Multi-group target tracking method based on variational Bayesian reasoning and joint probability data association

Abstract

The invention relates to a multi-group target tracking method based on variational Bayesian reasoning and joint probability data association. The method comprises the following steps: S1, obtaining a predicted value of a state parameter at a moment k; s2, performing initial variational iteration at the moment k, and updating the number of variational iterations; s3, calculating the variation posterior probability of the joint probability data association event after the first variation iteration; s4, variational posteriori parameters of each group target after the lth variational iteration at the moment k are obtained; s5, judging whether the number of variational iterations accumulatively reaches a preset upper limit Nsc of the number of variational iterations; if not, returning to S3; if yes, executing S6, and obtaining a state parameter posteriori estimation value at the moment k; s7, at the moment k, judging whether each group target leaves the monitoring area or not; if not, returning to S1; and if yes, executing S8, and ending tracking of each target group. According to the method, the shape of the group target can be estimated, shape estimation collapse is avoided, and higher adaptability is achieved.

Description

Technical Field

[0001] The present invention relates to the field of data processing technology, and in particular to a multi-group target tracking method based on variational Bayesian reasoning and joint probability data association. Background Art

[0002] With the development of group target detection and tracking technology, the research and development of cluster target tracking technology has become a demand object for modern battlefields and military operations. When the number of targets in a cluster is so large that the sensor cannot distinguish each point target point by point, the tracking scheme for this type of group target with dense multi-point targets in the group can directly track the cluster as an indistinguishable whole. At this time, in tracking, the indistinguishable group target (i.e., group target) will show the same measurement characteristics as the general extended target, and the purpose of tracking this type of target is not only to track the position information of the group center, but also to accurately determine the size and shape of the group target's outer envelope, i.e., the extended outer shape characteristics of the group target.

[0003] At present, the mainstream method is to regard the shape envelope of the group target as an ellipse or rectangle, which is consistent with the distribution characteristics of bird flock targets and drone group targets in the overall observation space in practice. For group targets modeled with conventional elliptical shapes, the most commonly used method is the random matrix model proposed by scholars, combined with the multi-target tracking method to achieve tracking of multiple group targets. For example, some scholars proposed combining the random matrix model with the joint probability data association method to achieve multi-group target tracking, and some scholars proposed combining the random matrix model with the trajectory set Poisson multi-Bernoulli filter to achieve multi-group target tracking. However, since the random matrix model itself does not accurately estimate the shape parameters of the group target (such as the orientation information and axis length information of the elliptical shape), the above method cannot accurately capture and track the shape envelope changes of the group target.

[0004] To address this problem, some scholars have proposed a multiplicative error model for effectively tracking and estimating the shape parameters of group targets. However, the multiplicative error model has the disadvantages of shape estimation collapse and slow convergence in scenarios with unknown measurement rates. Summary of the invention

[0005] In order to solve the above technical problems, the present invention proposes a multi-group target tracking method based on variational Bayesian reasoning and joint probability data association.

[0006] In a first aspect of the present invention, a multi-group target tracking method based on variational Bayesian reasoning and joint probability data association is proposed, the method comprising:

[0007] S1, predicting the state of each target group in the surveillance area of ​​the radar according to the posterior estimated value of the state parameter at time k-1, and obtaining the predicted value of the state parameter of each group target at time k; wherein the state of each target group includes: center of mass kinematic state, extended shape state and measurement rate state; the state parameters include: center of mass kinematic parameter, extended shape parameter and measurement rate parameter;

[0008] S2, initialize the current variational Bayesian inference iteration number l=0, and perform the initial variational iteration of each group target at time k and update the variational iteration number l=l+1 according to the predicted value of the state parameter of each group target at time k; wherein the initial variational iteration represents the variational posterior parameters of the initial state of each group target after the l=0th variational iteration at time k;

[0009] S3. At time k, based on the measurement data of each group target and the variational posterior parameters of the initial state obtained after the l-1th variational iteration, obtain the variational posterior probability of the joint probability data association event after normalization after the lth variational iteration; wherein the measurement data is data captured by the sensor and represented in a Cartesian coordinate system;

[0010] S4, according to the variational posterior probability of the joint probability data associated event after the normalization, the variational posterior parameters of the initialization state are updated to obtain the variational posterior parameters of the states of the various group targets after the lth variational iteration at time k and update the number of variational iterations l=l+1;

[0011] S5: Determine whether the cumulative number of variational iterations reaches the preset upper limit N of variational iterations. sc ;

[0012] If not, return to S3; if so, execute S6, at time k, according to the Nth sc The variational posterior parameters of the states of each group target after the variational iterations are used to obtain the posterior estimated values ​​of the state parameters at time k, so as to predict the states of each target group at time k+1.

[0013] S7, at time k, determining whether each group target has left the monitoring area;

[0014] If not, return to S1; if so, execute S8 to end the tracking of each target group.

[0015] Optionally, before S1, the method further includes:

[0016] In a rectangular coordinate system, a mathematical model of the state parameter distribution of each group target is established; wherein the mathematical model of the state parameter distribution includes a dynamic model of the kinematic state of the center of mass, a dynamic model of the shape state, and a group target measurement model;

[0017] At time k=0, the state parameters of each group target are initialized according to the prior information.

[0018] Optionally, the predicted values ​​of the state parameters of each group target at time k include: the predicted values ​​of the center of mass kinematic parameters of each group target at time k, the predicted values ​​of the extended shape parameters and the predicted values ​​of the measurement rate parameters; the predicted values ​​of the center of mass kinematic parameters of each group target at time k include: the predicted value of the mean of the kinematic parameters of each group target at time k and the predicted value of the kinematic parameter covariance of each group target at time k; the predicted values ​​of the extended shape parameters of each group target at time k include: the predicted value of the shape parameter degrees of freedom of each group target at time k and the predicted value of the shape parameter scaling matrix of each group target at time k; the predicted values ​​of the measurement rate parameters of each group target at time k include: the predicted value of the measurement rate parameter scale of each group target at time k and the predicted value of the measurement rate parameter scale of each group target at time k.

[0019] Optionally, the predicted values ​​of the kinematic parameters of the center of mass of each group target at time k are as follows:

[0020]

[0021] in, represents the predicted value of the mean kinematic parameter of group target n at time k, The dynamic matrix representing the kinematic state of the center of mass of the group target n at time k, is the posterior estimate of the mean kinematic parameter of group target n at time k-1, T represents the transposition operation, represents the predicted value of the covariance of the kinematic parameters of the group target n at time k, represents the posterior estimate of the covariance of the kinematic parameters of the group target n at time k-1, represents the process noise covariance matrix of group target n at time k;

[0022] The predicted values ​​of the extended shape parameters of each group target at time k are as follows:

[0023]

[0024] in, represents the predicted value of the degree of freedom of the shape parameters of the group target n at time k, represents the shape freedom of the group target n at time k, is an auxiliary variable, represents the posterior estimate of the degree of freedom of the shape parameters of the group target n at time k-1, n d To track the dimensions of the scene; represents the predicted value of the shape parameter scaling matrix of group target n at time k, represents the shape evolution description matrix of group target n at time k, Indicates n d The identity matrix of order, represents the posterior estimate of the scaling matrix of the shape parameters of the group target n at time k-1;

[0025] The predicted values ​​of the measurement rate parameters of each group target at time k are as follows:

[0026]

[0027] in, represents the predicted value of the measurement rate parameter scale of group target n at time k, represents the posterior estimate of the measurement rate parameter scale of the group target n at time k-1, represents the measurement rate forgetting factor of the group target n at time k-1, represents the predicted value of the measurement rate parameter scale of group target n at time k, Represents the posterior estimate of the measurement rate parameter scale of the group target n at time k-1.

[0028] Optionally, the normalized variational posterior probability reference of each joint probability data association event is expressed as follows:

[0029]

[0030] in, represents the normalized variational posterior probability of the t-th joint probability data association event in the l-th variational iteration at time k, is the total number of events associated with the joint probability data at the current k moment, express The variational posterior probability at the lth variational iteration, represents the t-th joint probability data association event at time k;

[0031] Refer to the following representation:

[0032]

[0033] Where ρ is the clutter density, λ c is the clutter Poisson rate, is the t-th joint probability data association event at the current k-th moment The number of clutter measurements. ∏ represents the product sign, n k Represents the total number of group targets at time k, the product term represents the measurement likelihood generated by the measurement assigned to the group target n under the tth joint probability data association event at time k, represents the set of measurements consisting of the measurements assigned to the group target n at the tth joint probability data association event at time k, yes The Measurements, represents the measurement matrix of group target n at time k, represents the predicted value of the mean kinematic parameter of group target n at time k, represents the innovation covariance matrix of group target n at time k, Represents the measurement rate factor.

[0034] Optionally, the measurement rate factor Refer to the following representation:

[0035]

[0036] in, It represents the updated measurement rate variational posterior parameter scale of the group target n at the l-1th variational iteration at time k, It represents the updated measurement rate variational posterior parameter scale of the group target n at the l-1th variational iteration at time k;

[0037] Innovation covariance matrix of group target n at time k Refer to the following representation:

[0038]

[0039] in, represents the shape distortion matrix of group target n at time k;

[0040] The shape distortion matrix of group target n at time k Refer to the following representation:

[0041]

[0042] in,(·) -1 / 2 It means to take the square root after inverting the matrix, that is s is the scaling constant, represents the true observation noise covariance matrix of group target n at time k, represents the expected prediction of the extended appearance state of group target n at time k;

[0043] represents the expected prediction of the extended appearance state of the group target n at time k Refer to the following representation:

[0044]

[0045] Among them, n d To track the dimensions of the scene.

[0046] Optionally, at time k, the variational posterior parameters of the states of the respective group targets after the l-th variational iteration include: at time k, the center of mass kinematic variational posterior parameters of the respective group targets after the l-th variational iteration; the center of mass kinematic variational posterior parameters include a kinematic variational posterior parameter mean and a kinematic variational posterior parameter covariance, and the center of mass kinematic variational posterior parameters are expressed as follows:

[0047]

[0048] in, represents the mean of the kinematic variational posterior parameters of the group target n updated in the lth variational iteration at time k; represents the Kalman gain matrix of group target n in the lth variational iteration at time k, represents the kinematic variational posterior parameter covariance of the group target n updated in the lth variational iteration at time k, Indicates the k-th time, the t-th joint probability data association event The equivalent measurement of the following group target n is,

[0049]

[0050] At time k, the Kalman gain matrix of group target n under the lth variational iteration is Refer to the following representation:

[0051]

[0052] in,(·) -1 Indicates the inversion of the matrix. It represents the updated shape variational posterior parameter scaling matrix of the group target n at the l-1th variational iteration at time k, It represents the degrees of freedom of the updated shape variational posterior parameters of the group target n at the l-1th variational iteration at time k.

[0053] Optionally, at time k, the variational posterior parameters of the states of the respective group targets after the l-th variational iteration further include: at time k, the extended shape variational posterior parameters of the respective group targets after the l-th variational iteration; the extended shape variational posterior parameters include: shape variational posterior parameter degrees of freedom and shape variational posterior parameter scaling matrix; the extended shape variational posterior parameters are represented by reference as follows:

[0054]

[0055] in, represents the degree of freedom of the updated shape variational posterior parameters of the group target n in the lth variational iteration at time k, represents the updated shape variational posterior parameter scaling matrix of the group target n in the lth variational iteration at time k, It represents the intermediate value of group target n under the tth joint probability data association event in the lth variational iteration at time k. variable;

[0056] At the k moment, in the current l-th variational iteration, the group target n is in the middle of the t-th joint probability data association event variable Refer to the following representation:

[0057]

[0058] in, Indicates the k-th time, the t-th joint probability data association event The equivalent measurement diffusion of the following group target n is,

[0059] Optionally, at time k, the variational posterior parameters of the states of the respective group targets after the l-th variational iteration further include: at time k, the measurement rate variational posterior parameters of the respective group targets after the l-th variational iteration; the measurement rate variational posterior parameters include the measurement rate variational posterior parameter scale and the measurement rate variational posterior parameter; the measurement rate variational posterior parameter reference is expressed as follows:

[0060]

[0061] in, represents the measurement rate variational posterior parameter scale of the updated group target n in the lth variational iteration at time k, It represents the updated measurement rate variational posterior parameter of the group target n in the lth variational iteration at time k.

[0062] The technical solution provided by the present invention may include the following beneficial effects:

[0063] The present invention describes the changes in the shape of group targets, so that the present invention can estimate the shape of group targets more accurately. The variational Bayesian inference method is used to estimate the state parameters of each target, which can effectively avoid the problem of shape estimation collapse. In view of the unknown measurement rate problem in the tracking scene, the corresponding parameters are modeled, which has stronger adaptability in complex tracking scenes.

[0064] Other features and advantages of the present invention will be described in detail in the following detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the following specific embodiments, they are used to explain the present invention but do not constitute a limitation of the present invention. In the accompanying drawings:

[0066] Figure 1 It is a flowchart of a multi-group target tracking method based on variational Bayesian reasoning and joint probability data association according to an exemplary embodiment of the present invention.

[0067] Figure 2 is a schematic diagram of actual trajectories of two target groups running in simulation according to an exemplary embodiment.

[0068] Figure 3 It is a schematic diagram showing a comparison between the present invention and the existing method according to an exemplary embodiment. DETAILED DESCRIPTION

[0069] Figure 1 is a flowchart of a multi-group target tracking method based on variational Bayesian reasoning and joint probability data association according to an exemplary embodiment of the present invention. Figure 1 As shown, the method comprises the following steps:

[0070] S1. According to the posterior estimated values ​​of the state parameters at time k-1, the states of each target group in the radar's surveillance area are predicted, and the predicted values ​​of the state parameters of each group target at time k are obtained respectively; wherein the state of each target group includes: center of mass kinematic state, extended shape state and measurement rate state; the state parameters include: center of mass kinematic parameters, extended shape parameters and measurement rate parameters.

[0071] Optionally, before S1, the method further includes:

[0072] In a rectangular coordinate system, a mathematical model of the state parameter distribution of each group target is established; wherein the mathematical model of the state parameter distribution includes a dynamic model of the kinematic state of the center of mass, a dynamic model of the shape state and a group target measurement model;

[0073] At time k=0, the state parameters of each group target are initialized according to the prior information.

[0074] It can be understood that existing methods for modeling the state of a single group target include using a random matrix model, a star convex expansion model, a Gaussian process model, and a complex mixture model.

[0075] This example uses a random matrix model with adaptive measurement rate modeling to model the kinematic parameters and extended shape of the group target, that is, the state of the group target is divided into three parts: the center of mass kinematic state, the extended shape state and the measurement rate state. Among them, the center of mass kinematic state is used to describe the behavior of the group target, and the corresponding parameter is called "center of mass kinematic parameter"; the extended shape state is used to describe the size of the group target or the specific shape of the shape contour, and the corresponding parameter is called "extended shape parameter"; the measurement rate state is used to indicate the number of measurements generated by the group target at the current moment, and the corresponding parameter is called "measurement rate parameter". Its implementation steps include the following:

[0076] For example, the mathematical model of the kinematic state x of the center of mass of the group target is described as a Gaussian distribution:

[0077]

[0078] Among them, the symbol “~” indicates the distribution form that the state conforms to. and They are the mean and covariance matrices of the kinematic states of the center of mass of the group targets modeled by Gaussian distribution, which constitute the “kinematic parameters” and are called “kinematic parameter mean” and “kinematic parameter covariance” respectively.

[0079] Furthermore, a dynamic model of the kinematic state of the center of mass of the group target is established. The dynamic model of the kinematic state of the group target is as follows:

[0080]

[0081] in, represents the kinematic state of the center of mass of group target n at time k, Φ k The dynamic matrix representing the kinematic state of the center of mass of group target n at time k, represents the kinematic state of the center of mass of the group target n at time k-1, represents the process noise of the group target n at time k, and obeys the mean Gaussian distribution represents the process noise covariance matrix of group target n at time k.

[0082] For example, the mathematical model of the extended shape state X of the group target is modeled as an inverse Wechsler distribution:

[0083]

[0084] in, and They are the degrees of freedom and scale matrix of the extended shape state of the group target modeled by the inverse Wiechter distribution, which constitute the "shape parameters" and are called "shape parameter degrees of freedom" and "shape parameter scale matrix" respectively.

[0085] Furthermore, a dynamic model of the group target extended appearance state is established. The dynamic model of the group target extended appearance state is as follows:

[0086]

[0087] Among them, the operation (·) T Indicates matrix transposition operation, distribution represents the Weichter distribution. represents the extended shape state of group target n at time k, represents the extended shape state of group target n at time k, is the shape evolution description matrix of group target n at time k, is the shape degrees of freedom of the group target n at time k.

[0088] For example, the mathematical model of the measurement rate state λ of the group target is modeled as a gamma distribution:

[0089]

[0090] in, and They are the scale and size of the group target measurement rate state modeled by the gamma distribution, which constitute the "measurement rate parameter" and are respectively called "measurement rate parameter scale" and "measurement rate parameter scale".

[0091] Furthermore, a group target measurement model is established. The group target measurement model is as follows:

[0092]

[0093] in, represents the first Measurements, is the observation matrix of group target n at time k, is the kinematic state of the center of mass of the group target n at time k. is the pseudo-measurement noise of group target n at time k, and follows a Gaussian distribution in, represents the shape distortion matrix of group target n at time k, Represents the extended shape state of group target n at time k.

[0094] It is worth mentioning that in the above model, the introduced time subscript "k" should represent all times greater than or equal to 1, that is, the above model is applicable when k>1.

[0095] Optionally, the predicted values ​​of the state parameters of each group target at time k include: the predicted values ​​of the center of mass kinematic parameters of each group target at time k, the predicted values ​​of the extended shape parameters and the predicted values ​​of the measurement rate parameters; the predicted values ​​of the center of mass kinematic parameters of each group target at time k include: the predicted value of the mean of the kinematic parameters of each group target at time k and the predicted value of the covariance of the kinematic parameters of each group target at time k; the predicted values ​​of the extended shape parameters of each group target at time k include: the predicted value of the degree of freedom of the shape parameters of each group target at time k and the predicted value of the shape parameter scale matrix of each group target at time k; the predicted values ​​of the measurement rate parameters of each group target at time k include: the predicted value of the measurement rate parameter scale of each group target at time k and the predicted value of the measurement rate parameter scale of each group target at time k.

[0096] Optionally, the predicted values ​​of the kinematic parameters of the center of mass of each group target at time k are as follows:

[0097]

[0098] in, represents the predicted value of the mean kinematic parameter of group target n at time k, The dynamic matrix representing the kinematic state of the center of mass of the group target n at time k, is the posterior estimate of the mean kinematic parameter of group target n at time k-1, T represents the transposition operation, represents the predicted value of the covariance of the kinematic parameters of the group target n at time k, represents the posterior estimate of the covariance of the kinematic parameters of the group target n at time k-1, represents the process noise covariance matrix of group target n at time k;

[0099] The predicted values ​​of the extended shape parameters of each group target at time k are as follows:

[0100]

[0101] in, represents the predicted value of the degree of freedom of the shape parameters of the group target n at time k, represents the shape freedom of the group target n at time k, is an auxiliary variable, represents the posterior estimate of the degree of freedom of the shape parameters of the group target n at time k-1, n d To track the dimensions of the scene; represents the predicted value of the shape parameter scaling matrix of group target n at time k, represents the shape evolution description matrix of group target n at time k, Indicates n d The identity matrix of order, represents the posterior estimate of the scaling matrix of the shape parameters of the group target n at time k-1;

[0102] The predicted values ​​of the measurement rate parameters of each group target at time k are as follows:

[0103]

[0104] in, represents the predicted value of the measurement rate parameter scale of group target n at time k, represents the posterior estimate of the measurement rate parameter scale of the group target n at time k-1, represents the measurement rate forgetting factor of the group target n at time k-1, represents the predicted value of the measurement rate parameter scale of group target n at time k, Represents the posterior estimate of the measurement rate parameter scale of the group target n at time k-1.

[0105] S2. Initialize the current variational Bayesian inference iteration number l=0, and perform initial variational iteration of each group target at time k and update the variational iteration number l=l+1 according to the predicted value of the state parameter of each group target at time k; wherein the initial variational iteration represents the variational posterior parameters of the initial state of each group target at time k after the l=0th variational iteration.

[0106] It can be understood that at the moment k>0, the current variational Bayesian inference iteration (hereinafter referred to as "variational iteration") number l=0 is initialized, and the variational posterior parameters of the center of mass kinematic state, extended shape state and measurement rate state are initialized according to the prediction results of each state of each group target. At the moment k, the current variational iteration number l=0 is initialized; at the moment k, when the variational iteration number l=0, the variational posterior parameters of the center of mass kinematic state of each group target are initialized. The variational posterior parameters of the center of mass kinematic state include "kinematic variational posterior parameter mean" and "kinematic variational posterior parameter covariance". Generally, the initialization process of the two parts of the parameters can be expressed as:

[0107]

[0108] Among them, the scalar l represents the number of current variational iterations, represents the mean value of the kinematic variational posterior parameters of the group target n at the 0th variational iteration (i.e., the initial variational iteration) at time k, represents the kinematic variational posterior parameter covariance of the group target n at the 0th variational iteration at time k.

[0109] At time k, when the number of variational iterations l = 0, the variational posterior parameters of the extended shape state of each group target are initialized. The variational posterior parameters of the extended shape state include two parts: "shape variational posterior parameter degrees of freedom" and "shape variational posterior parameter scaling matrix". In general, the initialization process of these two parts of parameters can be expressed as:

[0110]

[0111] in, represents the degree of freedom of the posterior parameters of the shape variation of the group target n at the 0th variational iteration at time k, It represents the scaling matrix of the shape variational posterior parameters of the group target n at the 0th variational iteration at time k.

[0112] At time k, when the number of variational iterations l = 0, the variational posterior parameters of the measurement rate state of each group target are initialized. The variational posterior parameters of the measurement rate include "measurement rate variational posterior parameter scale" and "measurement rate variational posterior parameter scale". In general, the initialization process of these two parts of the parameters can be expressed as:

[0113]

[0114] in, represents the variational posterior parameter scale of the measurement rate of the group target n at the 0th variational iteration at time k, It represents the scale of the variational posterior parameter of the measurement rate of the group target n at the 0th variational iteration at time K.

[0115] After the above initialization, the number of variational iterations l increases by 1, that is, l=l+1. At this time, l=1 and continue with the subsequent steps.

[0116] S3. At time k, based on the measurement data of each group target and the variational posterior parameters of the initial state obtained after the l-1th variational iteration, the variational posterior probability of the joint probability data association event after normalization after the lth variational iteration is obtained; wherein the measurement data is the data captured by the sensor and expressed in a Cartesian coordinate system.

[0117] It can be understood that the variational posterior parameters of the various states of each group target include: variational posterior parameters of the kinematic state of the center of mass of each group target, variational posterior parameters of the extended shape state of each group target, variational posterior parameters of the measurement rate state of each target, and three parts. Joint probability data association events can be, but are not limited to, also called "association events", "joint association events", "data association assumptions", "association assumptions", etc.

[0118] Optionally, the normalized variational posterior probability reference of each joint probability data association event is expressed as follows:

[0119]

[0120] in, represents the normalized variational posterior probability of the t-th joint probability data association event in the l-th variational iteration at time k, is the total number of events associated with the joint probability data at the current k moment, express The variational posterior probability at the lth variational iteration, represents the t-th joint probability data association event at time k;

[0121] Refer to the following representation:

[0122]

[0123] Where ρ is the clutter density, λ c is the clutter Poisson rate, is the t-th joint probability data association event at the current k-th moment The number of clutter measurements. ∏ represents the product sign, n k Represents the total number of group targets at time k, the product term represents the measurement likelihood generated by the measurement assigned to the group target n under the tth joint probability data association event at time k, represents the set of measurements consisting of the measurements assigned to the group target n at the tth joint probability data association event at time k, yes The Measurements, represents the measurement matrix of group target n at time k, represents the predicted value of the mean kinematic parameter of group target n at time k, represents the innovation covariance matrix of group target n at time k Represents the measurement rate factor.

[0124] Optionally, the measurement rate factor Refer to the following representation:

[0125]

[0126] in, It represents the updated measurement rate variational posterior parameter scale of the group target n at the l-1th variational iteration at time k, It represents the updated measurement rate variational posterior parameter scale of the group target n at the l-1th variational iteration at time k;

[0127] Innovation covariance matrix of group target n at time k Refer to the following representation:

[0128]

[0129] in, represents the shape distortion matrix of group target n at time k;

[0130] The shape distortion matrix of group target n at time k Refer to the following representation:

[0131]

[0132] in,(·) -1 / 2 It means to take the square root after inverting the matrix, that is s is the scaling constant, represents the true observation noise covariance matrix of group target n at time k, represents the expected prediction of the extended appearance state of group target n at time k;

[0133] represents the expected prediction of the extended appearance state of the group target n at time k Refer to the following representation:

[0134]

[0135] Among them, n d To track the dimensions of the scene.

[0136] S4. According to the variational posterior probability of the event associated with the normalized joint probability data, the variational posterior parameters of the initial state are updated to obtain the variational posterior parameters of the state of each group target after the lth variational iteration at time k and update the number of variational iterations l=l+1.

[0137] Optionally, at time k, the variational posterior parameters of the states of each group target after the l-th variational iteration include: at time k, the center of mass kinematic variational posterior parameters of each group target after the l-th variational iteration; the center of mass kinematic variational posterior parameters include the kinematic variational posterior parameter mean and the kinematic variational posterior parameter covariance, and the update reference of the center of mass kinematic variational posterior parameters is expressed as follows:

[0138]

[0139] in, represents the mean of the kinematic variational posterior parameters of the group target n updated in the lth variational iteration at time k; represents the Kalman gain matrix of group target n in the lth variational iteration at time k, represents the kinematic variational posterior parameter covariance of the group target n updated in the lth variational iteration at time k, Indicates the k-th time, the t-th joint probability data association event The equivalent measurement of the following group target n is,

[0140]

[0141] At time k, the Kalman gain matrix of group target n under the lth variational iteration is Refer to the following representation:

[0142]

[0143] in,(·) -1 Indicates the inversion of the matrix. It represents the updated shape variational posterior parameter scaling matrix of the group target n at the l-1th variational iteration at time k, It represents the degrees of freedom of the updated shape variational posterior parameters of the group target n at the l-1th variational iteration at time k.

[0144] Optionally, at time k, the variational posterior parameters of the states of each group target after the l-th variational iteration also include: at time k, the extended shape variational posterior parameters of each group target after the l-th variational iteration; the extended shape variational posterior parameters include: shape variational posterior parameter degrees of freedom and shape variational posterior parameter scaling matrix; the update reference of the extended shape variational posterior parameters is expressed as follows:

[0145]

[0146] in, represents the degree of freedom of the updated shape variational posterior parameters of the group target n in the lth variational iteration at time k, represents the updated shape variational posterior parameter scaling matrix of the group target n in the lth variational iteration at time k, It represents the intermediate value of group target n under the tth joint probability data association event in the lth variational iteration at time k. variable;

[0147] At time k, in the current l-th variational iteration, the group target n is in the middle of the t-th joint probability data association event variable Refer to the following representation:

[0148]

[0149] in, Indicates the k-th time, the t-th joint probability data association event The equivalent measurement diffusion of the following group target n is,

[0150] Optionally, at time k, the variational posterior parameters of the states of each group target after the l-th variational iteration also include: at time k, the measurement rate variational posterior parameters of each group target after the l-th variational iteration; the measurement rate variational posterior parameters include the measurement rate variational posterior parameter scale and the measurement rate variational posterior parameter; the update reference of the measurement rate variational posterior parameter is expressed as follows:

[0151]

[0152] in, represents the measurement rate variational posterior parameter scale of the updated group target n in the lth variational iteration at time k, It represents the updated measurement rate variational posterior parameter of the group target n in the lth variational iteration at time k.

[0153] It is worth mentioning that at time k, the current number of variational iterations l is incremented by 1, l=l+1.

[0154] S5: Determine whether the cumulative number of variational iterations reaches the preset upper limit N of variational iterations. sc .

[0155] If not, return to S3; if so, execute S6, at time k, according to the Nth sc The variational posterior parameters of the states of each group target after the variational iterations are used to obtain the posterior estimated values ​​of the state parameters at time k, so as to predict the states of each target group at time k+1.

[0156] It is understandable that at time k, using the Nth sc The variational posterior parameters of each state of each group target after the last variational iteration are assigned and updated to the posterior estimated values ​​of each state parameter of each group target at time k.

[0157] At time k, use the Nth sc The kinematic variational posterior parameters of each group target obtained after the variational iteration are used to update the posterior estimated values ​​of the kinematic parameters of each group target. In general, the posterior estimated value update process of the kinematic parameters of group target n at time k can be expressed as:

[0158]

[0159] in, represents the posterior estimate of the mean of the kinematic parameters of the group target n at time k; Indicates the kth moment, the Nth sc In the variational iteration, the mean of the kinematic variational posterior parameters of the group target n is updated; represents the a posteriori estimate of the covariance of the kinematic parameters of the group target n at time k; Indicates the kth moment, the Nthsc In the variational iteration, the kinematic variational posterior parameter covariance of the group target n is updated.

[0160] At time k, use the Nth sc The variational posterior parameters of the shape of each group target obtained after the variational iteration are used to update the posterior estimated values ​​of the shape parameters of each group target. In general, the update process of the posterior estimated values ​​of the shape parameters of group target n at time k can be expressed as:

[0161]

[0162] in, represents the posterior estimate of the degrees of freedom of the shape parameters of the group target n at time k; Indicates the kth moment, the Nth sc In the variational iteration, the degree of freedom of the shape variational posterior parameters of the group target n is updated; represents the posterior estimate of the scaling matrix of the shape parameters of the group target n at time k; Indicates the kth moment, the Nth sc In the variational iteration, the shape variation posterior parameter scaling matrix of the group target n is updated.

[0163] At time k, use the Nth sc The measurement rate variational posterior parameters of each group target obtained after the variational iterations are used to update the posterior estimated values ​​of the measurement parameters of each group target. In general, the update process of the posterior estimated value of the measurement rate parameter of the group target n at time K can be expressed as:

[0164]

[0165] in, represents the a posteriori estimate of the measurement rate parameter scale of group target n at time k; Indicates the kth moment, the Nth sc In the variational iteration, the measurement rate variational posterior parameter scale of the group target n is updated; represents the posterior estimate of the measurement rate parameter scale of group target n at time k; Indicates the kth moment, the Nth sc In the variational iteration, the measurement rate variational posterior parameter scale of the group target n is updated.

[0166] At time k, the time k is iterated by incrementing by 1, k=k+1; and after the current time k is incremented by 1, judgment S7 is entered.

[0167] S7: At time k, determine whether each group target has left the monitoring area.

[0168] If not, return to S1; if so, execute S8 to end the tracking of each target group.

[0169] In one embodiment, the above beneficial effects of the present invention are further illustrated by simulation experiments:

[0170] Simulation conditions: The simulation scene is a two-dimensional scene with a scene size of [0m, 610m] × [-320m, 320m]. The target group center position information is expressed in a rectangular coordinate system. There are two groups of targets of different sizes in the scene. They have the same motion mode and both maintain uniform linear motion, and cross over with time. Figure 2 is a schematic diagram of actual trajectories of two target groups running in simulation according to an exemplary embodiment.

[0171] The initial states of the two target groups are shown in Table 1:

[0172] Table 1

[0173]

[0174] State transfer model of two target groups: State transfer matrix of kinematic parameters: Process Noise: Where k is the time index, n is the index of the group target, and the operation diag(·) represents taking a diagonal matrix.

[0175] Measurement model of two target groups: Measurement matrix: H = [I2 O2]; Measurement noise: Among them, I n represents the n-order identity matrix, O n represents an n-th order zero matrix.

[0176] Simulation content: simulation software environment: MATLAB R2016a; simulation hardware environment: processor: 2.81GHz IntelCore i9 processor; memory: 16G. Under the above simulation conditions, the present invention and three existing multi-target group tracking methods RM-JPDA (Randomized Multiple Hypothesis Tracking with JointProbabilistic Data Association, a method based on joint probability data association), RM-T-PMB (Randomized Multi-Bernoulli with Track-Before-Detect, combining the technology of multi-Bernoulli model and Track-Before-Detect method), LJPDA-MEM (Low Complexity JPDA with MeasurementError Model) are used to track two group targets in the monitoring area: the simulation starts at 0s, and the two target groups with different extended shape sizes gradually approach at the same rate. At 30s, the two target groups cross, and the crossing process lasts for 3s. At 33s, the two target groups complete the crossing and continue to move, and gradually move away until the simulation ends at 60s. During the entire simulation process, 60 sampling moments were selected at intervals of T=1s.

[0177] Figure 3 FIG. 1 is a schematic diagram showing a comparison between the present invention and the existing method according to an exemplary embodiment. The Gauss-Wasserstein distance (GWD) results of the present invention and the existing three multi-target group tracking methods RM-JPDA, RM-T-PMB, and LJPDA-MEM after tracking two group targets in the above scenario are compared. The comparison results are shown in FIG. Figure 3 shown.

[0178] Simulation results analysis: Figure 3 It can be seen that the Gauss-Wasserstein distance (GWD) of the method of the present invention is always maintained at the lowest level for both the large group target 1 and the small group target 2, that is, the present invention has the highest overall accuracy in estimating the size of the group target's extended shape and the centroid position. It is verified that the present invention can be used to track multiple group targets under a certain clutter background, and compared with the current advanced correlation algorithms, it has stronger adaptability and higher accuracy.

[0179] The preferred embodiments of the present invention are described in detail above in conjunction with the accompanying drawings. However, the present invention is not limited to the specific details in the above embodiments. Within the technical concept of the present invention, a variety of simple modifications can be made to the technical solution of the present invention, and these simple modifications all belong to the protection scope of the present invention.

[0180] It should also be noted that the various specific technical features described in the above specific embodiments can be combined in any suitable manner without contradiction. In order to avoid unnecessary repetition, the present invention will not further describe various possible combinations.

[0181] In addition, various embodiments of the present invention may be arbitrarily combined, and as long as they do not violate the concept of the present invention, they should also be regarded as the contents disclosed by the present invention.

Claims

1. A multi-group target tracking method based on variational Bayesian reasoning and joint probability data association, characterized in that: The method comprises: S1, predicting the state of each target group in the surveillance area of ​​the radar according to the posterior estimated value of the state parameter at time k-1, and obtaining the predicted value of the state parameter of each group target at time k; wherein the state of each target group includes: center of mass kinematic state, extended shape state and measurement rate state; the state parameters include: center of mass kinematic parameter, extended shape parameter and measurement rate parameter; S2, initialize the current variational Bayesian inference iteration number l=0, and perform the initial variational iteration of each group target at time k and update the variational iteration number l=l+1 according to the predicted value of the state parameter of each group target at time k; wherein the initial variational iteration represents the variational posterior parameters of the initial state of each group target after the l=0th variational iteration at time k; S3. At time k, based on the measurement data of each group target and the variational posterior parameters of the initial state obtained after the l-1th variational iteration, obtain the variational posterior probability of the joint probability data association event after normalization after the lth variational iteration; wherein the measurement data is data captured by the sensor and represented in a Cartesian coordinate system; S4, according to the variational posterior probability of the joint probability data associated event after the normalization, the variational posterior parameters of the initialization state are updated to obtain the variational posterior parameters of the states of the various group targets after the lth variational iteration at time k and update the number of variational iterations l=l+1; S5: Determine whether the cumulative number of variational iterations reaches the preset upper limit N of variational iterations. sc ; If not, return to S3; if so, execute S6, at time k, according to the Nth sc The variational posterior parameters of the states of each group target after the variational iterations are used to obtain the posterior estimated values ​​of the state parameters at time k, so as to predict the states of each target group at time k+1. S7, at time k, determining whether each group target has left the monitoring area; If not, return to S1; if so, execute S8 to end the tracking of each target group.

2. The multi-group target tracking method based on variational Bayesian reasoning and joint probability data association according to claim 1 is characterized in that: Before S1, the method further includes: In a rectangular coordinate system, a mathematical model of the state parameter distribution of each group target is established; wherein the mathematical model of the state parameter distribution includes a dynamic model of the kinematic state of the center of mass, a dynamic model of the shape state, and a group target measurement model; At time k=0, the state parameters of each group target are initialized according to the prior information.

3. The multi-group target tracking method based on variational Bayesian reasoning and joint probability data association according to claim 1, characterized in that: The predicted values ​​of the state parameters of each group target at time k include: the predicted values ​​of the center of mass kinematic parameters of each group target at time k, the predicted values ​​of the extended shape parameters and the predicted values ​​of the measurement rate parameters; the predicted values ​​of the center of mass kinematic parameters of each group target at time k include: the predicted value of the mean of the kinematic parameters of each group target at time k and the predicted value of the kinematic parameter covariance of each group target at time k; the predicted values ​​of the extended shape parameters of each group target at time k include: the predicted value of the shape parameter freedom degree of each group target at time k and the predicted value of the shape parameter scale matrix of each group target at time k; the predicted values ​​of the measurement rate parameters of each group target at time k include: the predicted value of the measurement rate parameter scale of each group target at time k and the predicted value of the measurement rate parameter scale of each group target at time k.

4. The multi-group target tracking method based on variational Bayesian reasoning and joint probability data association according to claim 3 is characterized in that: The predicted values ​​of the kinematic parameters of the center of mass of each group target at time k are as follows: in, represents the predicted value of the mean kinematic parameter of group target n at time k, The dynamic matrix representing the kinematic state of the center of mass of the group target n at time k, is the posterior estimate of the mean kinematic parameter of group target n at time k-1, T represents the transposition operation, represents the predicted value of the covariance of the kinematic parameters of the group target n at time k, represents the posterior estimate of the covariance of the kinematic parameters of the group target n at time k-1, represents the process noise covariance matrix of group target n at time k; The predicted values ​​of the extended shape parameters of each group target at time k are as follows: in, represents the predicted value of the degree of freedom of the shape parameters of the group target n at time k, represents the shape freedom of the group target n at time k, is an auxiliary variable, represents the posterior estimate of the degree of freedom of the shape parameters of the group target n at time k-1, n d To track the dimensions of the scene; represents the predicted value of the shape parameter scaling matrix of group target n at time k, represents the shape evolution description matrix of group target n at time k, Indicates n d The identity matrix of order, represents the posterior estimate of the scaling matrix of the shape parameters of the group target n at time k-1; The predicted values ​​of the measurement rate parameters of each group target at time k are as follows: in, represents the predicted value of the measurement rate parameter scale of group target n at time k, represents the posterior estimate of the measurement rate parameter scale of the group target n at time k-1, represents the measurement rate forgetting factor of the group target n at time k-1, represents the predicted value of the measurement rate parameter scale of group target n at time k, Represents the posterior estimate of the measurement rate parameter scale of the group target n at time k-1.

5. The multi-group target tracking method based on variational Bayesian reasoning and joint probability data association according to claim 4 is characterized in that: The normalized variational posterior probability of each joint probability data association event is expressed as follows: in, represents the normalized variational posterior probability of the t-th joint probability data association event in the l-th variational iteration at time k, is the total number of events associated with the joint probability data at the current k moment, express The variational posterior probability at the lth variational iteration, represents the t-th joint probability data association event at time k; Refer to the following representation: Where ρ is the clutter density, λ c is the clutter Poisson rate, is the t-th joint probability data association event at the current k-th moment The number of clutter measurements. Π represents the sign of the product, n k Represents the total number of group targets at time k, the product term represents the measurement likelihood generated by the measurement assigned to the group target n under the tth joint probability data association event at time k, represents the set of measurements consisting of the measurements assigned to the group target n at the tth joint probability data association event at time k, yes The Measurements, represents the measurement matrix of group target n at time k, represents the predicted value of the mean kinematic parameter of group target n at time k, represents the innovation covariance matrix of group target n at time k, Represents the measurement rate factor.

6. The multi-group target tracking method based on variational Bayesian reasoning and joint probability data association according to claim 5, characterized in that:The measurement rate factor Refer to the following representation: in, It represents the updated measurement rate variational posterior parameter scale of the group target n at the l-1th variational iteration at time k, It represents the updated measurement rate variational posterior parameter scale of the group target n at the l-1th variational iteration at time k; Innovation covariance matrix of group target n at time k Refer to the following representation: in, represents the shape distortion matrix of group target n at time k; The shape distortion matrix of group target n at time k Refer to the following representation: Among them, (·)-1 / 2 means taking the square root after inverting the matrix, that is, s is the scaling constant, represents the true observation noise covariance matrix of group target n at time k, represents the expected prediction of the extended appearance state of group target n at time k; represents the expected prediction of the extended appearance state of the group target n at time k Refer to the following representation: Among them, n d To track the dimensions of the scene.

7. The multi-group target tracking method based on variational Bayesian reasoning and joint probability data association according to claim 6 is characterized in that: The variational posterior parameters of the states of the various group targets after the l-th variational iteration at the k moment include: the mass center kinematic variational posterior parameters of the various group targets after the l-th variational iteration at the k moment; the mass center kinematic variational posterior parameters include the kinematic variational posterior parameter mean and the kinematic variational posterior parameter covariance, and the update reference of the mass center kinematic variational posterior parameters is expressed as follows: in, represents the mean of the kinematic variational posterior parameters of the group target n updated in the lth variational iteration at time k; represents the Kalman gain matrix of group target n in the lth variational iteration at time k, represents the kinematic variational posterior parameter covariance of the group target n updated in the lth variational iteration at time k, Indicates the k-th time, the t-th joint probability data association event The equivalent measurement of the following group target n is, At time k, the Kalman gain matrix of group target n under the lth variational iteration is Refer to the following representation: in,(·) -1 Indicates the inversion of the matrix. It represents the updated shape variational posterior parameter scaling matrix of the group target n at the l-1th variational iteration at time k, It represents the degrees of freedom of the updated shape variational posterior parameters of the group target n at the l-1th variational iteration at time k.

8. The multi-group target tracking method based on variational Bayesian reasoning and joint probability data association according to claim 7, characterized in that: The variational posterior parameters of the states of the various group targets after the l-th variational iteration at the k-th time further include: the extended shape variational posterior parameters of the various group targets after the l-th variational iteration at the k-th time; the extended shape variational posterior parameters include: shape variational posterior parameter degrees of freedom and shape variational posterior parameter scaling matrix; the update reference of the extended shape variational posterior parameters is expressed as follows: in, represents the degree of freedom of the updated shape variational posterior parameters of the group target n in the lth variational iteration at time k, represents the updated shape variational posterior parameter scaling matrix of the group target n in the lth variational iteration at time k, It represents the intermediate value of group target n under the tth joint probability data association event in the lth variational iteration at time k. variable; At the k moment, in the current l-th variational iteration, the group target n is in the middle of the t-th joint probability data association event variable Refer to the following representation: in, Indicates the k-th time, the t-th joint probability data association event The equivalent measurement diffusion of the following group target n is, 9. The multi-group target tracking method based on variational Bayesian reasoning and joint probability data association according to claim 8, characterized in that: The variational posterior parameters of the states of the various group targets after the l-th variational iteration at the k-th time further include: the measurement rate variational posterior parameters of the various group targets after the l-th variational iteration at the k-th time; the measurement rate variational posterior parameters include the measurement rate variational posterior parameter scale and the measurement rate variational posterior parameter; the update reference of the measurement rate variational posterior parameter is expressed as follows: in, represents the measurement rate variational posterior parameter scale of the group target n updated in the lth variational iteration at time k, It represents the updated measurement rate variational posterior parameter of the group target n in the lth variational iteration at time k.

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