CN119716831B

CN119716831B - Multi-target tracking method in non-Gaussian noise environment

Info

Publication number: CN119716831B
Application number: CN202411318758.XA
Authority: CN
Inventors: 闫永胜; 王俊锴; 王海燕; 冷冰; 王柱颖; 张红伟
Original assignee: Northwestern Polytechnical University
Current assignee: Northwestern Polytechnical University
Priority date: 2024-09-20
Filing date: 2024-09-20
Publication date: 2025-10-03
Anticipated expiration: 2044-09-20
Also published as: CN119716831A

Abstract

This invention provides a multi-target tracking method in a non-Gaussian noise environment. A spatial coordinate system is established to obtain the sensor's position coordinates and monitoring area. The sensor periodically acquires a measurement set, including the number of targets and the associated measurement set for each target. Based on a target state-measurement model, the associated measurement set is iteratively updated using a Dirichlet process-hidden Markov chain hybrid model to determine the target state's posterior probability density. Based on the iterative updates of each frame, the track of each target is output. This invention significantly reduces tracking error and improves track estimation accuracy and track integrity. By adaptively and in real time jointly estimating the probability density distribution of the target state and observation noise through variational inference, tracking error is significantly reduced and track estimation accuracy and track integrity are improved.

Description

Multi-target tracking method in non-Gaussian noise environment

Technical Field

The invention relates to the technical field of target tracking, in particular to a multi-target tracking method in a non-Gaussian noise environment.

Background

With the development of technology, unmanned or unmanned aircraft are moving in the air and underwater more and more frequently, so that the monitoring of the aircraft is particularly important.

When targets such as unmanned underwater vehicles are tracked and positioned, multipath interference exists on signals received by a receiving end in an observation channel due to the influences of factors such as non-uniformity of a transmission medium, object reflection and interface reflection, so that the receiving end of the observation channel has multi-mode statistical characteristics in receiving measurement, meanwhile, the random time-varying space-variant characteristics of the observation channel can seriously influence on the on-off of a communication link, and the conditions of missed detection and false alarms often occur due to the existence of clutters or false targets in the transmission medium.

Standard random finite set algorithms assume that a priori knowledge of the sensor noise statistics is known and gaussian distributed, and in practice it is often difficult to construct an accurate model for the sensor noise. If such non-gaussian measurement errors are not considered in a practical system, a model mismatch of the multi-target tracking method may be caused, thereby causing degradation of tracking performance and even giving a completely erroneous target state estimate.

Therefore, accurate tracking and positioning of multiple targets in a non-Gaussian noise environment is a technical problem to be solved.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention provides a multi-target tracking method under a non-Gaussian noise environment, which is characterized by establishing a space coordinate system, acquiring position coordinates and a monitoring area of a sensor, periodically acquiring a measurement set by the sensor, wherein the measurement set is a set formed by the position of a real target and a false target position caused by clutter, the set of measurement information in an ith frame is marked as Z _i, acquiring the number of targets and the associated measurement set of each target, carrying out iterative update of target state posterior probability density by using the associated measurement set through a Dirichlet process-hidden Markov chain mixed model based on a target state-measurement model, and outputting each target track according to the iterative update of each frame. The invention adopts a generalized label multi-Bernoulli filtering and Dirichlet process-hidden Markov chain hybrid model, obviously reduces tracking error and improves track estimation precision and track integrity.

Aiming at the problems of track jump, high track omission factor, low tracking precision and the like of the traditional standard random finite set algorithm in a non-Gaussian noise environment, the invention provides a multi-target tracking method in the non-Gaussian noise environment, so as to improve the accuracy and the robustness of multi-target tracking.

The technical scheme adopted by the invention for solving the technical problems comprises the following steps:

Step 1, establishing a space coordinate system, and acquiring position coordinates and a monitoring area of a sensor;

Step 2, periodically acquiring a measurement set by a sensor, wherein the measurement set is a set formed by the position of a real target and the position of a false target caused by clutter, and the set of measurement information in the moment i is marked as Z _i;

Step 3, acquiring a related measurement set of the number of targets and each target through generalized tag multiple Bernoulli filtering based on the measurement set acquired by the sensor;

step 4, based on the target state-measuring model, establishing a dirichlet procedure-hidden Markov chain mixed model, and carrying out iterative updating on the posterior probability density of the target state by adopting a solution mode of variational inference according to the associated measuring set;

and 5, outputting each target estimated track according to the iterative updating of the posterior probability density of each target state.

Further, in the step 4, the solving step of the dirichlet procedure-hidden markov chain hybrid model and the variance inference is as follows:

The dirichlet process-hidden markov chain hybrid model construction process specifically comprises the following steps:

at time 1:t, periodically acquired metrology information for a sensor The measurement information is the real target position informationLocation information of spurious targets caused by clutterI.e.I is a time index, t represents a time t, and the number N of real targets and the state set of the real targets in the monitoring area are obtained through generalized label multiple Bernoulli filteringAnd (3) andAssociated measurementsWherein X isX _j is the state of the jth target, Y isY _j is the measurement corresponding to the jth target x _j, j is the target tag index, x _j,i is the state of the jth target at the moment i, and y _j,i is the measurement of the jth target at the moment i;

for the jth target Corresponding measurementThe target state-measurement model is as follows:

x_j,t＝Fx_j,t-1+w_j,t

y_j,t＝Hx_j,t+ξ_j,t

w_j,t~N(0,Q)

F is a state transition matrix, H is a measurement matrix, N (·) is a Gaussian distribution, w _j,t is state noise of a jth target at a moment t obeying zero-mean Gaussian distribution, Q is state noise variance, ζ _j,t is measurement noise of a jth target at a moment t and non-Gaussian distribution, the measurement noise is fitted through a Gaussian mixture model GMM, K is the number of Gaussian components in the Gaussian mixture model, e is a Gaussian component index, w _e is the amplitude of an e-th Gaussian component, and the requirements are met (Mu _ξe,Σ_ξe) is the distribution parameter of the e-th Gaussian component, which is the mean value and the variance respectively, x _j,t-1 is the state of the j-th target at the t-1 moment, x _j,t is the state of the j-th target at the t moment, and y _j,t is the measurement corresponding to the j-th target at the t moment;

The Dirichlet process-hidden Markov chain mixed model is established according to the target state-measurement model, a discrete distribution mathematical form obeying the Dirichlet process is constructed by adopting a broken rod model, and the specific construction mathematical process is as follows:

V_k~Beta(1,α)

alpha is a concentration parameter, represents a scalar that produces a degree of dispersion of the distribution, beta (·) is a Beta distribution, k is a first order index of the number of cuts, V _k is an intermediate parameter subject to the kth cut of the Beta distribution with parameter (1, alpha), and r is a second order index of the number of cuts. V _r is the intermediate parameter subject to the r-th truncation of the Beta distribution of parameter (1, α). Pi _k is the weight coefficient of the kth truncation, which satisfies S _j,t is an indicator of the jth target state x _j,t at time t, lambda is a base distribution parameter, G (lambda) is a base distribution, theta _k is a base obtained by kth sampling,Representing an infinite number of bases sampled, Σ being the covariance matrix of the gaussian distribution to which the measurement is subject.

Further, in the step 4, the solving mode of the variance inference of the dirichlet procedure-hidden markov chain hybrid model is specifically as follows:

The posterior probability density p (x _j,t,s_j,t,V,θ|y_j,1:t) for the jth target that needs to be estimated at time t:

v is a set of intermediate parameters V _k truncated infinitely, Y _j,1:t is the set of measurements for the jth target over a 1:t period,Y _j,1:t-1 is the set of measurements for the jth target over the 1:t-1 time period,

By means of the average field theory, the variational distribution family is adopted to replace the true posterior of the time points t and t-1:

Wherein q _p(x_j,t)＝∫q(x_j,t-1)p(x_j,t|x_j,t-1)dx_j,t-1,s_j,t-1 is an indicator of the jth target state x _j,t-1 at time t-1.

By means of conjugate prior, a prior distribution at time t is set for (x _j,t,s_j,t, V, θ):

The mean and variance of conjugate gaussian prior for the jth target x _j,t at time t, The mean and variance of conjugate Gaussian prior for the jth target x _j,t at time t-1,M _j,t isIs the one-step prediction mean of Sigma _j,t Mult (& gt) is a polynomial distribution,Is a parameter of the polynomial distribution at time t,The parameter is the parameter of the polynomial distribution of the kth time truncation at the t moment, (u _k,v_k) is the parameter of beta distribution; is a Gaussian distribution parameter, and (u _k,v_k) are compared with each other due to the need of iterative updating with time The definition is as follows: the parameter of the kth truncated beta distribution at time t-1, The parameters of the k-th truncated beta distribution at time t,The k-th truncated gaussian distribution at time t-1,The k-th truncated gaussian distribution parameter at time t.

And (3) carrying out variation inference according to (x _j,t,s_j,t, V, theta) and prior distribution thereof to obtain each prior distribution parameter recursion at the moment t as follows:

further, in the step 5, according to the iterative update of the posterior probability density of each target state, the estimated track of each target is output, which specifically includes the steps of:

for a multi-target associated track set: And (3) with By adopting the solution mode of variation inference, the posterior probability of x _j,i is iteratively updated at 1:t by the solution mode of variation inference, and finally an estimated track set of each target is obtainedBased on the estimated track set obtained above, the estimated tracks of each target in time can be presented through a visual operation.

An electronic device comprising one or more processors, memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs configured to perform the method as described above.

A computer readable storage medium storing program code that is callable by a processor to perform a method as described above.

The method has the advantages that the standard random finite set algorithm does not consider non-Gaussian measurement errors, so that the model mismatch of the multi-target tracking method is caused, the tracking performance is deteriorated, and even the completely wrong target state estimation is given. The probability density distribution of the target state and the observation noise is estimated in a combined mode in real time through variation inference self-adaption by utilizing a generalized label Bernoulli filtering and Dirichlet process-hidden Markov chain mixed model, so that tracking errors are reduced obviously, and track estimation precision and track integrity are improved.

Drawings

FIG. 1 is a flow chart of an embodiment of the present invention;

FIG. 2 is a flow chart of an embodiment of the present invention;

FIG. 3 is a schematic diagram of a multi-target real track in a monitored area in a simulation example of the present invention;

FIG. 4 is a schematic diagram of a non-Gaussian noise probability distribution function in a simulation example of the present invention;

FIG. 5 is a schematic diagram showing the comparison of the estimated track using two methods, DP-HMM-JointGLMB and JointGLMB, respectively, for the x-direction multi-target measurement in the simulation example of the present invention;

FIG. 6 is a schematic diagram showing the comparison of the estimated tracks of the simulation example of the present invention by using two methods, namely DP-HMM-JointGLMB and JointGLMB, respectively;

FIG. 7 is a schematic diagram showing the comparison of OSPA distance error, OSPA positioning error and OSPA potential error using two methods, DP-HMM-JointGLMB and JointGLMB, respectively, in a simulation example of the present invention;

FIG. 8 is a diagram showing the comparison of the number of multi-objective estimates using two methods, DP-HMM-JointGLMB and JointGLMB, respectively, in a simulation example of the present invention.

Detailed Description

The invention will be further described with reference to the drawings and examples.

As shown in fig. 1 to 8, the present invention provides a multi-target tracking method in a non-gaussian noise environment, comprising the steps of:

s1, setting a scene, namely establishing a two-dimensional or three-dimensional space coordinate system, taking a two-dimensional space coordinate system xoy as an example, and acquiring a position coordinate (x _s,y_s) of a sensor and a monitoring area x epsilon [ r _x1,r_x2],y∈[r_y1,r_y2 ];

S2, periodically acquiring a measurement set by the sensor, wherein the set of measurement information in the ith frame is marked as Z _i, and periodically acquiring the measurement information by the sensor in the 1:t time period The measurement information is real target position informationLocation information of spurious targets caused by clutterI.e.

S3, acquiring the number N of targets and the associated measurement set of each target, namely a target state set, through generalized label Bernoulli filtering (B.N.Vo,B.T.Vo,and H.G.Hoang,"An efficient implementation of the generalized labeled multi-Bernoulli filter,"IEEE Transactions on Signal Processing,vol.65,no.8,pp.1975–1987,Apr.2017.) based on the measurement set acquired by the sensorMeasurement associated therewithWherein X isX _j is the state of a certain target, Y isY _j is the corresponding measurement of target x _j.

S4, establishing a dirichlet procedure-hidden Markov chain hybrid model based on the target state-measurement model, and carrying out iterative update on the posterior probability density of the target state by adopting a solution mode of variational inference according to the associated measurement set;

S4.1 for the jth target Corresponding measurementThe target state-measurement model is as follows:

x_j,t＝Fx_j,t-1+w_j,t

y_j,t＝Hx_j,t+ξ_j,t

w_j,t~N(0,Q)

f is a state transition matrix, H is a measurement matrix, N (·) is a Gaussian distribution, w _j,t is state noise of the jth target at the moment t, which is subjected to zero-mean Gaussian distribution, Q is state noise variance, ζ _j,t is measurement noise of the jth target at the moment t, which is not Gaussian distribution, and is fitted through a Gaussian mixture model GMM, K is the number of Gaussian components in the Gaussian mixture model, e is a Gaussian component index, we is the amplitude of the ith Gaussian component, and the requirements are met (Mu _ξe,Σ_ξe) is the distribution parameter of the e-th Gaussian component, which is the mean value and the variance respectively, x _j,t-1 is the state of the j-th target at the t-1 moment, x _j,t is the state of the j-th target at the t moment, and y _j,t is the measurement corresponding to the j-th target at the t moment. The Dirichlet process-hidden Markov chain mixed model is established according to the target state-measurement model, a discrete distribution mathematical form obeying the Dirichlet process is constructed by adopting a broken rod model, and the specific construction mathematical process is as follows:

V_k~Beta(1,α)

Further, the solving mode of the variational inference of the dirichlet procedure-hidden markov chain hybrid model specifically comprises the following steps:

S4.2, adopting a solution mode of variational deduction of a dirichlet procedure-hidden Markov chain mixed model, wherein the solution mode specifically comprises the following steps:

Wherein q _p(x_j,t)＝∫q(x_j,t-1)p(x_j,t|x_j,t-1)dx_j,t-1,sj,t-₁ is an indicator of the jth target state xj, t- ₁ at time t-1.

And (3) carrying out variation inference according to (x _j,t,s_j,t, V, theta) and prior distribution thereof to obtain each prior distribution parameter recursion at the moment t:

S5, outputting estimated tracks of all targets according to iterative updating of the posterior probability density of each target state:

for a multi-target associated track set: And (3) with By adopting the solution mode of variation inference, the posterior probability of x _j,i is iteratively updated at 1:t by the solution mode of variation inference, and finally an estimated track set of each target is obtainedThe average value of conjugate Gaussian prior of the jth target x _j,t at the moment i is obtained. Based on the estimated track set obtained above, the estimated tracks of each target in time can be presented through a visual operation.

In order to better explain the technical scheme of the invention, the invention is further described below by combining simulation experiments:

The invention provides a multi-target tracking method aiming at non-Gaussian measurement based on a Dirichlet process-hidden Markov chain hybrid model on the basis of generalized label Bernoulli (Generalized Labeled Multi-Bernoulli, GLMB) filtering.

1. Simulation conditions

Under the two-dimensional space coordinate system, considering that the position coordinate of a single sensor node is (0, 0), 3 targets are tracked in the monitoring area of-1000, 1000 [ mu ] m [ x-1000, 1000] m. The sensor measurement covariance matrix isThe sampling period is t=1s, and the total tracking is 100s. The starting time of the different targets is {1,1,30}, the extinction time is {70,100,70}, and the real track is shown in FIG. 3.

The parameters of the generalized label bernoulli filter are set as follows, single target states including position/and velocity v:

C=x=[l_x,v_x,l_y,v_y];

Single target survival probability p _s =0.99, detection probability p _d =0.98. The target state transition matrix F and the covariance matrix Q are

Q is the standard deviation of the noise of the target process. Taking 0.1 in this example;

The measurement function is:

Target generation obeys GLMB distribution, and parameter sets are Wherein the method comprises the steps of Mean value ofAnd covariance matrix P _B is:

P_B=diag([5,5,5,5]);

The maximum track number is 1000, the maximum hypothesis number of the update step is 100, the track cut-off threshold is 10 ^-15, and the single track Gaussian component cut-off threshold is 10 ^-3.

The target estimated number N and the target state set can be obtained by the GLMB filterMeasurement associated therewithWherein X isX _j is the state of a certain target, Y isY _j is the corresponding measurement of target x _j.

For the jth targetCorresponding measurementThe following dirichlet procedure-hidden markov chain hybrid model is built:

V_k~Beta(1,α)

In this example, α=2, λ= [5,20], and the base distribution G (·) is a gaussian distribution.

Since k is e 1, ++ infinity a) of the above-mentioned components,Cutting k to make k be 1, K, constructing V _k -Beta (1, alpha) by means of broken stick model,When k=k, if it satisfiesThenAt this time satisfy

Solving according to a variation inference method:

Initializing parameters:

x _j,0 is the initial value of the j-th target state,

For a multi-target associated track set: By adopting the solution mode of variation inference, the posterior probability of x _j,i is iteratively updated at 1:t by the solution mode of variation inference, and finally an estimated track set of each target is obtained The mean value of the conjugate Gaussian prior of x _j,t of the jth target at the moment i is obtained. Based on the estimated track set obtained above, the estimated tracks of each target in time can be presented through a visual operation.

For the different methods, the error of the real track and the estimated track is measured based on the Optimal Sub-mode allocation (OSPA) of PATTEN ASSIGNMENT, it scales the distance D _p,c (a, B) of the two sets a= { a ₁,a₂,…,a_m } and b= { B ₁,b₂,…,b_n }, m, n e {0,1,2, & gt, by a distance sensitivity parameter p (1 +≤p +.sub.infinity) and an associated sensitivity parameter c (c > 0):

d^(c)(a,b)=min(c,||a-b||);

N _n represents all permutations on the set {1,2,3,., n };

OSPA distance The method can be decomposed into a positioning error distance and a potential error distance:

taking c=100, p=1 to obtain the OSPA distance of the real track from the estimated track.

2. Simulation result analysis

The JointGLMB algorithm in the figure is a more efficient implementation algorithm proposed by (B.N.Vo,B.T.Vo,and H.G.Hoang,"An efficient implementation of the generalized labeled multi-Bernoulli filter,"IEEE Transactions on Signal Processing,vol.65,no.8,pp.1975–1987,Apr.2017.) on the basis of the GLMB algorithm.

FIGS. 5 and 6 show estimated trajectories in the x-direction and y-direction for the proposed methods DP-HMM-JointGLMB and JointGLMB algorithms;

The estimated track OSPA distance, positioning error distance and potential error distance of the proposed method DP-HMM-JointGLMB and JointGLMB algorithm are given in fig. 7. As can be seen from the figure, the tracking accuracy of the DP-HMM-JointGLMB method is obviously better than that of the JointGLMB algorithm.

Fig. 8 shows the estimated number of targets for the proposed methods DP-HMM-JointGLMB and JointGLMB algorithm, and it can be seen from fig. 8 that both methods have the same performance in estimating the number of targets.

It will be understood that the above-described embodiments are merely illustrative and not restrictive, and that all obvious or equivalent modifications and substitutions to the details given above may be made by those skilled in the art without departing from the underlying principles of the invention, are intended to be included within the scope of the appended claims.

Claims

1. The multi-target tracking method in the non-Gaussian noise environment is characterized by comprising the following steps of:

2. The method for multi-target tracking in a non-gaussian noise environment according to claim 1, wherein:

in the step 4, the dirichlet procedure-hidden markov chain hybrid model construction procedure specifically includes:

x_j,t＝Fx_j,t-1+w_j,t

y_j,t＝Hx_j,t+ξ_j,t

w_j,t~N(0,Q)

V_k~Beta(1,α)

Alpha is a concentration parameter, represents a scalar which generates a discrete degree of distribution and is greater than 0, beta (&) is Beta distribution, k is a first order index of the number of cuts, V _k is an intermediate parameter of the kth cut of Beta distribution obeying a parameter of (1, alpha), r is a second order index of the number of cuts, V _r is an intermediate parameter of the kth cut of Beta distribution obeying a parameter of (1, alpha), pi _k is a weight coefficient of the kth cut, and the requirements are satisfied S _j,t is an indicator of the jth target state x _j,t at time t, lambda is a base distribution parameter, G (lambda) is a base distribution, theta _k is a base obtained by kth sampling,Representing an infinite number of bases sampled, Σ being the covariance matrix of the gaussian distribution to which the measurement is subject.

3. A multi-target tracking method in a non-gaussian noise environment according to claim 2, characterized in that:

in the step 4, the solving mode of the variational inference of the dirichlet procedure-hidden markov chain hybrid model is specifically as follows:

wherein q _p(x_j,t)＝∫q(x_j,t-1)p(x_j,t|x_j,t-1)dx_j,t-1,s_j,t-1 is an indicator of the jth target state x _j,t-1 at time t-1;

The mean and variance of conjugate gaussian prior for the jth target x _j,t at time t, The mean and variance of conjugate Gaussian prior for the jth target x _j,t at time t-1,M _j,t isIs the one-step prediction mean of Sigma _j,t Mult (& gt) is a polynomial distribution,Is a parameter of the polynomial distribution at time t,The parameter is the parameter of the polynomial distribution of the kth time truncation at the t moment, (u _k,v_k) is the parameter of beta distribution; is a Gaussian distribution parameter, and (u _k,v_k) are compared with each other due to the need of iterative updating with time The definition is as follows: the parameter of the kth truncated beta distribution at time t-1, The parameters of the k-th truncated beta distribution at time t,The k-th truncated gaussian distribution at time t-1,The parameters of the kth truncated Gaussian distribution at the t moment are obtained;

4. A multi-target tracking method in a non-gaussian noise environment according to claim 3, wherein:

In the step 5, according to the iterative update of the posterior probability density of each target state, the estimated track of each target is output, and the specific steps are as follows:

5. An electronic device, comprising:

One or more processors;

A memory;

One or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs configured to perform the method of any of claims 1-4.

6. A computer readable storage medium storing program code which is callable by a processor to perform the method according to any one of claims 1-4.