A target tracking method based on variational bayesian gaussian sum filter

Abstract

The application relates to the technical field of target tracking, in particular to a target tracking method based on a variational Bayes Gaussian and filter, which comprises the following steps: constructing a tracking filter nonlinear tracking model considering measurement noise; predicting the target state at a current moment by using a state estimation value at a previous moment and a prior probability density, so as to obtain a one-step prediction value of the target state and a one-step prediction covariance of the target state; updating a non-Gaussian noise hyperparameter to be estimated by using a forgetting factor; introducing a random variable, and rewriting a likelihood function in a Gaussian mixture form into a Gaussian hierarchical distribution; iteratively updating the target state and the unknown non-Gaussian noise hyperparameter by using a variational Bayes method until the KL divergence of the tracking filter is minimized, so as to obtain a posterior estimation of the target state at the current moment. The application can realize tracking and positioning of a target disturbed by non-Gaussian and unknown statistical characteristic measurement noise, and improve tracking precision.

Description

Technical Field

[0001] This invention relates to the field of target tracking technology, and more specifically to a target tracking method based on variational Bayesian Gaussian filtering. Background Technology

[0002] Target tracking involves acquiring various measurement information about a target through various sensors, thereby estimating the target's position, velocity, acceleration, and other states. It has wide applications in military, autonomous driving, and traffic control.

[0003] In the target tracking process, the filtering algorithm determines the positioning accuracy. Commonly used extended Kalman and unscented Kalman filters usually assume that the measurement noise follows a Gaussian distribution and that the statistical characteristics are known. However, this assumption is often difficult to meet in practical applications. Due to complex environmental interference and unknown electromagnetic characteristics, the measurement noise in the real tracking system may exhibit non-Gaussian characteristics and its statistical information may not match the prior information. If the traditional Kalman filtering method is used to process this type of target tracking problem according to the prior information, problems such as decreased estimation accuracy or even divergence may occur.

[0004] How to estimate unknown and time-varying non-Gaussian measurement noise in order to improve tracking accuracy is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] In view of this, the present invention provides a target tracking method based on variational Bayesian Gaussian filtering, which can track and locate targets affected by non-Gaussian measurement noise with unknown statistical characteristics and improve tracking accuracy.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A target tracking method based on variational Bayesian Gaussian filtering is characterized by comprising:

[0008] S1. Construct a nonlinear tracking model for the tracking filter that considers measurement noise; the nonlinear tracking model includes the target motion equation and the sensor measurement equation;

[0009] S2. Update the target state variables over time using the target motion equation, and predict the target state at the current time using the state estimate of the previous time and the prior probability density to obtain the one-step predicted value of the target state and its one-step predicted covariance.

[0010] S3. Before updating the measurement at the current time, update the non-Gaussian noise hyperparameter to be estimated using the forgetting factor;

[0011] S4. Introduce random variables and rewrite the likelihood function in Gaussian mixture form as a Gaussian hierarchical distribution;

[0012] S5. After obtaining the measurement information at the current moment based on the sensor measurement equation, the variational Bayesian method is used to iteratively update the target state and the unknown non-Gaussian noise hyperparameters until the KL divergence of the tracking filter is minimized, thus obtaining the posterior estimate of the target state at the current moment.

[0013] Furthermore, the nonlinear tracking model is represented as follows:

[0014] x k =f(x) k-1 )+w k-1

[0015] z k =h(x k )+v k

[0016] in, The state vector of the tracked target is an n-dimensional vector, which contains information on position, velocity, and acceleration in each direction. Let f(·) and h(·) be the m-dimensional measurement vector of the sensor; f(·) and h(·) are the known nonlinear target motion equation and sensor measurement equation, respectively; subscripts k, k-1 represent discrete time series. Let the variance be Q k n-dimensional process noise; For m-dimensional non-Gaussian measurement noise, v k The probability density function p(v) k The model is constructed using a Gaussian mixture model, as shown below:

[0017]

[0018] Where N(·) represents a Gaussian distribution, N v The number of Gaussian components. Let be the variance of the j-th Gaussian component. Let the weight of the j-th Gaussian component satisfy the following condition:

[0019] Furthermore, the prior probability density of the states is in Gaussian mixture form, as follows:

[0020]

[0021] Among them, z 1:k-1 To accumulate all measurement information from the start to time k-1, I k-1 The state x at the previous time step k-1 The number of Gaussian components, and These are the state mean, error covariance, and corresponding weights of the i-th Gaussian component in the posterior state estimate of the previous time step, respectively, and the weights satisfy the following...

[0022] Furthermore, S2 includes:

[0023] The capacitive Kalman method is used to predict the state, and the mean of the one-step prediction of the i-th Gaussian component is obtained. And one-step prediction of covariance As shown below:

[0024]

[0025]

[0026] Among them, i=1,...,I k-1 Q k-1 The process noise corresponding to the target motion model; g = 1, 2, ..., 2n are the state volume points generated based on the posterior estimate of the target state at the previous time step, and are generated by the following formula:

[0027]

[0028] in, This is the posterior estimate of the state at time k-1; satisfy That is, P k-1|k-1 Cholesky decomposition, P k-1|k-1 Let ζ be the posterior error covariance of the previous time step. g Let g be the g-th column of the following formula:

[0029]

[0030] Where n is the state dimension;

[0031] The one-step prediction probability of the state p(x) k|k-1 |z 1:k-1 (This is a Gaussian mixture form:)

[0032]

[0033] Where, x k|k-1 This is a one-step prediction of the state.

[0034] Furthermore, S3 includes:

[0035] S31. Assumptions on the distribution of the variable to be estimated: Assumptions are made using the distributions of two parameters: the variance of the measured noise and the weights. Specifically, the noise variance of the j-th Gaussian component in non-Gaussian noise is defined as Gaussian and... Prior distribution The distribution is an inverse Wishart distribution IW(·), as shown below:

[0036]

[0037] In the formula, m is the dimension of the measurement vector. These are the prior degrees of freedom parameters. Let Γ be the prior inverse scaling matrix, tr[·] be the trace operation, and Γ be the inverse scaling matrix. d (·) represents a multivariate gamma function;

[0038] Define the weight π of the j-th Gaussian component in Gaussian and non-Gaussian noise of the form Gaussian and non-Gaussian. k Prior distribution p(π) k |z 1:k-1 It conforms to the Dirichlet distribution D(·), as shown below:

[0039]

[0040] In the formula, These are the prior distribution parameters;

[0041] S32. Hyperparameter Time Update: This involves updating the prior degrees of freedom parameters from the previous time step using the forgetting factor ρ. Inverse scaling matrix Distribution parameters These three hyperparameters are updated to obtain the predicted degrees of freedom parameters at the current time step. Predicting inverse scaling parameters and predicted distribution parameters The calculation formula is as follows:

[0042]

[0043] Where ρ is the forgetting factor. These are the hyperparameters in the prediction distribution.

[0044] Furthermore, S4 includes:

[0045] Introducing a set of random variables Its constituent binary random variable elements satisfy:

[0046]

[0047] N v This represents the number of Gaussian components contained in the non-Gaussian measurement noise. For the elements in the introduced binary auxiliary random variable set, The weight of the j-th Gaussian component;

[0048] Gaussian mixture form of likelihood function p(z)k |Θ k )for:

[0049]

[0050] Where Θ k ={x k ,π k ,y k ,R k} represents the variable to be estimated;

[0051] Take advantage of y k The likelihood function described above can be rewritten as a Gaussian hierarchical distribution as follows:

[0052]

[0053] Where П represents the summation operation.

[0054] Furthermore, in S5, variational Bayes estimates the parameters to be estimated by minimizing the following index function:

[0055] J=KL(q(Θ k )||p(Θ k |z 1:k ))

[0056] Wherein KL(q(Θ) k )||p(Θ k |z 1:k )) represents the calculation of q(Θ) k ) and p(Θ k |z 1:k The KL divergence between two variables, q(·) is an approximation of the distribution of the parameter to be estimated, and p(Θ) k |z 1:k Let be the posterior distribution of the parameter to be estimated; the solution to the above index function is:

[0057]

[0058] Where E[·] represents the expectation operation, For Θ k One of the elements in Indicates that the set contains, except for Other elements, Indicates and The relevant constants; Θ k Substituting the elements in the index function in sequence yields the variational Bayesian update of the corresponding parameters to be estimated.

[0059] Furthermore, S5 includes:

[0060] S51, Random variable y kThe variational Bayes update is:

[0061]

[0062] Where, q (n+1) (y k () is an approximation of the distribution of auxiliary parameters; Let n be the parameter representing the multinomial distribution, and the superscript (n) indicates the nth iteration. For the introduced auxiliary binary random variable elements;

[0063] S52, Weight π k The variational Bayesian measurement is updated as follows:

[0064]

[0065] S53, Measurement noise covariance matrix R k The variational Bayesian measurement is updated as follows:

[0066]

[0067] in, Let be the hyperparameter of the posterior distribution in the (n+1)th iteration;

[0068] S54, Target State x k Variational Bayesian measurement update:

[0069] Calculate the cross-covariance of the i-th Gaussian component. and measurement covariance

[0070]

[0071]

[0072] Where, N x Let be the dimension of the target parameter to be estimated; The predicted state of the g-th state volume point; The mean of the one-step prediction for the i-th Gaussian component of the state; These are the measurement prediction values ​​calculated based on the state prediction values; the superscript T indicates transpose. The measurement noise covariance matrix is ​​the estimated Gaussian component of the measurement noise.

[0073] Calculate the gain matrix

[0074]

[0075] Calculate the state estimate of the i-th state in Gaussian mixture form. and error covariance

[0076]

[0077]

[0078] Calculate the weight of the i-th Gaussian component

[0079]

[0080] Update the current number of Gaussian components to I. k =I k-1 N v ;

[0081] Update the posterior distribution of the state as follows:

[0082]

[0083] Among them, I k The number of Gaussian components at time k; For the posterior estimate of the target state, P kk Let be the covariance of the target state.

[0084] Furthermore, in S51:

[0085]

[0086]

[0087] Where ∝ represents proportional to, the variational Bayes update process requires N iterations, the superscript (n) represents the result of the nth iteration; log(·) represents the logarithm operation; Represents finding a matrix The model; B k The intermediate auxiliary calculation parameters are:

[0088]

[0089]

[0090]

[0091]

[0092] Where ψ(·) is the double gamma function, Let (n+1) represent the covariance of the measurement vector, and (n+1) denote the (n+1)th iteration. Let be the measurement covariance of the nth iteration.

[0093] Furthermore, in S54, the posterior estimation of the target state... Covariance P k|k The expression is:

[0094]

[0095] in, x represents the weight of each Gaussian component; Estimate the mean of the Gaussian components for the i-th state. Estimate the covariance of the Gaussian component for the i-th state.

[0096] As can be seen from the above technical solutions, compared with the prior art, the present invention discloses a target tracking method based on variational Bayesian Gaussian filtering. By modeling non-Gaussian noise as a Gaussian mixture and using the variational Bayesian method to estimate the unknown statistical characteristics of the noise, it can effectively track and locate targets that are affected by non-Gaussian measurement noise with unknown statistical characteristics. This can effectively solve the problem that nonlinear target tracking systems are affected by non-Gaussian measurement noise with unknown statistical characteristics and time-varying characteristics, which leads to a decrease in tracking accuracy or even divergence. Attached Figure Description

[0097] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0098] Figure 1 Flowchart of the target tracking method based on variational Bayesian Gaussian filtering provided by the present invention;

[0099] Figure 2 This is a comparison chart of the position estimation errors of the method of this invention and CKF;

[0100] Figure 3 This is a comparison chart of the speed error estimation between the method of this invention and CKF. Detailed Implementation

[0101] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0102] like Figure 1As shown, this embodiment of the invention discloses a target tracking method based on variational Bayesian Gaussian sum filtering, including:

[0103] S1. Construct a nonlinear tracking model for the tracking filter that considers measurement noise; the nonlinear tracking model includes the target motion equation and the sensor measurement equation;

[0104] S2. Update the target state variables over time using the target motion equation, and predict the target state at the current time using the state estimate of the previous time step and the prior probability density, to obtain the one-step predicted value of the target state and its one-step predicted covariance.

[0105] S3. Before updating the measurement at the current time, update the non-Gaussian noise hyperparameter to be estimated using the forgetting factor;

[0106] S4. Introduce random variables and rewrite the likelihood function in Gaussian mixture form as a Gaussian hierarchical distribution;

[0107] S5. After obtaining the measurement information at the current moment based on the sensor measurement equation, the variational Bayesian method is used to iteratively update the target state and the unknown non-Gaussian noise hyperparameters until the KL divergence of the tracking filter is minimized, thus obtaining the posterior estimate of the target state at the current moment.

[0108] The following is a further explanation of each of the above steps.

[0109] In S1, the nonlinear tracking model is represented as follows:

[0110] x k =f(x) k-1 )+w k-1 (1.1)

[0111] z k =h(x k )+v k (1.2)

[0112] in, The state vector of the tracked target is an n-dimensional vector, which contains information on position, velocity, and acceleration in each direction. Let f(·) and h(·) be the m-dimensional measurement vector of the sensor; f(·) and h(·) are the known nonlinear target motion equation and sensor measurement equation, respectively; subscripts k, k-1 represent discrete time series. Let the variance be Q k n-dimensional process noise; For m-dimensional non-Gaussian measurement noise, v k The probability density function p(v) k The model is constructed using a Gaussian mixture model, as shown below:

[0113]

[0114] Where N(·) represents a Gaussian distribution, N v The number of Gaussian components. Let be the variance of the j-th Gaussian component. Let the weight of the j-th Gaussian component satisfy the following condition:

[0115] In Gaussian and filtering algorithms, the prior probability density p(x) of the state k-1 |z 1:k-1 ) is in Gaussian mixture form, that is:

[0116]

[0117] Among them, z 1:k-1 To accumulate all measurement information from the start to time k-1, I k-1 The state x at the previous time step k-1 The number of Gaussian components, and These are the state mean, error covariance, and corresponding weights of the i-th Gaussian component in the posterior state estimate of the previous time step, respectively, and the weights satisfy the following...

[0118] S2, State Time Update, includes:

[0119] The capacitive Kalman method is used to predict the state, and the mean of the one-step prediction of the i-th Gaussian component is obtained. And one-step prediction of covariance As shown below:

[0120]

[0121]

[0122] Among them, i=1,...,I k-1 Q k-1 The process noise corresponding to the target motion model; The state volume point, generated based on the posterior estimate of the target state at the previous time step, is produced by the following formula:

[0123]

[0124] in, This is the posterior estimate of the state at time k-1; satisfy Right now Cholesky decomposition, Let ζ be the posterior error covariance of the previous time step. g Let g be the g-th column of the following formula:

[0125]

[0126] Where n is the state dimension;

[0127] The one-step prediction probability of the state p(x) k|k-1 |z 1:k-1 (This is a Gaussian mixture form:)

[0128]

[0129] Where, x k|k-1 This is a one-step prediction of the state.

[0130] S3, Non-Gaussian noise hyperparameter update: In addition to updating the estimated state over time, to accommodate the potential time-varying characteristics of non-Gaussian noise, the estimated non-Gaussian noise also needs to be updated using a forgetting factor before the measurement update. Specifically, this includes:

[0131] S31. Assumptions on the distribution of the variable to be estimated: In order to effectively estimate unknown non-Gaussian noise, it is first necessary to make assumptions about the distribution of its parameters. Since this invention models non-Gaussian noise as a Gaussian sum with zero mean, it can be described by two parameters: the noise variance and the weights.

[0132] First, define the noise variance of the j-th Gaussian component in Gaussian and non-Gaussian noise in the form of Gaussian and non-Gaussian noise. Prior distribution The distribution is an inverse Wishart distribution IW(·), as shown below:

[0133]

[0134] In the formula, m is the dimension of the measurement vector. These are the prior degrees of freedom parameters. Let Γ be the prior inverse scaling matrix, tr[·] be the trace operation, and Γ be the inverse scaling matrix. d (·) represents a multivariate gamma function;

[0135] Then, the weight π of the j-th Gaussian component in Gaussian and non-Gaussian noise is defined. k Prior distribution p(π) k |z 1:k-1 It conforms to the Dirichlet distribution D(·), as shown below:

[0136]

[0137] In the formula, These are the prior distribution parameters;

[0138] S32, Hyperparameter Time Update:

[0139] Considering that the noise characteristics are time-varying, the prior degree of freedom parameters at the previous time step are processed by the forgetting factor ρ. Inverse scaling matrix Distribution parameters These three hyperparameters are updated to obtain the predicted degrees of freedom parameters at the current time step. Predicting inverse scaling parameters and predicted distribution parameters The calculation formula is as follows:

[0140]

[0141] Where ρ is the forgetting factor. These are the hyperparameters in the prediction distribution.

[0142] S4, rewritten likelihood function:

[0143] Since the probability density of the Gaussian mixture form does not belong to the conjugate prior distribution, it cannot be updated using the variational Bayesian method. Therefore, a random variable is introduced. Rewrite it, and it contains binary random variable elements. satisfy:

[0144]

[0145] Where, N v The number of Gaussian components contained in the non-Gaussian measurement noise. For the elements in the introduced binary auxiliary random variable set, The weight of the j-th Gaussian component;

[0146] Gaussian mixture form of likelihood function p(z) k |Θ k )for:

[0147]

[0148] Where, Θ k ={x k ,π k ,y k ,R k} represents the variable to be estimated; when both the state prediction distribution and the measurement noise distribution are Gaussian mixture distributions, the likelihood function estimated by Bayes is also a Gaussian mixture distribution;

[0149] Take advantage of y k The likelihood function described above can be rewritten as a Gaussian hierarchical distribution as follows:

[0150]

[0151] Here, Π represents the summation operation. After rewriting the likelihood function, the variational Bayesian method can be used to calculate the unknown parameter Θ. k Perform joint iterative estimation.

[0152] S5. Variational Bayesian Measurement Update Steps: After obtaining the measurement information at the current moment, the variational Bayesian method is used to update the state and unknown non-Gaussian noise.

[0153] Variational Bayes estimates the parameters to be estimated by minimizing the following index function:

[0154] J=KL(q(Θ k )||p(Θ k |z 1:k (1.16)

[0155] Wherein KL(q(Θ) k )||p(Θ k |z 1:k )) is used to calculate the KL divergence, indicating the calculation of q(Θ). k ) and p(Θ k |z 1:k The KL divergence between two variables, q(Θ) k p(Θ) is an approximation of the distribution of the parameter to be estimated. k |z 1:k Let be the posterior distribution of the parameter to be estimated; the solution to the above index function is:

[0156]

[0157] Where E[·] represents the expectation operation, For Θ k One of the elements in Indicates that the set contains, except for Other elements, Indicates and The relevant constants; Θ k Substituting the elements in the index function in sequence yields the variational Bayesian update of the corresponding parameters to be estimated.

[0158] Specifically, it includes:

[0159] S51, Random variable y k Update, make Substituting into equation (1.16), the random variable y k The variational Bayes update is:

[0160]

[0161] Where, q (n+1) (y k() is an approximation of the distribution of auxiliary parameters; Let n be the parameter representing the multinomial distribution, and the superscript (n) indicates the nth iteration. For the introduced auxiliary binary random variable elements;

[0162] In equation (1.18),

[0163]

[0164]

[0165] Where ∝ represents proportional to, the variational Bayes update process requires N iterations, and the superscript (n) represents the result of the nth iteration; This represents the logarithmic operation; B represents finding the modulus of a matrix; k The intermediate auxiliary calculation parameters are represented as follows:

[0166]

[0167]

[0168]

[0169]

[0170] Where ψ(·) is the double gamma function, Let (n+1) represent the covariance of the measurement vector, and (n+1) denote the (n+1)th iteration. Let be the measurement covariance of the nth iteration.

[0171] S52, Weight π k Update: Order Substituting into equation (1.16), we obtain the weight π. k Variational Bayesian measurement update:

[0172]

[0173] S53, Measurement noise covariance matrix R k Update. Order Substituting into equation (1.16), we obtain the measurement noise covariance matrix R. k Variational Bayesian measurement update:

[0174]

[0175] in, Let be the hyperparameter of the posterior distribution in the (n+1)th iteration;

[0176] S54, Target State x krenew:

[0177] S51-S53 completes the estimation of the measurement noise characteristics of the unknown non-Gaussian distribution. After that, the measurement update process of the capacitive Kalman gaussian method can be used to estimate the state, that is, to obtain the posterior estimate of the state of the target in the (n+1)th iteration.

[0178] Calculate the cross-covariance of the i-th Gaussian component. and measurement covariance

[0179]

[0180]

[0181] Where, N x Let be the dimension of the target parameter to be estimated; The predicted state of the g-th state volume point; The mean of the one-step prediction for the i-th Gaussian component of the state; These are the measurement prediction values ​​calculated based on the state prediction values; the superscript T indicates transpose. The measurement noise covariance matrix is ​​the estimated Gaussian component of the measurement noise.

[0182] Calculate the gain matrix

[0183]

[0184] Calculate the state estimate of the i-th state in Gaussian mixture form. and error covariance

[0185]

[0186]

[0187] Calculate the weight of the i-th Gaussian component

[0188]

[0189] Update the current number of Gaussian components to I. k =I k-1 N v ;

[0190] Update the posterior distribution of the state as follows:

[0191]

[0192] Among them, I k The number of Gaussian components at time k; For the posterior estimate of the target state, P k|k Let be the covariance of the target state.

[0193] Since the variational Bayesian method approximates the true value through iterative solutions, it requires multiple iterations of S51-S54.

[0194] Finally, the state distribution of the Gaussian and sum forms is approximated as a Gaussian distribution, and the posterior estimate of the target state is output. Covariance P k|k Its expression is:

[0195]

[0196] in, x represents the weight of each Gaussian component; Estimate the mean of the Gaussian components for the i-th state; Estimate the covariance of the Gaussian component for the i-th state.

[0197] The present invention also conducted simulation verification of the above method, specifically as follows:

[0198] If a ground target is moving at a constant velocity in a straight line, its motion model can be described by a constant velocity model.

[0199]

[0200] in, Let I represent the target's position and velocity in two directions, with a simulation step size of T = 0.1 s, and I² represent the two-dimensional identity matrix. The tracking filter can obtain the target's position information; therefore, the measurement equation can be expressed as:

[0201] z t =[I2 0]x t +v t (1.37)

[0202] The distribution characteristics of non-Gaussian noise conform to:

[0203]

[0204] in,

[0205] The target state consists of position and velocity in two directions, with initial values ​​as follows:

[0206] x0=[2000m,5000m,30m / s,50m / s] T The initial covariance is:

[0207] P0 = diag[(100m)] 2 (100m)2 (10m / s) 2 (10m / s) 2 ].

[0208] The system process noise is:

[0209] Assuming the prior measurement noise information is inaccurate,

[0210] After conducting 100 Monte Carlo trials, the proposed algorithm and the results of CKF were compared to, for example... Figures 2-3 As shown, it can be seen that the algorithm of the present invention can achieve accurate estimation of the target when the noise exhibits non-Gaussian characteristics and the statistical properties are unknown. Therefore, it can solve the problem of non-Gaussian measurement noise interference with unknown statistical properties during the tracking process.

[0211] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0212] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A target tracking method based on variational Bayesian Gaussian sum filtering, characterized in that, include: S1. Construct a nonlinear tracking model for the tracking filter that considers measurement noise; The nonlinear tracking model includes the target motion equation and the sensor measurement equation; S2. Update the target state variables over time using the target motion equation, and predict the target state at the current time using the state estimate of the previous time and the prior probability density to obtain the one-step predicted value of the target state and its one-step predicted covariance. S3. Before updating the measurement at the current time, update the non-Gaussian noise hyperparameter to be estimated using the forgetting factor; S4. Introduce random variables and rewrite the likelihood function in Gaussian mixture form as a Gaussian hierarchical distribution; S5. After obtaining the measurement information at the current moment based on the sensor measurement equation, the target state and the unknown non-Gaussian noise hyperparameters are iteratively updated using the variational Bayesian method until the KL divergence of the tracking filter is minimized, thus obtaining the posterior estimate of the target state at the current moment; In S5, variational Bayes estimates the parameters to be estimated by minimizing the following index function: ； in, Indicates calculation and KL divergence between two variables As an approximation of the distribution of the parameter to be estimated, Let be the posterior distribution of the parameter to be estimated; the solution to the above index function is: ； in, To achieve the desired operation, for One of the elements in Indicates that the set contains, except for Other elements, Indicates and Relevant constants; will Substituting the elements in the index function in sequence, we obtain the variational Bayes update of the corresponding parameters to be estimated. S5 includes: S51, Random Variables The variational Bayes update is: ； in, This is an approximation of the distribution of auxiliary parameters; Let n be the parameter representing the multinomial distribution, and the superscript (n) indicates the nth iteration. For the introduced auxiliary binary random variable elements; ； ； in, This indicates that the variational Bayesian update process requires iterations. Next, superscript Indicates the first The result of the next iteration; This represents the logarithmic operation; Represents finding a matrix The model; B k The intermediate auxiliary calculation parameters are: ； ； ； ； in, It is a double gamma function. To measure vector covariance, Indicates the first Round iteration, Let be the measurement covariance of the nth iteration; S52, Weight The variational Bayesian measurement is updated as follows: ； S53, Measurement Noise Covariance Matrix The variational Bayesian measurement is updated as follows: ； in, , , Let be the hyperparameter of the posterior distribution in the (n+1)th iteration; S54, Target Status Variational Bayesian measurement update: Calculate the first Cross-covariance of Gaussian components and measurement covariance ; ； ； Where, N x Let be the dimension of the target parameter to be estimated; The predicted state of the g-th state volume point; The mean of the one-step prediction for the i-th Gaussian component of the state; These are the measurement prediction values ​​calculated based on the state prediction values; the superscript T indicates transpose. The measurement noise covariance matrix is ​​the estimated Gaussian component of the measurement noise. Calculate the gain matrix ; ； Calculate the state of the Gaussian mixture form. State estimation and error covariance ; ； ； Calculate the first The weight of each Gaussian component ; ； Update the current number of Gaussian components to... ; Update the posterior distribution of the state as follows: ； Among them, I k The number of Gaussian components at time k. For the posterior estimate of the target state, Let be the covariance of the target state.

2. The target tracking method based on variational Bayesian Gaussian sum filtering according to claim 1, characterized in that, The nonlinear tracking model is represented as follows: ； ； in, For the tracked target A state vector of 3D, containing position, velocity, and acceleration information in each direction; To detect sensors Dimensional measurement vector; and These are the known equations of motion for the nonlinear target and the measurement equations for the sensor, respectively; subscript Represents a discrete time series; The variance is of Dimensional process noise; for Vifgaussian measurement noise, probability density function Modeling is performed using a Gaussian mixture model, as shown below: ； in, Indicates a Gaussian distribution. The number of Gaussian components. For the first The variance of the Gaussian components, For the first The weights of the Gaussian components satisfy the following conditions: .

3. The target tracking method based on variational Bayesian Gaussian filtering according to claim 2, characterized in that, The prior probability density of the states is in Gaussian mixture form, as follows: ； in, From start to time The sum of all measurement information State of the previous moment The number of Gaussian components, , and These are the posterior estimates of the state at the previous time step. The state mean, error covariance, and corresponding weights of each Gaussian component, wherein the weights satisfy... .

4. The target tracking method based on variational Bayesian Gaussian filtering according to claim 3, characterized in that, S2 include: The capacitive Kalman method is used to predict the state and obtain the first... One-step prediction mean of Gaussian components And one-step prediction of covariance As shown below: ； ； Among them, i=1,...,I k-1 Q k-1 The process noise corresponding to the target motion model; The state volume point, generated based on the posterior estimate of the target state at the previous time step, is produced by the following formula: ； in, This is the posterior estimate of the state at time k-1; satisfy ,Right now Cholesky decomposition, Let $\mathbf{a}$ be the posterior error covariance of the previous time step. For the following formula, the first List: ； in, Let be the dimension of the state; One-step prediction probability of a state In Gaussian mixture form: ； in, This is a one-step prediction of the state.

5. The target tracking method based on variational Bayesian Gaussian filtering according to claim 4, characterized in that, S3 include: S31. Distribution Assumptions for the Variables to be Estimated: Assumptions are made based on the distributions of two parameters: the variance of the measurement noise and the weights. Specifically, the distribution of the non-Gaussian noise in the form of Gaussian and weights is defined as follows: Noise variance of Gaussian components Prior distribution Inverse Wishart distribution As shown below: ； In the formula, To measure the dimension of the vector, These are the prior degrees of freedom parameters. The prior inverse scaling matrix, For trace extraction operation, It is a multivariate gamma function; Define Gaussian and non-Gaussian noise in the form of the first Weights of Gaussian components Prior distribution Conforms to Dirichlet distribution As shown below: ； In the formula, These are the prior distribution parameters; S32, Hyperparameter Time Update: Using Forgetting Factor Prior degrees of freedom parameters at the previous time step Inverse scaling matrix Distribution parameters These three hyperparameters are updated to obtain the predicted degrees of freedom parameters at the current time step. Predicting inverse scaling parameters and predicted distribution parameters The calculation formula is as follows: ； in, Forgetting factor, These are the hyperparameters in the prediction distribution.

6. The target tracking method based on variational Bayesian Gaussian filtering according to claim 5, characterized in that, S4 include: Introducing a set of random variables Its constituent binary random variable elements satisfy: ； N v This represents the number of Gaussian components contained in the non-Gaussian measurement noise. For the elements in the introduced binary auxiliary random variable set, The weight of the j-th Gaussian component; Likelihood function in Gaussian mixture form for: ； in The variable to be estimated; use The likelihood function described above can be rewritten as a Gaussian hierarchical distribution as follows: ； in, This indicates the product operation.

7. The target tracking method based on variational Bayesian Gaussian filtering according to claim 1, characterized in that, In S54, the posterior estimation of the target state Covariance The expression is: ； in, The weights of each Gaussian component; Estimate the mean of the Gaussian components for the i-th state; Estimate the covariance of the Gaussian component for the i-th state.

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