Radar target tracking method based on GSM-PHD

Abstract

The invention relates to the technical field of radar target tracking, in particular to a GSM-PHD-based radar target tracking method, which comprises the following steps of: firstly, modeling process noise and measurement noise into a Gaussian scale mixture distribution model (GSMD), and constructing a layered Gaussian state space model; then, simultaneously deducing probability density functions of a state vector, a mixed parameter, a scale matrix and a shape parameter by using a variational Bayesian method, and deducing a measurement likelihood function for filtering updating; and finally, on the basis of the specific GSMD and a measurement likelihood function, a GSM-PHD filter similar to Gaussian mixture is deduced. A simulation result verifies that although the GSM-PHD filter in the invention runs for a long time, the GSM-PHD filter is generally superior to the existing filter in the aspects of state estimation precision and target number estimation deviation.

Description

Technical Field

[0001] The present invention relates to the technical field of radar target tracking, and particularly to a radar target tracking method based on GSM-PHD. Background Art

[0002] Radar multi-target tracking (MTT) technology is widely applied in various fields such as cooperative positioning, situation assessment, video surveillance, intelligent transportation, and marine exploration. Traditional MTT methods usually require that the number of targets in the radar monitoring area is known and does not change over time. When the number of targets is large, the computational complexity of data association will increase significantly. With the proposal of the random finite set (RFS) theory, multi-target tracking algorithms no longer process the state of a single target and a single observation value separately, but regard all target states and observation values at each moment as a whole, thus avoiding the complex data association problem.

[0003] In recent years, with the upgrading of the battlefield situation, in the face of a complex electromagnetic environment, the enemy will use active jamming equipment, such as pulse jamming signals, to interfere with the radar system. Such interference signals are emitted by the jammer according to a certain strategy and are random in nature. Their probability density function often exhibits non-Gaussian characteristics such as heavy tails or skewness. However, most of the existing RFS-based filter algorithms assume that the process noise and measurement noise follow a Gaussian distribution, which leads to poor tracking performance or failure of the RFS filter algorithms based on Gaussian distribution, such as the probability hypothesis density (PHD) filter algorithm. Summary of the Invention

[0004] The purpose of the present invention is to provide a radar target tracking method based on GSM-PHD, aiming to solve the technical problem of poor estimation effect of the existing PHD filter in the case of non-Gaussian process noise and measurement noise.

[0005] To achieve the above purpose, the present invention provides a radar target tracking method based on GSM-PHD, including the following steps:

[0006] Step 1: Model the moving target and measurement as an RFS to obtain the target state model and measurement model;

[0007] Step 2: Based on the target state model and measurement model, model the process noise and measurement noise as GSMD, and use the variational Bayesian method to simultaneously estimate the probability density functions of the state vector, mixing parameters, scale matrix, and shape parameters, and at the same time derive the measurement likelihood function for PHD update;

[0008] Step 3: Predict the PHD at time k based on the posterior PHD at time k-1;

[0009] Step 4: Update the PHD at time k. The detection term in the update term is approximately rewritten in a hierarchical Gaussian form, and the probability density functions of the iterative state vector, mixing parameters, scale matrix, and shape parameters are updated by the variational Bayesian method;

[0010] Step 5: Take all PHD components greater than the threshold as the state values at time k.

[0011] Optionally, the state model for obtaining the target in Step 1 is

[0012] x k|k-1 = F k-1 x k-1 + w k-1

[0013] The measurement model is

[0014] z k = H k x k + v k

[0015] where k is the discrete-time index, and are the state vector and measurement vector respectively, n x and n z are the dimensions of the state vector and measurement vector respectively, F k-1 and H k are the state transition matrix and measurement matrix respectively, w k-1 and v k are the process noise and measurement noise respectively.

[0016] Optionally, the execution process of Step 2 includes the following steps:

[0017] Step 2.1: Assume that the process noise and measurement noise have heavy-tailed and / or skewed distributions and are modeled as GSMD, i.e., where ξ k , θ 1 (ξ k ), β 1 , Q k-1 are the mixing parameter, scale function, mixture density function, shape parameter, and scale matrix of the process noise respectively, λ k , θ 2 (λ k ), β 2 , R k are the mixing parameter, scale function, mixture density function, shape parameter, and scale matrix of the measurement noise respectively.

[0018] Further predict the PDF p(x k|z 1:k-1 ) and the likelihood PDF p(z k |x k ) are represented in a hierarchical Gaussian form, i.e.,

[0019]

[0020] where the state mean vector and the state covariance matrix P k|k-1 are obtained by KF prediction, i.e., The prior PDFs of the mixing parameters ξ k and λ k are given by p(ξ k ) = θ 1 (ξ k ), p(λ k ) = θ 2 (λ k ). The scale matrices P k|k-1 and R k and the shape parameters β 1 and β 2 are inaccurate. Therefore, the prior distributions of the scale matrix and the shape parameter are modeled as IWD and GD respectively, i.e., p(P k|k-1 ) = IW(P k|k-1 , f k , F k ), p(R k ) = IW(R k , u k , U k ), where f k , u k , F k and U k are the DOF parameters and the inverse scale matrices of the prior distributions p(P k|k-1 ) and p(R k ) respectively, and F k = f k P k|k-1 , U k = u k R k . and are the means of the skewness parameters respectively, and σ 1 and σ 2 are the tool parameters that control the confidence value of the covariance matrix, and represent the n x -dimensional and n z -dimensional identity matrices respectively.

[0021] Step 2.2: Calculate the joint posterior PDF p(Ξ|z1:k ), where Ξ = {x k , P k|k-1 , R k , ξ k , λ k , β 1 , β 2}, and then use the VB method to derive the separable approximation of the joint posterior PDF, i.e.,

[0022] p(Ξ|z 1:k ) ≈ q(x k )q(P k|k-1 )q(R k )q(ξ k )q(λ k )q(β 1 )q(β 2 );

[0023] Step 2.3: The KLD between the joint posterior PDF and its separable approximation

[0024]

[0025] Minimizing the KLD gives where E[·] is the expectation, is any element in Ξ, and denotes the set of all elements in Ξ except , and is the constant value with respect to the variable . Then use the fixed-point iteration method to obtain the posterior PDF form of multiple parameters, i.e., where a is the iteration number, δ(·) is the Dirac function, and the new measurement likelihood PDF q(z k ) is expressed as q(z k ) = exp(lnp(z k ))。

[0026] Optionally, in Step 3, assume that the posterior PHD at time k - 1 is J k-1 represents the number of Gaussian components in the posterior intensity, represents the weight of the i-th Gaussian component. Then the predicted PHD at time k is v k|k-1 (x) = v S,k|k-1 (x) + γ k (x), which consists of two parts: birth and survival. The probability hypothesis density of the birth is where J γ,k represents the number of Gaussian components in the birth intensity, Represents the weight of the i-th newborn Gaussian component. The probability of survival is assumed to have a density of where and are obtained through the prediction step of the KF.

[0027] Optionally, the prediction intensity at time k in step 4 is denoted as where J k|k-1 represents the number of Gaussian components in the prediction intensity, represents the weight of the i-th Gaussian component. Based on the latest measurement set Z k obtained by the sensor at time k, the target posterior intensity v k (x) is denoted as where v D,k (x|z) is approximately rewritten in a hierarchical Gaussian form according to the probability density functions of the state vector, mixing parameters, scale matrix, and shape parameters

[0028]

[0029] After that, the variational Bayesian iteration v D,k (x|z) is used to obtain a weighted GM form

[0030]

[0031] where q (i) (z) is the measurement likelihood function.

[0032] Optionally, in step 5, a threshold weight threshold T is set to retain the Gaussian components with weights greater than the threshold T1.

[0033] The present invention provides a radar target tracking method based on GSM-PHD. First, the process noise and measurement noise are modeled as a Gaussian scale mixture distribution model GSMD, and a hierarchical Gaussian state space model is constructed. Then, the variational Bayesian method is used to simultaneously infer the probability density functions of the state vector, mixing parameters, scale matrix, and shape parameters, and the measurement likelihood function for filter update is derived. Finally, based on a specific GSMD and the measurement likelihood function, an approximate Gaussian mixture GSM-PHD filter is derived. Verified by simulation results, although the GSM-PHD filter in the present invention has a longer running time, it is generally superior to existing filters in terms of state estimation accuracy and target number estimation deviation. Description of the Drawings

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings required for the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can be obtained based on these drawings.

[0035] Figure 1 It is a schematic diagram of the step flow of a radar target tracking method based on GSM-PHD of the present invention.

[0036] Figure 2 It is a schematic diagram of the target motion trajectory in a specific embodiment of the present invention.

[0037] Figure 3 It is a comparison diagram of the target number estimation results between the specific embodiment of the present invention and the existing algorithm at λ c = 10.

[0038] Figure 4 It is a comparison diagram of the OSPA estimation results between the specific embodiment of the present invention and the existing algorithm at λ c = 10.

[0039] Figure 5 It is a comparison diagram of the target number estimation results between the specific embodiment of the present invention and the existing algorithm at λ c = 30.

[0040] Figure 6 It is a comparison diagram of the OSPA estimation results between the specific embodiment of the present invention and the existing algorithm at λ c = 30.

[0041] Figure 7 It is a comparison diagram of the target number estimation results between the specific embodiment of the present invention and the existing algorithm at λ c = 50.

[0042] Figure 8 It is a comparison diagram of the OSPA estimation results between the specific embodiment of the present invention and the existing algorithm at λ c = 50. Detailed implementation manners

[0043] The following will describe in detail the embodiments of the present invention. The examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals represent the same or similar elements or elements with the same or similar functions from beginning to end. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present invention, but should not be construed as a limitation to the present invention.

[0044] In the present invention application, the following terms are used: "RFS" represents Random Finite Set, "GSM" represents Gaussian Scale Mixture, "GSM" represents Gaussian Scale Mixture Distribution, "PHD" represents Probability Hypothesis Density Filtering, "GSM-PHD" represents Gaussian Scale Mixture Probability Hypothesis Density Filtering Algorithm, "VB" represents Variational Bayesian, "PDF" represents Posterior Probability Density, "GD" represents Gaussian Distribution, "IWD" represents Inverse Wishart Distribution, "DOF" represents Inverse Scale Matrix, and "KF" represents Kalman Filtering.

[0045] Please refer to Figure 1 , the present invention provides a radar target tracking method based on GSM-PHD, including the following steps:

[0046] S1: Model the moving target and measurements as an RFS to obtain the target state model and measurement model;

[0047] S2: Based on the target state model and measurement model, model the process noise and measurement noise as GSMD, and use the variational Bayesian method to simultaneously estimate the probability density functions of the state vector, mixture parameters, scale matrix, and shape parameters, and at the same time derive the measurement likelihood function for PHD update;

[0048] S3: Predict the PHD at time k based on the posterior PHD at time k-1;

[0049] S4: Update the PHD at time k. The detection term in the update term is approximately rewritten in a hierarchical Gaussian form, and the probability density functions of the state vector, mixture parameters, scale matrix, and shape parameters are updated iteratively by the variational Bayesian method;

[0050] S5: Take all PHD components greater than the threshold as the state values at time k.

[0051] In step S1, model the moving target and measurements as an RFS, and the obtained target state model is x k|k-1 = F k-1 x k-1 + w k-1 , and the measurement model is z k = H k x k + v k , where k is the discrete time index, and are the state vector and measurement vector respectively, n x and n z are the dimensions of the state vector and measurement vector respectively, F k-1 and H k are the state transition matrix and measurement matrix respectively, w k-1 and v kThey are the process noise and the measurement noise respectively.

[0052] Step S2 assumes that the process noise and the measurement noise have heavy-tailed and / or skewed distributions, and are modeled as GSMD, that is where ξ k , θ 1 (ξ k ), β 1 , Q k-1 are the mixing parameter, scale function, mixture density function, shape parameter, and scale matrix of the process noise respectively, λ k , θ 2 (λ k ), β 2 , R k are the mixing parameter, scale function, mixture density function, shape parameter, and scale matrix of the measurement noise respectively.

[0053] Furthermore, the predicted PDF p(x k |z 1:k-1 ) and the likelihood PDF p(z k |x k ) are represented in a hierarchical Gaussian form, that is

[0054]

[0055] where the state mean vector and the state covariance matrix P k|k-1 are obtained by KF prediction, that is The prior PDFs of the mixing parameters ξ k and λ k are given by the two equations p(ξ k ) = θ 1 (ξ k ), p(λ k ) = θ 2 (λ k ). The scale matrices P k|k-1 and R k as well as the shape parameters β 1 and β 2 are inaccurate. Therefore, the prior distributions of the scale matrices and shape parameters are modeled as IWD and GD respectively, that is p(R k ) = IW(R k , u k , U k ), where, f k , u k , F k and U kare the DOF parameters and the inverse scale matrices of the prior distributions p(P k|k-1 ) and p(R k ) respectively, and F k = f k P k|k-1 , U k = u k R k . and are the means of the skewness parameters respectively, σ 1 and σ 2 are the tool parameters that control the confidence values of the covariance matrix, and represent the identity matrices of dimension n x and n z respectively.

[0056] To estimate the state vector, mixing parameters, scale matrix, and shape parameters simultaneously, it is necessary to calculate the joint posterior PDF p(Ξ|z 1:k ), where Ξ = {x k , P k|k-1 , R k , ξ k , λ k , β 1 , β 2 [[ID=51}}. However, for the hierarchical Gaussian state space model, the optimal solution of the joint posterior PDF is not available. Therefore, the VB method is used to derive a separable approximation of the joint posterior PDF, that is, p(Ξ|z 1:k ) ≈ q(x k )q(P k|k-1 )q(R k )q(ξ k )q(λ k )q(β 1 )q(β 2 ). The KLD between the joint posterior PDF and its separable approximation is derived as follows

[0057]

[0058] Minimizing the KLD gives where E[·] is the expectation, is any element in Ξ, and represents the set of all elements in Ξ except , and is the constant value with respect to the variable . However, due to the mutually dependent and coupled variational parameters, it is impossible to solve analytically. Usually, the fixed-point iteration method is adopted to obtain the form of the posterior PDF, that is, where a is the number of iterations and δ(·) is the Dirac function. Then the new measurement likelihood PDF q(z k ) can be expressed as q(z k ) = exp(ln p(z k ))

[0059] In step S3, assume that the posterior PHD at time k - 1 is J k-1 represents the number of Gaussian components in the posterior intensity, represents the weight of the i-th Gaussian component. Then the predicted PHD at time k is v k|k-1 (x) = v S,k|k-1 (x) + γ k (x), which consists of two parts: birth and survival. The probability hypothesis density of the birth part is where J γ,k represents the number of Gaussian components in the birth intensity, represents the weight of the i-th birth Gaussian component. The probability hypothesis density of the survival part is where, and are obtained through the prediction step of the KF

[0060] In step S4, update the PHD at time k. The detection term in the update item is approximately rewritten in a hierarchical Gaussian form, and the probability density functions of the iterative state vector, mixing parameters, scale matrix, and shape parameters are updated by the variational Bayesian method

[0061] The predicted intensity at time k can be expressed as where J k|k-1 represents the number of Gaussian components in the predicted intensity, represents the weight of the i-th Gaussian component. Based on the latest measurement set Z k obtained by the sensor at time k, the target posterior intensity v k (x) can be expressed as where v D,k (x|z) is approximately rewritten in a hierarchical Gaussian form according to the probability density functions of the state vector, mixing parameters, scale matrix, and shape parameters in step S4

[0062]

[0063] After that, use the variational Bayesian iteration v D,k (x|z) to obtain the weighted GM form

[0064]

[0065] where q(i) (z) is the measurement likelihood function obtained in step S4. Thus, the variational updates of the state vector, mixing parameters, scale matrix, and shape parameters in step S4, together with the calculation of the measurement likelihood q (i) (z), jointly constitute the Gaussian component update process of GSM-PHD.

[0066] In step S5, a threshold weight threshold T is set, and Gaussian components with weights greater than the threshold T1 are retained.

[0067] Furthermore, the present invention also provides specific examples to conduct simulation experiments on the GSM-PHD filter algorithm and compare its performance with existing R-STM-PHD, GM-LMB, EKF-PHD, and track initiation IMM-PDA filters. In the simulation experiments, the OSPA distance and running time are used to evaluate the filter performance, where the cardinality penalty factor parameter p of OSPA is set to 2, and the truncation parameter c is set to 100.

[0068] 1. Simulation conditions: The present invention completes the simulation on a computer with an Intel(R) Core(TM) i5-14600K@3.50 and 32.0GB of memory.

[0069] 2. Simulation scenario settings:

[0070] In a two-dimensional plane, the surveillance area size is [0, 2000] × [0, 2000] meters, and 4 UAV targets appear. Their motion trajectories, initial positions, and birth and death times are as Figure 2 shown in Table 1

[0071] Table 1 Target parameters

[0072]

[0073] The state transition matrix and measurement matrix are respectively where T = 1s is the sampling interval. The state vector at time k is denoted as x k = [p x,k , v x,k , p y,k , v y,k , which includes the position components (p x,k , p y,k ) and velocity components (v x,k , v y,k ) on the x-axis and y-axis. The process noise covariance and measurement noise covariance are respectively where σ P is the standard deviation of the process noise, set to σ P = 5. σ v is the standard deviation of the measurement noise, set to σ v= 10. The process noise with a heavy-tailed distribution and the measurement noise with a skewed distribution are respectively where p w represents the superposition ratio, which can be used to adjust the heavy-tailed degree of the process noise, and is set to p w = 0.8. Ω is the shape parameter and is set to Ω = 100I 2 . u k is the auxiliary random vector. Λ k is a 2×2 angular matrix, and its random diagonal elements [Λ k ii are independently and identically distributed, following the GH skew student’s t distribution, and the DOF parameter v = 5. The newborn targets are modeled as a Poisson RFS, and the PHD intensity is where represents the weight of the newborn targets, represents the state mean of the newborn targets, represents the state covariance of the newborn targets, and the specific settings are shown in Table 2

[0074] Table 2 Newborn Target Parameters

[0075]

[0076] During the filtering process, the clutter follows a Poisson distribution and the clutter rate is λ c , the target survival probability is set to p S = 0.99, the detection probability is set to p D = 0.99, the Gaussian component pruning threshold is set to T P = 10 -5 , the Gaussian component merging threshold is set to T m = 4, and the Gaussian component upper limit threshold is set to T c = 100. In the GSM-PHD update, the parameters of the IW distribution are set to f 0 = 5 and u 0 = 5. The DOF parameters of the Pearson type-Ⅶ and GH skew student‘s t distributions are respectively set to w = 5, v = 5. The mean parameter of the skewed distribution is set to and The scaling parameter of the covariance of the skewed distribution is set to σ 1 = 0 and σ 2 = 1.

[0077] To verify the performance of different filters, multi-target scenarios with clutter rates of λ c = 10, λ c = 30, and λ c = 50 are respectively set, and 100 Monte Carlo simulation experiments are carried out. Figures 3 - 8 ​The estimated number of targets and the OSPA estimation results of different filters under different clutter rates are given respectively when the maximum number of variational iterations is Nmax = 20. In addition, Table 3 gives the average running time and the average OSPA estimation results of different filters under different clutter rates. From Figures 3 - 8 and Table 3, it can be seen that compared with the existing R-STM-PHD, GM-LMB, track initiation IMM-PDA and EKF-PHD filters, the GSM-PHD filter in the present invention shows better performance in target number estimation and OSPA evaluation. However, as the clutter rate increases, the performance of GSM-PHD decreases. When λ c = 30, overestimation occurs. When λ c = 50, missed detections occur in the time period of 40s - 60s, and at the same time, the deviation of the OSPA estimation accuracy also increases. The main reason for this is that as the clutter rate increases, the outliers in the heavy-tailed noise and skewed noise will increase significantly, and these outliers will seriously interfere with the update process of the filter, resulting in deviations and instabilities in state and number estimation.

[0078] Table 3 Performance of filters under different clutter rates

[0079]

[0080] Further analyzing Table 3, the average implementation time of the GSM-PHD filter is longer than that of other filters. This is mainly because in the GSM-PHD filter, since multiple variables such as the state vector, mixing parameters, scale matrix, and shape parameters need to be inferred simultaneously, and each iteration involves the update of different parameters, which significantly increases its computational burden. Generally speaking, the GSM-PHD filter is generally superior to the existing filters in terms of state estimation accuracy and target number estimation deviation, but its running time is longer.

[0081] In summary, the present invention has the following advantages compared with the prior art:

[0082] 1. When the process noise and measurement noise change suddenly, the number of targets can be better estimated, and at the same time, the state estimation accuracy can be improved.

[0083] 2. Modeling moving targets and measurements as RFS can better estimate the number of targets and target states in a high clutter environment.

[0084] The above-disclosed is only a preferred embodiment of the present invention. Of course, it cannot be used to limit the scope of the rights of the present invention. Those of ordinary skill in the art can understand all or part of the processes of implementing the above embodiments, and the equivalent changes made according to the claims of the present invention still fall within the scope covered by the invention.

Claims

1. A radar target tracking method based on GSM-PHD, characterized in that: The following steps are involved: Step 1: Model the moving target and measurement as RFS to obtain the target state model and measurement model; Step 2: Based on the target state model and the measurement model, the process noise and measurement noise are modeled as GSMD, and the probability density functions of the state vector, mixing parameters, scale matrix and shape parameters are estimated simultaneously using the variational Bayes method, and the measurement likelihood function for PHD update is derived; Step 3: Predict the PHD at time k based on the posterior PHD at time k-1; Step 4: Update the PHD at time k. The detection items in the update items are approximately rewritten as hierarchical Gaussian forms. The probability density functions of the iterative state vector, mixing parameters, scale matrix, and shape parameters are updated by the variational Bayes method. Step 5: Take all PHD components greater than the threshold as the state values ​​at time k.

2. The radar target tracking method based on GSM-PHD as claimed in claim 1, characterized in that: The state model of the target in step 1 is x k|k-1 =F k-1 x k-1 +w k-1 The measurement model is z k =H k x k +v k Where k is the discrete time index, and are the state vector and the measurement vector, n x and n z are the dimensions of the state vector and the measurement vector, respectively, and F k-1 and H k are the state transfer matrix and the measurement matrix, w k-1 and v k They are process noise and measurement noise respectively.

3. The radar target tracking method based on GSM-PHD as claimed in claim 2, characterized in that: The execution process of step 2 includes the following steps: Step 2.1: Assume that the process noise and measurement noise have heavy-tailed and / or skewed distributions and are modeled as GSMD, i.e. where ξ k , θ1(ξ k ), β1, Q k-1 are the mixing parameters, scale function, mixing density function, shape parameter and scale matrix of process noise, respectively. k , θ2(λ k ), β2, R k They are the mixing parameters, scale function, mixture density function, shape parameter and scale matrix of the measurement noise; Further predict the PDF p(x k |z 1:k-1 ) and the likelihood PDF p(z k |x k ) is expressed in layered Gaussian form, i.e. Among them, the state mean vector and the state covariance matrix P k|k-1 is obtained by KF prediction, that is, Mixing parameter ξ k and λ k The prior PDF of is given by p(ξ k )=θ1(ξ k ),p(λ k )=θ2(λ k ) are given by the two formulas, the scale matrix P k|k-1 and R k As well as the shape parameters β1 and β2 are inaccurate, the prior distributions of the scale matrix and shape parameters are modeled as IWD and GD, respectively, i.e., p(P k|k-1 )=IW(P k|k-1 ,f k ,F k ), p(R k )=IW(R k ,u k ,U k ), Among them, f k 、u k 、F k and U k They are the prior distribution p(P k|k-1 ) and p(R k )’s DOF ​​parameters and inverse scale matrix, and F k =f k P k|k-1 , U k =u k R k , and are the means of the skew parameters, σ1 and σ2 are instrumental parameters that control the confidence values ​​of the covariance matrix, and Respectively represent n x Peacekeeping z dimensional identity matrix; Step 2.2: Calculate the joint posterior PDFp(Ξ|z 1:k ), where Ξ={x k ,P k|k-1 ,R k ,ξ k ,λ k ,β1,β2}, and then use the VB method to derive a separable approximation of the joint posterior PDF, that is, p(Ξ|z 1:k )≈q(x k )q(P k|k-1 )q(R k )q(ξ k )q(λ k )q(β1)q(β2); Step 2.3: KLD between the joint posterior PDF and its separable approximation, Minimizing KLD gives where E[·] is the expectation, is any element in Ξ, and In addition to The set of all elements except Ξ, It is about variables The fixed-point iteration method is then used to obtain the multi-parameter posterior PDF form, that is, Where a is the number of iterations and δ(·) is the Dirac function, then the new measurement likelihood PDFq(z k ) is expressed as q(z k )=exp(lnp(z k )).

4. The radar target tracking method based on GSM-PHD as claimed in claim 3, characterized in that: In step 3, assume that the posterior PHD at time k-1 is J k-1 represents the number of Gaussian components in the posterior intensity, represents the weight of the i-th Gaussian component, then the predicted PHD at time k is v k|k-1 (x) = v S,k|k-1 (x)+γ k (x), consists of two parts: newborn and survivor, where the probability density of newborn is Among them J γ,k represents the number of Gaussian components in the new intensity, represents the weight of the i-th new Gaussian component; the probability density of survival is assumed to be in, and It is obtained through the prediction step of KF.

5. The radar target tracking method based on GSM-PHD as claimed in claim 4, characterized in that: The prediction strength at time k in step 4 is expressed as Among them J k|k-1 represents the number of Gaussian components in the predicted intensity, represents the weight of the i-th Gaussian component; based on the latest measurement set Z obtained by the sensor at time k k , target posterior strength v k (x) is expressed as where v D,k The probability density function of (x|z) in terms of the state vector, mixing parameters, scale matrix and shape parameters is approximately rewritten as a hierarchical Gaussian Then use variational Bayes iterative v D,k (x|z), we get the weighted GM form in q (i) (z) is the measurement likelihood function.

6. The radar target tracking method based on GSM-PHD as claimed in claim 5, characterized in that: In step 5, a threshold weight threshold T is set, and Gaussian components with weights greater than threshold T1 are retained.

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