Figure BDA00027241283800000315
represents the updated survival target covariance,
using the new target measurement value set Z extracted in step threeγ,kFor predicted new target intensity function vγ,k|k-1(x) Updating, the updated new target intensity function vγ,k(x) Can be expressed as:
Figure BDA0002724128380000041
wherein,
Figure BDA0002724128380000042
representing the new updated target weight value of the new object,
Figure BDA0002724128380000043
represents the updated new-born target mean value,
Figure BDA0002724128380000044
representing the updated new target covariance,
finally, the updated target intensity function vk|k(x) Expressed as:
vk|k(x)＝vs,k(x)+vγ,k(x) (6)。
further, in step five, specifically, a pruning threshold T is utilizedthAnd combining the threshold value U with the target intensity function v updated in the fourth stepk|k(x) Pruning and merging are carried out to obtain a target intensity function of
Figure BDA0002724128380000045
Wherein
Figure BDA0002724128380000046
The weight value of the object is represented,
Figure BDA0002724128380000047
the mean value is represented by the average value,
Figure BDA0002724128380000048
the covariance is indicated.
Further, in step six, specifically, a target state extraction threshold w is setthAnd extracting the target intensity function v in the step fivek(x)：
Figure BDA0002724128380000049
Wherein Xk(x) A set of functions representing the intensity of the object,
Figure BDA00027241283800000410
representing the target state vector, JkRepresenting the target number.
The main advantages of the invention are:
(1) the method can adaptively estimate the intensity of the new target, and overcome the problem that the traditional EK-PHD filter cannot track the target in the actual tracking environment.
(2) By dividing the measurement value set, the clutter measurement value can be prevented from participating in the updating process, and the accuracy of the algorithm can be improved while the calculation amount is reduced.
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FIG. 1 is a flow chart of a multi-target tracking method based on an adaptive extended Kalman probability hypothesis density filter according to the present invention;
FIG. 2 is a diagram of the true motion trajectory of an object;
FIG. 3 is a graph of azimuth and range measurements;
FIG. 4 is a diagram of the tracking result of One-Step Initialization Extended Kalman Probability Hypothesis Density filter (OSI-EKPHD);
FIG. 5 is a diagram of the tracking result of a Two-Step Initialization Extended Kalman Probability Hypothesis Density filter (TSI-EKPHD);
FIG. 6 is a graph of the Improved Extended Kalman probabilistic Hypothesis Density filter (IABI-EKPHD) tracking results for adaptively estimating the Intensity of a newborn target;
FIG. 7 is a graph of the Optimal Sub-pattern assignment (OSPA) distance error for different algorithms;
FIG. 8 is a Number of Target Estimation (NTE) error plot for different algorithms;
FIG. 9 is a graph of OSPA average distance error for different algorithms for different numbers of clutters;
FIG. 10 is a graph of the average estimation error of the number of targets in different algorithms for different numbers of clutters.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, a multi-target tracking method based on an adaptive extended kalman probabilistic hypothesis density filter includes the following steps:
step one, initializing a newborn intensity function v0(x)；
Step two, according to the new strength function v0(x) Predicted survival target intensity function vs,k|k-1(x) And a new target intensity function vγ,k|k-1(x)；
Step three, dividing the measurement value set, and extracting a survival target measurement value and a new target measurement value from the measurement value set;
step four, updating the intensity function predicted in the step two by respectively utilizing the survival target measured value and the new target measured value to obtain an updated survival target intensity function vs,k(x) And a new target intensity function vγ,k(x) The final updated target intensity function is vk|k(x)；
Step five, utilizing a pruning threshold TthAnd combining the updated intensity function v of the threshold U versus the step fourk|k(x) Pruning and merging are carried out to obtain a target intensity function vk(x)；
Step six, setting a target state extraction threshold value wthAnd from the target intensity function v of step fivek(x) The weight value of the middle extraction is more than wthAs a final tracking result.
In step one, specifically, the intensity function v is initialized0(x) Expressed as:
Figure BDA0002724128380000061
wherein
Figure BDA0002724128380000062
Represents a mean value of
Figure BDA0002724128380000063
Covariance of
Figure BDA0002724128380000064
A gaussian density function of, and
Figure BDA0002724128380000065
weight of object, J0To initialize the target number.
In step two, specifically, predictionIntensity function v of surviving objectss,k|k-1(x) The expression is as follows:
Figure BDA0002724128380000066
wherein
Figure BDA0002724128380000067
Represents a mean value of
Figure BDA0002724128380000068
Covariance of
Figure BDA0002724128380000069
A gaussian density function of, and
Figure BDA00027241283800000610
as a predicted survival target weight, Js,k|k-1In order to predict the number of surviving objects,
predicting an intensity function v of a nascent objectγ,k|k-1(x) The expression is as follows:
Figure BDA0002724128380000071
wherein
Figure BDA0002724128380000072
Represents a mean value of
Figure BDA0002724128380000073
Covariance of
Figure BDA0002724128380000074
A gaussian density function of, and
Figure BDA0002724128380000075
to predict the new target weight, Jγ,k|k-1Is the predicted number of new targets.
In step three, specifically, the measurementSet of magnitudes ZkIs divided from the measured value set ZkExtracting a survival target measurement value set Zs,kAnd a new set of target measurements Zγ,k。
In step four, the survival target measurement value set Z extracted in step three is useds,kFor predicted survival target intensity function vs,k|k-1(x) Updating, the updated surviving objective intensity function vs,k(x) Expressed as:
Figure BDA0002724128380000076
wherein p isD,kThe probability of detection is indicated and,
Figure BDA0002724128380000077
represents the updated survival target weight value of the current system,
Figure BDA0002724128380000078
represents the updated mean value of the surviving objects,
Figure BDA0002724128380000079
represents the updated survival target covariance,
using the new target measurement value set Z extracted in step threeγ,kFor predicted new target intensity function vγ,k|k-1(x) Updating, the updated new target intensity function vγ,k(x) Can be expressed as:
Figure BDA00027241283800000710
wherein,
Figure BDA00027241283800000711
representing the new updated target weight value of the new object,
Figure BDA00027241283800000712
represents the updated new-born target mean value,
Figure BDA00027241283800000713
representing the updated new target covariance,
finally, the updated target intensity function vk|k(x) Expressed as:
vk|k(x)＝vs,k(x)+vγ,k(x) (6)。
in the fifth step, specifically, a pruning threshold T is utilizedthAnd combining the threshold value U with the target intensity function v updated in the fourth stepk|k(x) Pruning and merging are carried out to obtain a target intensity function of
Figure BDA0002724128380000081
Wherein
Figure BDA0002724128380000082
The weight value of the object is represented,
Figure BDA0002724128380000083
the mean value is represented by the average value,
Figure BDA0002724128380000084
the covariance is indicated.
In step six, specifically, a target state extraction threshold value w is setthAnd extracting the target intensity function v in the step fivek(x)：
Figure BDA0002724128380000085
Wherein Xk(x) A set of functions representing the intensity of the object,
Figure BDA0002724128380000086
representing the target state vector, JkRepresenting the target number.
The above detailed description of the improved extended kalman probabilistic hypothesis density filter for adaptively estimating the new target strength of the present invention is provided, and the principle and the implementation of the present invention are explained in detail herein by applying specific examples, and the description of the above examples is only used to help understanding the method of the present invention and the core idea thereof; meanwhile, for a person skilled in the art, according to the idea of the present invention, there may be variations in the specific embodiments and the application scope, and in summary, the content of the present specification should not be construed as a limitation to the present invention.
The following is a simulation result of the extended kalman probabilistic hypothesis density filter for adaptively estimating the new target strength of the present invention:
the target being in a two-dimensional region [ -2000,2000](m)×[0,2000](m) moving in the space, fixing the sensor at the origin of coordinates, and taking the observed quantity as the azimuth angle and the distance between the sensor and the target. At a sampling time k, the state vector of the target is
Figure BDA0002724128380000087
Wherein (p)x,k,py,k) The position of the object is indicated and,
Figure BDA0002724128380000088
representing the velocity, w, of the targetkIndicating the turning rate of the target. The dynamic model and the measured value model of the object motion are respectively
Figure BDA0002724128380000091
Figure BDA0002724128380000092
Wherein wkIs process noise, vkTo measure noise. Probability of detection pD,k0.98, pruning threshold Tth0.00001, merging threshold U is 4, target state extraction threshold wth0.5. As shown in fig. 2 and 3, the measured values at each sampling time include the measured values from the targetAlso contains a measurement from clutter and the intensity function of the clutter is
Figure BDA0002724128380000093
Where u (z) is the uniform density of the target active area, V2000 pi (radm) is the area of the target active area, and λc＝6.37×10-3(radm)-1Represents the average clutter return per unit volume, so there are 40 measurements from clutter interference at each sample time within the range of motion of the target.
The initialized target intensities are respectively
Figure BDA0002724128380000094
The weight is
Figure BDA0002724128380000095
The covariance matrix is
Figure BDA0002724128380000096
Fig. 4-6 show the tracking results of the OSI-EKPHD algorithm, the TSI-EKPHD algorithm, and the IABI-EKPHD algorithm, respectively. It can be seen from the tracking result diagram that the number of error tracks in the tracking results of the OSI-EKPHD algorithm and the TSI-EKPHD algorithm is relatively large, and the number of error tracks in the tracking results of the IABI-EKPHD algorithm is relatively small, mainly because the IABI-EKPHD algorithm can accurately estimate the intensity of a new target, and an accurate new target measurement value set and a survival target measurement value set can be obtained when the measurement value sets are divided, thereby eliminating the interference of clutter measurement values and improving the tracking accuracy.
FIG. 7 shows an OSPA distance error map of the OSI-EKPHD algorithm, the TSI-EKPHD algorithm, and the IABI-EKPHD algorithm. As can be seen from fig. 7, the OSPA distance error of the TSI-EKPHD algorithm is smaller than that of the OSI-EKPHD algorithm at most sampling moments, which is mainly because the TSI-EKPHD algorithm can estimate the intensity of a new target relatively accurately, and avoid tracking a track erroneously. The IABI-EKPHD algorithm can not only accurately estimate the intensity of the newborn target, but also avoid the interference of clutter measurement values, so the OSPA distance error of the IABI-GMPHD algorithm is smaller than that of the OSI-EKPHD algorithm and the TSI-EKPHD algorithm in the whole experimental process.
FIG. 8 is a graph showing target number estimation errors of OSI-EKPHD algorithm, TSI-EKPHD algorithm, and IABI-EKPHD algorithm. As can be seen from FIG. 8, the target number estimation error of the TSI-EKPHD algorithm is smaller than that of the OSI-EKPHD algorithm at most sampling moments, so the precision of the TSI-EKPHD algorithm is higher than that of the OSI-EKPHD algorithm. Except the moment when the new target appears, the target number estimation error of the IABI-EKPHD algorithm is smaller than that of the other two algorithms, so the performance of the IABI-EKPHD algorithm is better than that of the OSI-GMPHD algorithm and the TSI-EKPHD algorithm.
FIG. 9 is a graph showing OSPA average distance error of different algorithms for different numbers of clutters. It can be seen from fig. 9 that the OSPA average distance errors of the three algorithms increase with the increase of the number of the clutter, but the OSPA average error of the IABI-EKPHD algorithm is the smallest under the condition that the number of the clutter is the same, so the robustness and the stability of the IABI-EKPHD algorithm are relatively good.
Fig. 10 is a graph showing the average estimation error of the target numbers of different algorithms for different clutter numbers. It can be seen from fig. 10 that as the number of clutter increases, the average estimation error growth speed of the number of targets estimated by the IABI-EKPHD algorithm is relatively slow compared with the other two algorithms, and therefore, the IABI-EKPHD algorithm can adapt to different clutter environments and has stronger robustness.

Claims (7)

1. A multi-target tracking method based on an adaptive extended Kalman probability hypothesis density filter is characterized by comprising the following steps:
step one, initializing a newborn intensity function v0(x)；
Step two, according to the new strength function v0(x) Predicted survival target intensity function vs,k|k-1(x) And a new target intensity function vγ,k|k-1(x)；
Step three, dividing the measurement value set, and extracting a survival target measurement value and a new target measurement value from the measurement value set;
step four, respectively utilizing the survival target measurement value and the newborn targetUpdating the intensity function predicted in the step two by the measured value to obtain an updated survival target intensity function vs,k(x) And a new target intensity function vγ,k(x) The final updated target intensity function is vk|k(x)；
Step five, utilizing a pruning threshold TthAnd combining the updated intensity function v of the threshold U versus the step fourk|k(x) Pruning and merging are carried out to obtain a target intensity function vk(x)；
Step six, setting a target state extraction threshold value wthAnd from the target intensity function v of step fivek(x) The weight value of the middle extraction is more than wthAs a final tracking result.
2. The multi-target tracking method based on the adaptive extended Kalman probability hypothesis density filter as claimed in claim 1, wherein in the first step, specifically, an intensity function v is initialized0(x) Expressed as:
Figure FDA0002724128370000011
wherein
Figure FDA0002724128370000012
Represents a mean value of
Figure FDA0002724128370000013
Covariance of
Figure FDA0002724128370000014
A gaussian density function of, and
Figure FDA0002724128370000015
weight of object, J0To initialize the target number.
3. The multi-target tracking method based on the adaptive extended Kalman probability hypothesis density filter as claimed in claim 1, wherein in step two, specifically,
intensity function v for predicting survival targetss,k|k-1(x) The expression is as follows:
Figure FDA0002724128370000021
wherein
Figure FDA0002724128370000022
Represents a mean value of
Figure FDA0002724128370000023
Covariance of
Figure FDA0002724128370000024
A gaussian density function of, and
Figure FDA0002724128370000025
as a predicted survival target weight, Js,k|k-1In order to predict the number of surviving objects,
predicting an intensity function v of a nascent objectγ,k|k-1(x) The expression is as follows:
Figure FDA0002724128370000026
wherein
Figure FDA0002724128370000027
Represents a mean value of
Figure FDA0002724128370000028
Covariance of
Figure FDA0002724128370000029
A gaussian density function of, and
Figure FDA00027241283700000210
to predict the new target weight, Jγ,k|k-1Is the predicted number of new targets.
4. The multi-target tracking method based on the adaptive extended Kalman probability hypothesis density filter as claimed in claim 1, wherein in the third step, specifically, for the measurement value set ZkIs divided from the measured value set ZkExtracting a survival target measurement value set Zs,kAnd a new set of target measurements Zγ,k。
5. The multi-target tracking method based on the adaptive extended Kalman probability hypothesis density filter as claimed in claim 1, wherein in step four, specifically, the surviving target measurement value set Z extracted in step three is utilizeds,kFor predicted survival target intensity function vs,k|k-1(x) Updating, the updated surviving objective intensity function vs,k(x) Expressed as:
Figure FDA00027241283700000211
wherein p isD,kThe probability of detection is indicated and,
Figure FDA00027241283700000212
represents the updated survival target weight value of the current system,
Figure FDA00027241283700000213
represents the updated mean value of the surviving objects,
Figure FDA00027241283700000214
represents the updated survival target covariance,
using the new target measurement value set Z extracted in step threeγ,kFor predicted neogenesisTarget intensity function vγ,k|k-1(x) Updating, the updated new target intensity function vγ,k(x) Can be expressed as:
Figure FDA0002724128370000031
wherein,
Figure FDA0002724128370000032
representing the new updated target weight value of the new object,
Figure FDA0002724128370000033
represents the updated new-born target mean value,
Figure FDA0002724128370000034
representing the updated new target covariance,
finally, the updated target intensity function vk|k(x) Expressed as:
vk|k(x)＝vs,k(x)+vγ,k(x) (6)。
6. the multi-target tracking method based on the adaptive extended Kalman probability hypothesis density filter as claimed in claim 1, wherein in the fifth step, specifically, a pruning threshold T is utilizedthAnd combining the threshold value U with the target intensity function v updated in the fourth stepk|k(x) Pruning and merging are carried out to obtain a target intensity function of
Figure FDA0002724128370000035
Wherein
Figure FDA0002724128370000036
The weight value of the object is represented,
Figure FDA0002724128370000037
the mean value is represented by the average value,
Figure FDA0002724128370000038
the covariance is indicated.
7. The multi-target tracking method based on the adaptive extended Kalman probability hypothesis density filter as claimed in claim 1, wherein in step six, specifically, a target state extraction threshold w is setthAnd extracting the target intensity function v in the step fivek(x)：
Figure FDA0002724128370000039
Wherein Xk(x) A set of functions representing the intensity of the object,
Figure FDA00027241283700000310
representing the target state vector, JkRepresenting the target number.
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