Extended target tracking method based on non-stationary abnormal noise environment

Abstract

The invention discloses an extended target tracking method based on a non-stationary abnormal noise environment, and the method comprises the steps: S1, carrying out the initialization of a motion state and an extended state of a target, and obtaining the initialization information of the states; s2, obtaining a measurement model of a target according to the initialization information of the state; s3, taking the measurement model and the motion state model of the target as GSTM distribution, and constructing a layered Gaussian state space model by introducing a Bernoulli variable and further predicting the density and the measurement likelihood function of the target state; s4, on the basis of the layered Gaussian state space model, predicting and updating the motion state and the extension state of the target; and S5, the target state parameters are measured and updated through a variational Bayesian method, whether tracking continues or not is judged, if tracking continues, the step S4 is executed, and otherwise, extended target tracking is completed. According to the method, the problem that the extended target tracking effect is poor in a complex noise environment is effectively solved, and higher robustness and adaptability are achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of extended target tracking under complex noise, and in particular to an extended target tracking method based on a non-stationary abnormal noise environment. Background Art

[0002] As the resolution of sensors gradually increases, targets can occupy multiple resolution units, that is, each target can correspond to multiple resolution units at each moment, that is, the target can correspond to multiple measurements at each moment. Such targets are called extended targets. Extended target tracking can use the spatial distribution information of multiple measurements to jointly estimate the motion and shape information of the target. Generally, the extended target shape of the target is approximated as an ellipse. Koch uses a symmetric positive definite random matrix to characterize the ellipse shape, and obtains a joint estimate of its motion state and extended state based on multi-source measurements at the same time. Feldmann considers the impact of noise on target shape tracking and modifies the measurement likelihood function. Yang et al. proposed a multiplicative error model that models the shape as a three-dimensional vector containing orientation and major and minor axes, thereby parameterizing the elliptical target. However, the above methods all track extended targets under the assumption of Gaussian noise. Under the abnormal noise conditions of actual working conditions, the process and measurement noise present a non-Gaussian heavy-tailed distribution. In order to accurately track the target under such noise, some scholars have developed Student-t filters and robust Student-t filters. However, in actual engineering applications, due to environmental changes, state anomalies and measurement anomalies may appear in different time periods, resulting in non-stationary heavy-tailed process noise and measurement noise. These noises may sometimes obey Gaussian distribution, sometimes obey heavy-tailed distribution, and their distribution parameters may be different. For example, when an extended target moves in a complex scene with many obstructions, the target's echo signal may be interfered by a large amount of abnormal noise, which can be modeled as thick-tailed noise; when the target enters an open environment, the signal's abnormal values ​​will be significantly reduced, which can be modeled as Gaussian noise. Huang proposed a Gaussian-Student t mixed distribution to adapt to the non-stationary noise environment. The GSTM distribution can describe the non-stationarity of noise through the mixed probability, and can be converted into a single Gaussian noise or thick-tailed noise by setting the mixed probability value, so that it can accommodate abnormal noise between the Gaussian distribution and the Student's t distribution. Therefore, for the problem of extended target tracking in a complex environment, it is necessary to propose a method that can accurately track the target's motion state and extended state when the measurement noise and process noise are non-stationary and thick-tailed. Summary of the invention

[0003] To solve the above technical problems, the present invention proposes an extended target tracking method based on a non-stationary abnormal noise environment, which effectively solves the problem of poor extended target tracking effect in a complex noise environment and has stronger robustness and adaptability.

[0004] To achieve the above object, the present invention provides an extended target tracking method based on a non-stationary abnormal noise environment, comprising:

[0005] S1. Initialize the motion state and expansion state of the target to obtain the initialization information of the state;

[0006] S2. Obtaining a measurement model of the target according to the initialization information of the state;

[0007] S3, the measurement model and motion state model of the target are GSTM distribution, and by introducing Bernoulli variables, the target state one-step prediction density and measurement likelihood function are constructed to construct a hierarchical Gaussian state space model;

[0008] S4. Based on the hierarchical Gaussian state space model, predict and update the motion state and expansion state of the target;

[0009] S5. Update the target state parameter measurement through the variational Bayes method to determine whether to continue tracking. If so, return to S4. Otherwise, complete the extended target tracking.

[0010] Optionally, the method for initializing the target's motion state and expansion state is:

[0011] Set k time to expand the target state using set ζ k :

[0012] ζ k =(x k ,X k ) (1)

[0013] Among them, x k Indicates the motion state of the target, in two-dimensional space, Indicates that it contains position and speed information; X k is a symmetric positive definite matrix, representing the extended form of the target;

[0014] The target state space at time k is:

[0015]

[0016] Set the state transfer matrix T is the sampling period, N is the number of sampling times, I d represents the identity matrix of d dimensions; represents the Kronecker product; w k-1 Denote the covariance as Q k-1 Non-stationary abnormal noise;

[0017] Assume that the posterior probability density of the extended state p(X k-1 ∣Zk-1 ) follows the inverse Wishart distribution,

[0018] p(X k-1 ∣Z k-1 )=IW(X k-1 ; ν k-1|k-1 ,V k-1|k-1 ) (3)

[0019] Among them, Z k-1 represents all measurements before k-1 moments; ν k-1|k-1 and V k-1|k-1 represent the degree of freedom parameter and parameter matrix in the inverse Wishart distribution respectively;

[0020] Assume that the state transition probability density p(X k |X k-1 ) follows the Wishart distribution,

[0021]

[0022] Among them, δ k|k-1 represents the degree of freedom parameter.

[0023] Optionally, according to the initialization information of the state, a method for obtaining a measurement model of the target is:

[0024]

[0025] in, represents the location of the measurement source, Denote the covariance as sX k +R k The non-stationary abnormal measurement noise, s is the scaling factor, and the total measurement set corresponding to the target at time k is n k Represents the number of measurements generated by the target at time k.

[0026] Optionally, the method of converting the measurement model and motion state model of the target into GSTM distribution is:

[0027] The probability density function of the random variable r that satisfies the GSTM distribution is expressed as:

[0028]

[0029] Where N(·) represents Gaussian distribution, St(·) represents Student's t distribution; μ, Σ, and v are the mean vector, scale matrix, and degree of freedom parameter, respectively; the mixing probability It obeys Beta distribution, and the probability density function is expressed as:

[0030]

[0031] Where l represents the prior shape parameter;

[0032] Using equations (6) and (7), the probability density function of the random vector r of the GSTM distribution is expressed as:

[0033]

[0034] Introducing the hidden variable ε, formula (9) is expressed as:

[0035] p(r)=lN(r;μ,Σ)+(1-l)N(r;μ,Σ / ε) (9).

[0036] Optionally, by introducing a Bernoulli variable, the method of transforming the target state one-step prediction density and measurement likelihood function is as follows: by introducing a Bernoulli random variable c represented as a Bernoulli distribution,

[0037] p(c|ζ)=ζ c (1-ζ) 1-c (10)

[0038] The probability density function of the proposed GSTM is expressed in the following layered Gaussian form,

[0039] p(r|c,ε)=[N(r;μ,Σ)] c [N(r;μ,Σ / ε)] (1-c) (11)

[0040] When the process noise and measurement noise are non-stationary thick-tailed noise, when the Bernoulli variable is introduced, the one-step prediction function and measurement likelihood function of the motion state of the extended target are written as:

[0041]

[0042]

[0043] in, and P k|k-1 Predict values ​​and states for states; is the measurement matrix; X k For the extended state; Z k is the set of all measurements corresponding to the target at time k, Z k-1 represents all measurements before k-1 moments; t k and γ k is the Bernoulli variable, σ k and ρ k is a hidden variable, τ k and π k is the mixing probability, ω k and u kis the degree of freedom parameter, q0 and g0 are the prior shape parameters of the Beta distribution; N(·), G(·) and Be(·) are Gaussian distribution, Gamma distribution and Beta distribution, respectively.

[0044] Optionally, the method for predicting and updating the motion state and expansion state of the target is:

[0045] In the Bayesian filtering framework, the joint prediction density of the target's motion state and expansion state is expressed as,

[0046] p(x k ,X k ∣Z k-1 )=p(x k ∣X k ,Z k-1 )p(X k ∣Z k-1 )(14)

[0047] The mean vector and scale matrix in formula (13) are expressed as:

[0048]

[0049] Based on the assumptions about the posterior probability density of the extended state and the state transition probability density, the predicted density of the extended state is expressed as:

[0050]

[0051] in:

[0052]

[0053]

[0054] The joint prediction probability density function p(x k ,X k ∣Z k-1 ,σ k ,t k ) is written as follows,

[0055]

[0056] Optionally, the method for updating the target state parameter measurement by the variational Bayes method is: given the target's motion state and expansion state and the number of measurements, the likelihood function is updated as follows:

[0057]

[0058] The measurement center of mass z k and the scattering matrix It is expressed as,

[0059]

[0060] The variational Bayes method is used to obtain an approximate solution of the state.

[0061]

[0062] Among them, its joint distribution p(Φ k ,Z k ) is expressed as,

[0063]

[0064] Among them, the target state is updated as follows:

[0065]

[0066] in, and It is expressed as,

[0067]

[0068] Among them, the target extension status is updated as follows:

[0069]

[0070] Technical effect of the invention: The present invention discloses an extended target tracking method based on a non-stationary abnormal noise environment, models the noise as a Gaussian-fat-tailed switching distribution, expresses it as a layered Gaussian form by introducing a Bernoulli random variable, and models the extended state of the target as an inverse Wishart distribution, and obtains the motion state and extended state of the target under the variational Bayesian method; effectively solves the problem of poor extended target tracking effect in a complex noise environment, and has stronger robustness and adaptability. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0072] Figure 1 It is a flowchart of an extended target tracking method in a non-stationary abnormal noise environment according to an embodiment of the present invention;

[0073] Figure 2 It is a schematic diagram of trajectory tracking and local magnification of an extended target tracking method in a non-stationary abnormal noise environment when the shape, size and direction of the target remain unchanged according to an embodiment of the present invention;

[0074] Figure 3It is a schematic diagram of the centroid RMSE of the extended target tracking method in a non-stationary abnormal noise environment according to an embodiment of the present invention when the target shape, size and direction remain unchanged;

[0075] Figure 4 It is a schematic diagram of the extended state GWD of the extended target tracking method in a non-stationary abnormal noise environment according to an embodiment of the present invention when the shape, size and direction of the target remain unchanged;

[0076] Figure 5 It is a schematic diagram of trajectory tracking and local amplification when the shape, size and direction of the target change based on the extended target tracking method in a non-stationary abnormal noise environment according to an embodiment of the present invention;

[0077] Figure 6 It is a schematic diagram of the centroid RMSE when the target shape, size and direction change based on the extended target tracking method in a non-stationary abnormal noise environment according to an embodiment of the present invention;

[0078] Figure 7 It is a schematic diagram of the extended state GWD when the shape, size and direction of the target change according to the extended target tracking method in a non-stationary abnormal noise environment according to an embodiment of the present invention. DETAILED DESCRIPTION

[0079] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0080] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0081] like Figure 1 As shown, this embodiment provides an extended target tracking method based on a non-stationary abnormal noise environment, including:

[0082] S1. Initialize the motion state and expansion state of the target to obtain the initialization information of the state;

[0083] S2. Obtaining a measurement model of the target according to the initialization information of the state;

[0084] S3, the measurement model and motion state model of the target are GSTM distribution, and by introducing Bernoulli variables, the target state one-step prediction density and measurement likelihood function are constructed to construct a hierarchical Gaussian state space model;

[0085] S4. Based on the hierarchical Gaussian state space model, predict and update the motion state and expansion state of the target;

[0086] S5, update the target state parameter measurement by the variational Bayes method, determine whether to continue tracking, if continue tracking then return to S4, otherwise complete extended target tracking. The present invention solves the problem that the traditional elliptical extended target algorithm is only applicable to Gaussian noise environment and cannot accurately track in non-stationary complex noise environment.

[0087] Furthermore, the method for initializing the motion state and expansion state of the target is:

[0088] Set k time to expand the target state using set ζ k The description is as follows,

[0089] ζ k =(x k ,X k ) (1)

[0090] Among them, x k Indicates the motion state of the target, in two-dimensional space, Indicates that it contains position and speed information; X k is a symmetric positive definite matrix, representing the extended form of the target;

[0091] The target state space at time k is:

[0092]

[0093] Set the state transfer matrix T is the sampling period, N is the number of sampling times, I d represents the identity matrix of d dimensions; represents the Kronecker product; w k-1 Denote the covariance as Q k-1 Non-stationary abnormal noise;

[0094] Assume that the posterior probability density of the extended state p(X k-1 ∣Z k-1 ) follows the inverse Wishart distribution,

[0095] p(X k-1 ∣Z k-1 )=IW(X k-1 ; ν k-1|k-1 ,V k-1|k-1 ) (3)

[0096] Among them, Z k-1 represents all measurements before k-1 moments; ν k-1|k-1 and V k-1|k-1 represent the degree of freedom parameter and parameter matrix in the inverse Wishart distribution respectively;

[0097] Assume that the state transition probability density p(X k |X k-1 ) follows the Wishart distribution,

[0098]

[0099] Among them, δ k|k-1 represents the degree of freedom parameter.

[0100] The shape of the extended target evolves over time, generally manifested as changes in the size and direction of the target. Assuming that the shape matrix obeys the inverse Wishart distribution, this distribution can naturally describe the covariance matrix of the target, provide a conjugate prior to simplify the Bayesian inference calculation, and effectively describe the uncertainty of the target shape and measurement error, so it can be used to model elliptical targets. The state transition probability density of the extended state obeys the Wishart distribution, and the Wishart distribution and the inverse Wishart distribution are conjugate in Bayesian inference, ensuring that the posterior distribution is still the inverse Wishart distribution when performing variational Bayesian updating.

[0101] Furthermore, according to the initialization information of the state, a method for obtaining a measurement model of the target is:

[0102]

[0103] in, represents the location of the measurement source, Denote the covariance as sX k +R k The non-stationary abnormal measurement noise, s is the scaling factor, and the total measurement set corresponding to the target at time k is n k Represents the number of measurements generated by the target at time k.

[0104] The extended shape change of the target will also have an impact on the measurement noise. By scaling the factor s, this uncertainty is included in the covariance matrix of the measurement noise, which improves the adaptability and prediction accuracy of the measurement model in complex environments. The measurement noise here is modeled as a GSTM distribution to adapt to the complex environment of noise switching in extended target tracking.

[0105] Furthermore, the method of converting the measurement model and motion state model of the target into GSTM distribution is as follows:

[0106] The probability density function of the random variable r that satisfies the GSTM distribution is expressed as:

[0107]

[0108] Where N(·) represents Gaussian distribution, St(·) represents Student's t distribution; μ, Σ, and v are the mean vector, scale matrix, and degree of freedom parameter, respectively; the mixing probability It obeys Beta distribution, and the probability density function is expressed as:

[0109]

[0110] Where l represents the prior shape parameter;

[0111] Using equations (6) and (7), the probability density function of the random vector r of the GSTM distribution is expressed as:

[0112]

[0113] Introducing the hidden variable ε, formula (9) is expressed as:

[0114] p(r)=lN(r;μ,Σ)+(1-l)N(r;μ,Σ / ε) (9).

[0115] The noise is modeled as a GSTM model to adaptively update the noise model in extended target tracking, improve the flexibility of the model, and robustly track extended targets in non-stationary complex noise environments. Since the probability of the posterior distribution is unknown, it is modeled as a Beta distribution so that the posterior distribution and the prior distribution are in the same form, so as to achieve online update of the mixed probability. And by introducing the hidden variable ε, the Student's t distribution is transformed into a Gaussian distribution, which can simplify the subsequent calculations, and by modeling it as a gamma distribution, it can characterize the Student's t distribution with different degrees of "thick tail" in the tracking process.

[0116] Furthermore, by introducing the Bernoulli variable, the method of transforming the target state one-step prediction density and measurement likelihood function is as follows: by introducing the Bernoulli random variable c, it is expressed as a Bernoulli distribution,

[0117] p(c|ζ)=ζ c (1-ζ) 1-c (9)

[0118] The probability density function of the proposed GSTM is expressed in the following layered Gaussian form,

[0119] p(r|c,ε)=[N(r;μ,Σ)] c [N(r;μ,Σ / ε)] (1-c) (11)

[0120] When the process noise and measurement noise are non-stationary thick-tailed noise, when the Bernoulli variable is introduced, the one-step prediction function of the motion state of the extended target and the measurement likelihood function are written as follows:

[0121]

[0122] in, and P k|k-1 Predict values ​​and states for states; is the measurement matrix; X k For the extended state; Z k is the set of all measurements corresponding to the target at time k, Z k-1 represents all measurements before k-1 moments; t k and γ k is the Bernoulli variable, σ k and ρ k is a hidden variable, τ k and π k is the mixing probability, ω k and u k is the degree of freedom parameter, q0 and g0 are the prior shape parameters of the Beta distribution; N(·), G(·) and Be(·) are Gaussian distribution, Gamma distribution and Beta distribution, respectively.

[0123] In a non-stationary abnormal noise environment, the noise switches between Gaussian noise and thick-tailed noise. If the traditional method is used, in the subsequent state update, all probability densities of the extended target need to be modeled as Gaussian distribution or Student t distribution to solve the current state respectively; when the above layered Gaussian form is used, the state update of extended target tracking can be simplified, and the noise shape can be modeled more accurately through the parameters of the gamma distribution.

[0124] Furthermore, the method for predicting and updating the motion state and expansion state of the target is:

[0125] In the Bayesian filtering framework, the joint prediction density of the target's motion state and expansion state is expressed as,

[0126] p(x k ,X k ∣Z k-1 )=p(x k ∣X k ,Z k-1 )p(X k ∣Z k-1 )(14)

[0127] The mean vector and scale matrix in formula (13) are expressed as:

[0128]

[0129] Based on the assumptions about the posterior probability density of the extended state and the state transition probability density, the predicted density of the extended state is expressed as:

[0130]

[0131] in:

[0132]

[0133] The joint prediction probability density function p(x k ,X k ∣Z k-1 ,σ k ,t k ) is written as follows,

[0134]

[0135] For the above target one-step prediction density, its mean vector and scale matrix are obtained. The joint prediction density of the target state is obtained from the hierarchical Gaussian form of the motion state and the one-step prediction density of the extended state, so that the posterior probability density can be obtained using the variational Bayesian method later to update the motion state and the extended state.

[0136] Furthermore, the method for updating the target state parameter measurement by the variational Bayes method is:

[0137] Given the target's motion state and expansion state and the number of measurements, the likelihood function is updated as follows:

[0138]

[0139] The measurement center of mass z k and the scattering matrix It is expressed as,

[0140]

[0141] The variational Bayesian method is used to obtain an approximate solution of the state.

[0142]

[0143] Among them, its joint distribution p(Φ k ,Z k ) is expressed as,

[0144]

[0145] Among them, the target state is updated as follows:

[0146]

[0147] in, and It is expressed as,

[0148]

[0149] Among them, the target extension status is updated as follows:

[0150]

[0151] when and q i+1 (t k ) and q i+1 (γ k ) is updated to Bernoulli distribution, when t k and γ k The probability of taking 0 or 1 respectively is,

[0152]

[0153] when and When q i+1 (σ k ) and q i+1 (ρ k ) is updated to a gamma distribution with a shape parameter and rate parameters It is expressed as,

[0154]

[0155] when and When q i+1 (τ k ) and q i+1 (π k ) is updated to a Beta distribution with shape parameter and It is expressed as,

[0156]

[0157] Since there is a coupling relationship between the required state vector and the parameters, the joint posterior distribution of the motion state and the extended state obtained by analytical methods is very complicated, so the variational Bayes fixed-point iteration method is used to solve and simplify the update of the parameters and state vector. This can adaptively handle the changes in the state and parameters in the model, and update the extended state and motion state and various parameters in real time. By updating the parameters, the switching of noise during online tracking motion, and updating the mixing probability between Gaussian noise and thick-tailed noise, the optimal noise model can be automatically selected during the tracking process, thereby obtaining the optimal solution for the motion state and the extended state. Protect the accuracy, robustness and real-time performance of online tracking in extended target tracking.

[0158] The content of the present invention is further introduced below in combination with simulation experiments.

[0159] Experiment 1: When the target shape, size and orientation do not change

[0160] Construct an elliptical extended target tracking scenario under non-stationary thick-tailed noise conditions, and the initial motion state of the target is x0 = [30, 10, 15, 15] T , the initial degree of freedom parameter of the extended target is ν0 = 7, the scale matrix P 0|0 =diag[(1,1)], the semi-major axis of the elliptical expansion target A=8, a=4, the sampling time interval T=1s, the total number of sampling times N=40, the number of measurements n k Subject to mean n p = 20 Poisson distribution. The filtering algorithm of the present invention is used to track the target in two-dimensional space. The target motion state obeys the linear model of constant speed, that is,

[0161]

[0162] H k =[1 0](49)

[0163] The modeling of non-stationary thick-tailed process noise and measurement noise is as follows:

[0164]

[0165] Formula (50) represents the process noise w k With 75% probability, the covariance is Q k The Gaussian distribution of is derived from a Gaussian distribution with a severe increase in covariance with a probability of 25%. Equation (51) measures the noise e k With 85% probability, the covariance is R k The Gaussian distribution of , with a probability of 15%, comes from a Gaussian distribution with severely increased covariance. This severely increased covariance is used to represent the tail of the thick-tailed noise, and different times are set to characterize the non-stationarity of the noise.

[0166] Figure 2 It is a tracking effect and a local magnified diagram of an elliptical extended target filter in a non-stationary complex noise environment in a linear scene provided by an embodiment of the present invention when the target shape, size and direction remain unchanged, Figure 3 is the target center of mass state estimation error map, Figure 4 It is the target extended state estimation error diagram. It can be seen from the figure that the elliptical extended target filter based on the non-stationary complex noise environment can effectively estimate the motion state and shape information of the target, which also verifies that the algorithm of the present invention is effective.

[0167] Experiment 2: When the target shape, size and orientation change

[0168] In order to further verify the robustness of the algorithm proposed in the present invention, in the above-mentioned simulation experimental environment, the shape, size and direction of the target are changed, the major and minor axes of the ellipse are gradually enlarged according to multiples of coe=1.02 / s, and the change rate of the target's direction angle cos=1.1 / s is changed, and the following simulation diagram is obtained.

[0169] Figure 5 This is the trajectory tracking and local magnification diagram obtained when the target shape, size and direction change. Figure 6 is the target motion state estimation error map, Figure 7 This is a target shape expansion estimation error diagram. It can be seen from the diagram that the algorithm proposed in the present invention can still estimate the target more accurately, thereby verifying the robustness of the proposed algorithm.

[0170] In an embodiment of the present invention, an extended target tracking method in a non-stationary abnormal noise environment is provided. The noise is modeled as a Gaussian-fat-tailed switching distribution, which is expressed as a hierarchical Gaussian form by introducing a Bernoulli random variable, and the extended state of the target is modeled as an inverse Wishart distribution. The motion state and extended state of the target are obtained under the Variational Bayes (VB) method. In the experimental simulation, MSE is used as an evaluation index for the estimation of the center of mass position of the extended target, and GWD is used to further demonstrate the superiority of the GSTMRMM algorithm for extended target tracking in complex noise.

[0171] The present invention discloses an extended target tracking method based on a non-stationary abnormal noise environment, in which the noise is modeled as a Gaussian-fat-tail switching distribution, which is expressed as a layered Gaussian form by introducing a Bernoulli random variable, and the extended state of the target is modeled as an inverse Wishart distribution, and the motion state and extended state of the target are obtained under the variational Bayesian method; the problem of poor extended target tracking effect in a complex noise environment is effectively solved, and the method has stronger robustness and adaptability.

[0172] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. An extended target tracking method based on a non-stationary abnormal noise environment is characterized by: include: S1. Initialize the motion state and expansion state of the target to obtain the initialization information of the state; S2. Obtaining a measurement model of the target according to the initialization information of the state; S3, the measurement model and motion state model of the target are GSTM distribution, and by introducing Bernoulli variables, the target state one-step prediction density and measurement likelihood function are constructed to construct a hierarchical Gaussian state space model; S4. Based on the hierarchical Gaussian state space model, predict and update the motion state and expansion state of the target; S5. Update the target state parameter measurement through the variational Bayes method to determine whether to continue tracking. If so, return to S4. Otherwise, complete the extended target tracking.

2. The extended target tracking method based on a non-stationary abnormal noise environment according to claim 1, characterized in that: The method to initialize the motion state and expansion state of the target is: Set k time to expand the target state using set ζ k : g k =(x k ,X k ) (1) Among them, x k Indicates the motion state of the target, in two-dimensional space, Indicates that it contains position and speed information; X k is a symmetric positive definite matrix, representing the extended form of the target; The target state space at time k is: Set the state transfer matrix T is the sampling period, N is the number of sampling times, I d represents the identity matrix of d dimensions; represents the Kronecker product; w k-1 Denote the covariance as Q k-1 Non-stationary abnormal noise; Assume that the posterior probability density of the extended state p(X k-1 ∣Z k-1 ) follows the inverse Wishart distribution, p(X k-1 ∣Z k-1 )=IW(X k-1 ;n k-1|k-1 ,V k-1|k-1 ) (3) Among them, Z k-1 represents all measurements before k-1 moments; ν k-1|k-1 and V k-1|k-1 represent the degree of freedom parameter and parameter matrix in the inverse Wishart distribution respectively; Assume that the state transition probability density p(X k |X k-1 ) follows the Wishart distribution, Among them, δ k|k-1 represents the degree of freedom parameter.

3. The extended target tracking method based on a non-stationary abnormal noise environment according to claim 1, characterized in that: According to the initialization information of the state, the method of obtaining the measurement model of the target is: in, represents the location of the measurement source, Denote the covariance as sX k +R k The non-stationary abnormal measurement noise, s is the scaling factor, and the total measurement set corresponding to the target at time k is n k Represents the number of measurements generated by the target at time k.

4. The extended target tracking method based on a non-stationary abnormal noise environment according to claim 1, characterized in that: The method of converting the measurement model and motion state model of the target into GSTM distribution is: The probability density function of the random variable r that satisfies the GSTM distribution is expressed as: Where N(·) represents Gaussian distribution, St(·) represents Student's t distribution; μ, Σ, and v are the mean vector, scale matrix, and degree of freedom parameter, respectively; the mixing probability It obeys Beta distribution, and the probability density function is expressed as: Where l represents the prior shape parameter; Using equations (6) and (7), the probability density function of the random vector r of the GSTM distribution is expressed as: Introducing the hidden variable ε, formula (9) is expressed as: p(r)=lN(r;μ,Σ)+(1-l)N(r;μ,Σ / ε) (9).

5. The extended target tracking method based on a non-stationary abnormal noise environment according to claim 1, characterized in that: By introducing the Bernoulli variable, the method of transforming the target state one-step prediction density and measurement likelihood function is as follows: By introducing the Bernoulli random variable c, it is expressed as a Bernoulli distribution. p(c|ζ)=ζ c (1-g) 1-c (10) The probability density function of the proposed GSTM is expressed in the following layered Gaussian form, p(r|c,ε)=[N(r;μ,Σ)] c [N(r;μ,Σ / ε)] (1-c) (11) When the process noise and measurement noise are non-stationary thick-tailed noise, when the Bernoulli variable is introduced, the one-step prediction function and measurement likelihood function of the motion state of the extended target are written as: in, and P k|k-1 Predict values ​​and states for states; is the measurement matrix; X k For the extended state; Z k is the set of all measurements corresponding to the target at time k, Z k-1 represents all measurements before k-1 moments; t k and γ k is the Bernoulli variable, σ k and ρ k is a hidden variable, τ k and π k is the mixing probability, ω k and u k is the degree of freedom parameter, q0 and g0 are the prior shape parameters of the Beta distribution; N(·), G(·) and Be(·) are Gaussian distribution, Gamma distribution and Beta distribution, respectively.

6. The extended target tracking method based on a non-stationary abnormal noise environment according to claim 1, characterized in that: The method for predicting and updating the target's motion state and expansion state is: In the Bayesian filtering framework, the joint prediction density of the target's motion state and expansion state is expressed as, p(x k ,X k ∣Z k-1 )=p(x k ∣X k ,Z k-1 )p(X k ∣Z k-1 )(14) The mean vector and scale matrix in formula (13) are expressed as: Based on the assumptions about the posterior probability density of the extended state and the state transition probability density, the predicted density of the extended state is expressed as: in: The joint prediction probability density function p(x k ,X k ∣Z k-1 ,σ k ,t k ) is written as follows, 7. The extended target tracking method based on a non-stationary abnormal noise environment according to claim 1, characterized in that: The method for updating the target state parameter measurement by the variational Bayes method is: Given the target's motion state and expansion state and the number of measurements, the likelihood function is updated as follows: The measurement center of mass z k and the scattering matrix It is expressed as, The variational Bayes method is used to obtain an approximate solution of the state. Among them, its joint distribution p(Φ k ,Z k ) is expressed as, Among them, the target state is updated as follows: in, and It is expressed as, Among them, the target extension status is updated as follows:

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