A distributed state estimation method for maneuvering targets in the presence of trailing noise

Abstract

The present invention belongs to the field of intelligent signal processing technology, and specifically, is a distributed state estimation method for a maneuvering target under the background of tail noise. The present invention proposes a distributed state estimation method for a maneuvering target under the background of tail noise. The present invention assumes that both the process noise and the measurement noise of the maneuvering target are tail noises. The tail noise is modeled as a Gaussian-Gamma distribution, and the variational Bayes method is used to estimate the process tail noise and measure the distribution parameters related to the tail noise. The process noise estimation accuracy is improved by performing consistency fusion processing on the distribution parameters related to the process noise. Next, the pseudo-likelihood of each maneuvering model is solved, thereby solving the problem of multi-model state estimation of maneuvering targets under the background of tail noise. Finally, the target state posterior estimation results are consistently fused based on GCI fusion, thereby improving the estimation accuracy of the target motion state.

Description

Technical Field

[0001] The invention belongs to the technical field of intelligent signal processing, and in particular is a distributed maneuvering target state estimation method under a trailing noise background. Background Art

[0002] Scenarios of tracking agile maneuvering targets and outlier-corrupted measurements often involve state estimation problems in the context of heavy-tailed noise. In these cases, even if the state space model is linear, the performance of the Kalman filter (KF) that models the noise as Gaussian deteriorates, and outlier robust estimators based on heavy-tailed distributions emerge. For example, the Student's-t distribution used to model process and measurement noise can be viewed as a generalized Gaussian distribution, and the degrees of freedom (Dof) in the tail of the distribution is increased by an adjustable parameter to ensure the tailing characteristics of the noise. Assuming that the joint probability density function (PDF) of the state and process and measurement noise is Student's-t distributed, and based on the linear transformation of the t distribution, the predicted and posterior state PDFs are also approximated as Student's-t, or the Student's-t distribution is extended to Gaussian and gamma distributions, the heavy-tailed estimation problem is solved based on this.

[0003] So far, most of the existing Student's-t filters are implemented for non-maneuvering targets or on the basis of a single sensor, seeking the optimal fusion of Student's-t in the sense of minimum variance (MV) estimation. First, these fusion methods prefer regular Gaussian distributions, which lack consistency with the idea of ​​heavy-tailed estimation. The robustness of outliers in heavy-tailed estimation stems from heavy-tailed posteriors, and when it comes to large-scale sensor networks where both communication and computation are highly constrained, computational efficiency and tolerance to node failures are also important factors to consider.

[0004] Based on the above problems, the present invention proposes a multi-sensor Student's-t filter to solve the distributed state estimation problem of maneuvering targets under the background of tail noise. It does not seek optimal fusion like MV, but suboptimal robust fusion consistent with heavy-tail estimation. To this end, the present invention adopts GCI fusion and variational Bayesian estimation. First, the distribution parameters of the relevant process tail and measurement tail are estimated by the variational Bayesian method, and the parameters such as the process tail noise related distribution parameters and the target motion model probability are fused based on the estimation results, thereby improving the accuracy and robustness of the distributed state estimation of maneuvering targets under the background of tail noise. Summary of the invention

[0005] In view of the above problems, the present invention proposes a distributed state estimation method for a maneuvering target under the background of tail noise. The present invention assumes that the process noise and measurement noise of the maneuvering target are both tail noise. By modeling the tail noise as a Gaussian-gamma distribution, the variational Bayesian method is used to estimate the process tail noise and measure the distribution parameters related to the tail noise, and the process noise related distribution parameters are subjected to consistency fusion processing to improve the estimation accuracy of the process noise. Next, the pseudo-likelihood of each maneuvering model is solved, thereby solving the multi-model state estimation problem of the maneuvering target under the background of tail noise. Finally, the posterior estimation results of the target state are subjected to consistency fusion based on GCI fusion, thereby improving the estimation accuracy of the target motion state. The method of the present invention solves the distributed state estimation problem of the maneuvering target under the background of tail noise in actual engineering applications, where both the process noise and the measurement noise are tail noise. It has the advantages of high parameter estimation accuracy, state estimation accuracy, good adaptability and robustness to complex application backgrounds, high computational efficiency and tolerance to node failures, and can meet the needs of engineering applications. The present invention greatly improves the adaptability and robustness of the algorithm to complex scenes, and improves the estimation accuracy of the distributed state of the maneuvering target under the background of tail noise.

[0006] The technical solution of the present invention is:

[0007] A distributed state estimation method for a maneuvering target under a trailing noise background comprises the following steps:

[0008] S1. Initialize system parameters.

[0009] Initialize sensor network parameters: define the sensor network The sensor node S represents the node that receives and processes data, the communication node C represents the node that completes data transmission, and the connection link Represents the communication link between communicable nodes, and initializes the adjacent node set of the sth sensor as Where p represents the neighboring node of sensor s, and the initial sensor consistency weight coefficient is w;

[0010] Initialize the discrete time state space transfer model: define the set of target motion models at time k as Where M represents the number of motion models included in the target motion process, and the motion state of the sth sensor at time k is defined as Then we have:

[0011]

[0012] in Indicates that the model at the kth moment is i, f i (·) represents the state transfer function of the i-th motion model; process noise Follow tailing distribution where p(·) represents the probability density function, St(x|μ,Σ,v) represents the Student's-t distribution with mean μ, scale matrix Σ, and degrees of freedom v;

[0013] Initialize the measurement space transfer model:

[0014]

[0015] in Indicates the measured value, h s,i (·) represents the measurement transfer function corresponding to the i-th motion model in the s-th sensor, and the measurement noise Follow tailing distribution

[0016] S2, model interaction of the motion states of each target model,

[0017] Combine the following formula to calculate the model prediction probability of the sth sensor target model j: Probability of interacting with the model

[0018]

[0019] in represents the probability update value of model i at time k-1 (obtained from the previous moment), represents the Markov transition probability matrix (TPM) at time k, where Pr(·) represents the probability value;

[0020] Combine the following formula to calculate the motion state interaction result of the target i-th model: Interaction results with state covariance

[0021]

[0022] in, and They represent the state estimation value and state estimation covariance matrix (obtained from the previous moment) of model j at moment k-1 respectively, and ∑· represents the summation operation.

[0023] S3, perform one-step prediction calculation on the motion state value and motion state covariance matrix of each target model,

[0024] Combine the following formula to calculate the one-step prediction value of the motion state of the target's sth sensor's ith model: and the one-step forecast covariance matrix

[0025]

[0026] Among them, F i (·) represents the state transition function f i The Jacobian matrix of (·), represents the process noise covariance matrix of model i at time k, (·) T Represents a transpose operation.

[0027] S4. Decompose the target motion state distribution and measurement distribution into the following probability density function:

[0028] The target motion state distribution is decomposed as follows:

[0029]

[0030] in, represents the set of sensor measurements of the target from the initial moment to the k-1 moment, N(x|μ,Σ) represents a Gaussian distribution with mean μ and variance Σ; Obey the scale matrix The degrees of freedom are The inverse-Wishart distribution, that is G(x; a, b) represents the gamma distribution with shape parameter a and scale parameter b; ∫· represents the integral operation;

[0031] The target measurement distribution is decomposed as follows:

[0032]

[0033] in Obey the scale matrix The degrees of freedom are The inverse-Wishart distribution, that is

[0034] S5. Model interaction is performed on the distribution prior parameters of each sensor of the target and each motion model, including:

[0035] Combine the following formula to calculate the inverse-Wishart distribution of the motion state and measurement-related parameters of the target i model in step S4: and Parameter Degree of Freedom Interaction Results Interaction results with the scale matrix

[0036]

[0037] in and They represent the inverse-Wishart distribution at time k-1 respectively. and degrees of freedom, and They represent the inverse-Wishart distribution at time k-1 respectively. and The scale matrix of

[0038] Combine the following formula to calculate the gamma distribution of the i-th motion model and Shape parameter interaction results Parameter interaction results Interaction results with scale parameters

[0039]

[0040] S6. Perform one-step prediction calculation on the target model latent variable parameters, including:

[0041] Combine the following formula to calculate the inverse-Wishart distribution of the i-th model and Parameter degrees of freedom predicted value Predicted values ​​with scale matrix

[0042]

[0043] where n x represents the dimension of the motion state vector, represents the dimension of the measurement state vector, and ρ represents the forgetting factor.

[0044] Combine the following formula to calculate the gamma distribution and Shape parameter prediction results Prediction results with scale parameters

[0045]

[0046] S7, combining the variational Bayesian algorithm to solve the target state update method of each sensor and the hyperparameter update method of the related parameter distribution,

[0047] Set the target motion state and distribution parameter set of each sensor at time k Combine the following formula to solve the joint probability density function corresponding to the above distribution parameter set:

[0048]

[0049] Combined with the above joint probability density function, the marginal probability density (VB-marginal) of the target distribution parameters of each sensor is calculated and the corresponding hyperparameter update method is determined.

[0050] Combine the following formula to calculate the motion state of the sth sensor target: Marginal log-likelihood,

[0051]

[0052] in E(·) represents the expected operation, E q(x) (x) = ∫xq(x)dx, where (·) -1 represents the inverse operation, Representation and Unrelated constant terms, combined with the above formula, we can get the state update value corresponding to the target i-th model and the state update covariance

[0053]

[0054] Among them, H s,i h represents the transfer function of the ith model measurement of the sth sensor s,i The Jacobian matrix of (·), represents the innovation covariance matrix.

[0055] Combine the following formula to calculate Marginal likelihood,

[0056]

[0057] Among them, det(·) represents the determinant operation, Represents the joint probability density function with irrelevant expected constant term; and:

[0058]

[0059] In summary, we can get The corresponding hyperparameter update step is,

[0060]

[0061] Combine the following formula to calculate Marginal likelihood,

[0062]

[0063] in Representation and Irrelevant constant term; assuming Combine the following formula to calculate Hyperparameter update step,

[0064]

[0065] Combine the following formula to calculate Marginal likelihood,

[0066]

[0067] Sure Hyperparameter update step,

[0068]

[0069] in Ψ(·) denotes a two-parameter gamma distribution.

[0070] The hyperparameter update steps corresponding to the measurement-related distribution can be obtained:

[0071] Sure Hyperparameter update step,

[0072]

[0073] in,

[0074]

[0075] assumed Sure Hyperparameter update step,

[0076]

[0077] in Sure Hyperparameter update step:

[0078]

[0079] in

[0080] S8, the process noise correlation distribution in step S7 is combined with the inverse Wishart distribution and the gamma distribution parameters to perform multi-sensor consistency fusion processing according to the following formula:

[0081]

[0082]

[0083]

[0084]

[0085] Where w represents the fusion weight coefficient, and L represents the number of consistent fusions.

[0086] S9, calculate the pseudo-likelihood value corresponding to each target sensor and each motion model and the model probability update value corresponding to time k,

[0087] The pseudo-likelihood result is obtained by combining the variational Bayes principle with the following formula:

[0088]

[0089] Where D KL (p||q) represents the KL divergence between function p and function q. Combining the results of S7, we can solve the above equation to obtain the following pseudo-likelihood value:

[0090]

[0091] According to the obtained pseudo-likelihood results, the model probability update value of the i-th model at time k is obtained by combining the following formula:

[0092]

[0093] Where ∝ means proportional to.

[0094] S10, updating the model probability value in step S9 Combine the following formula to perform multi-sensor consistency fusion processing:

[0095]

[0096] S11, based on the target motion model probability update value and the state estimation covariance matrix

[0097]

[0098] in Represents the model probability update value after the Lth fusion.

[0099] In summary, the state estimation values ​​of each sensor and the state estimation covariance matrix of the target at the current moment are obtained to complete the state update.

[0100] The benefits of the present invention are:

[0101] 1. Aiming at the problem of agile maneuvering target tracking under the background of process and measurement noise tailing, the present invention estimates the covariance distribution parameters of the target's process noise and measurement noise in real time based on the distributed variational Bayesian technology, thereby improving the state estimation accuracy of the maneuvering target under the background of tailing noise, and making up for the defect of the traditional Kalman filter that the estimation accuracy of tailing noise drops sharply;

[0102] 2. The present invention improves the accuracy of variational estimation by performing consistency fusion processing on the process noise distribution related parameters obtained by each sensor in the variational Bayesian parameter estimation process, thereby improving the state estimation accuracy under the target trailing noise background. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] Figure 1 It is the overall flow chart of the present invention;

[0104] Figure 2 It is a sensor distribution map and a target trajectory distribution map using the method of the present invention;

[0105] Figure 3 This is a comparison chart of the accuracy of the estimated distance and speed of distributed targets when the optimal state estimation is used, no parameter estimation is performed, and the method of the present invention is used, wherein the number of Monte Carlo times is 100;

[0106] Figure 4 This is a comparison chart of the distance estimation accuracy of a single sensor and a distributed target when the method of the present invention is used, where the number of Monte Carlo times is 100;

[0107] Figure 5 is the model probability estimation value when the optimal state estimation is adopted, parameter estimation is not performed, and the method of the present invention is adopted, wherein the number of Monte Carlo times is 100;

[0108] Figure 6 This is a comparison chart of the estimation results using the method of the present invention and that using a single sensor. DETAILED DESCRIPTION

[0109] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings and embodiments:

[0110] Example

[0111] Step 1: Initialize system parameters.

[0112] 1.1 Initialize sensor network parameters: define the sensor network The sensor node S represents the node that receives and processes data, the communication node C represents the node that completes data transmission, and the connection link Represents the communication link between communicable nodes, and initializes the adjacent node set of the sth sensor as Where p represents the neighboring node of sensor s, and the initial sensor consistency weight coefficient is w;

[0113] This example selects but is not limited to 10 sensor nodes. The sensor adjacent node determination method is: when the distance between two sensors is less than a certain determination threshold, the two sensors are determined to be adjacent nodes. The specific sensor distribution and communication relationship are as follows: Figure 2 shown.

[0114] 1.2 Initialize the discrete time state space transfer model: define the set of target motion models at time k as Where M represents the number of motion models included in the target motion process, and the motion state of the sth sensor at time k is defined as Then we have:

[0115]

[0116] in Indicates that the model at the kth moment is i, f i (·) represents the state transfer function of the i-th motion model; process noise Follow tailing distribution where p(·) represents the probability density function, and St(x|μ,Σ,v) represents the Student's-t distribution with mean μ, scale matrix Σ, and degrees of freedom v.

[0117] This example selects but is not limited to the number of target motion models M=3, which are uniform motion, left and right turning models with a known turning rate of ±0.1rad / s, where model 1 indicates that the target is in uniform motion, and its state transfer matrix is ​​expressed as:

[0118]

[0119] T represents the sampling time interval. This example selects but is not limited to T=1s. Models 2 and 3 represent turning models with known turning rates. Their state transfer matrices are expressed as:

[0120]

[0121] This example uses but is not limited to F 2 =F(w 1 ),w 1 =0.1rad / s, F 3 =F(w 2 ),w 2 =-0.1rad / sw;

[0122] This example uses but is not limited to three motion models corresponding to the motion state vectors: Where x and y represent the distance of the target on the x-axis and y-axis respectively. and Represent the speed of the target on the x-axis and y-axis respectively. The process noise variance of the three motion states is 1m / s 2 ;

[0123] 1.3 Initialize the measurement space transfer model:

[0124]

[0125] in Indicates the measured value, h s,i (·) represents the measurement transfer function corresponding to the i-th motion model in the s-th sensor, and the measurement noise Follow tailing distribution

[0126] This example uses but is not limited to the measurement vectors under three motion models: [R,θ] T , where R represents the target distance, θ represents the target azimuth, and the measurement noise of each sensor under the three models is initialized to σ R =10m,σ θ =0.2°.

[0127] Step 2: Model interaction of the motion states of each target model.

[0128] 2.1 Calculate the model prediction probability of the sth sensor target model j by combining the following formula: Probability of interacting with the model

[0129]

[0130] in represents the probability update value of model i at time k-1 (obtained from the previous moment), represents the Markov transition probability matrix (TPM) at time k, where Pr(·) represents the probability value.

[0131] In this example, the model probability is initialized as The Markov transition probability matrix (TPM) is initialized to the following values:

[0132]

[0133] 2.2 Calculate the motion state interaction result of the target i-th model by combining the following formula: Interaction results with state covariance

[0134]

[0135] in, and They represent the state estimation value and state estimation covariance matrix (obtained from the previous moment) of model j at moment k-1 respectively, and ∑· represents the summation operation.

[0136] Step 3 performs one-step prediction calculation on the motion state value and motion state covariance matrix of each target model.

[0137] Combine the following formula to calculate the one-step prediction value of the motion state of the target's sth sensor's ith model: and the one-step forecast covariance matrix

[0138]

[0139] where F i Represents the state transition function f i The Jacobian matrix of (·), represents the process noise covariance matrix of model i at time k, (·) T Represents a transpose operation.

[0140] Step 4 performs the following probability density function decomposition on the target motion state distribution and the measurement distribution:

[0141] 4.1 Decompose the target motion state distribution as follows:

[0142]

[0143] in, represents the set of sensor measurements of the target from the initial moment to the k-1 moment, N(x|μ,Σ) represents a Gaussian distribution with mean μ and variance Σ; Obey the scale matrix The degrees of freedom are The inverse-Wishart distribution, that is G(x; a, b) represents the gamma distribution with shape parameter a and scale parameter b; ∫· represents the integral operation;

[0144] 4.2 The target measurement distribution is decomposed as follows:

[0145]

[0146] in Obey the scale matrix The degrees of freedom are The inverse-Wishart distribution, that is

[0147] Step 5 performs model interaction on the distribution prior parameters of each target sensor and each motion model, including:

[0148] 5.1 Calculate the inverse-Wishart distribution of the motion state and measurement-related parameters of the target i model in step S4 by combining the following formula: and Parameter Degree of Freedom Interaction Results Interaction results with the scale matrix

[0149]

[0150] in and They represent the inverse-Wishart distribution at time k-1 respectively. and degrees of freedom, and They represent the inverse-Wishart distribution at time k-1 respectively. and The scale matrix of .

[0151] This example uses but is not limited to the following parameters to initialize the results:

[0152]

[0153] Where t represents the tuning parameter and t=5, n x =4,

[0154] 5.2 Calculate the gamma distribution of the i-th motion model by combining the following formula and Shape parameter interaction results Parameter interaction results Interaction results with scale parameters

[0155]

[0156] This example uses but is not limited to the following parameters to initialize the results:

[0157]

[0158] Step 6 performs one-step prediction calculation on the target model latent variable parameters, including:

[0159] 6.1. Calculate the inverse-Wishart distribution of the ith model by the following formula: and Parameter degrees of freedom predicted value Predicted values ​​with scale matrix

[0160]

[0161] where n x represents the dimension of the motion state vector, represents the dimension of the measurement state vector, ρ represents the forgetting factor, and this example selects but is not limited to ρ=0.98.

[0162] 6.2. Calculate the gamma distribution by combining the following formula and Shape parameter prediction results Prediction results with scale parameters

[0163]

[0164] Step 7 combines the variational Bayesian algorithm to solve the hyperparameter update method of each sensor target state update method and the related parameter distribution,

[0165] 7.1 Setting the target motion state and distribution parameter set of each sensor at time k Combine the following formula to solve the joint probability density function corresponding to the above distribution parameter set:

[0166]

[0167] 7.2 Combine the above joint probability density function to calculate the marginal probability density (VB-marginal) of the target distribution parameters of each sensor and determine the corresponding hyperparameter update method.

[0168] 7.2.1 Calculate the target motion state of the sth sensor by combining the following formula: Marginal log-likelihood,

[0169]

[0170] in E(·) represents the expected operation, E q(x) (x) = ∫xq(x)dx, where (·) -1 represents the inverse operation, Representation and Unrelated constant terms, combined with the above formula, we can get the state update value corresponding to the target i-th model and the state update covariance

[0171]

[0172] Among them, H s,i h represents the transfer function of the ith model measurement of the sth sensor s,i The Jacobian matrix of (·), represents the innovation covariance matrix.

[0173] 7.2.2 Calculate using the following formula Marginal likelihood,

[0174]

[0175] Among them, det(·) represents the determinant operation, Represents the joint probability density function with irrelevant expected constant term; and:

[0176]

[0177] In summary, we can get The corresponding hyperparameter update step is,

[0178]

[0179] 7.2.3 Calculate by the following formula Marginal likelihood,

[0180]

[0181] in Representation and Irrelevant constant term; assuming Combine the following formula to calculate Hyperparameter update step,

[0182]

[0183] 7.2.4 Calculate by the following formula Marginal likelihood,

[0184]

[0185] Sure Hyperparameter update step,

[0186]

[0187] in Ψ(·) denotes a two-parameter gamma distribution.

[0188] 7.2.5 Refer to 6.2.1 to 6.2.4 to obtain the hyperparameter update steps corresponding to the measurement-related distribution:

[0189] Sure Hyperparameter update step,

[0190]

[0191] in,

[0192]

[0193] assumed Sure Hyperparameter update step,

[0194]

[0195] in Sure Hyperparameter update step:

[0196]

[0197] in

[0198] Step 8 combines the inverse-Wishart distribution of the process noise correlation distribution in step 7 with the gamma distribution parameters to perform multi-sensor consistency fusion processing:

[0199]

[0200]

[0201]

[0202]

[0203] Wherein w represents the fusion weight coefficient, L represents the number of consistent fusions, and this example selects but is not limited to L=5.

[0204] Step 9 calculates the pseudo-likelihood values ​​corresponding to each target sensor and each motion model and the model probability update value corresponding to time k.

[0205] 9.1 The pseudo-likelihood result is obtained by combining the variational Bayes principle with the following formula:

[0206]

[0207] Where D KL (p||q) represents the KL divergence between function p and function q. Combined with the result of step 8, the above equation is solved to obtain the following pseudo-likelihood value:

[0208]

[0209] 9.2 Based on the pseudo-likelihood result obtained in 1, the model probability update value of the i-th model at time k is obtained by combining the following formula:

[0210]

[0211] Where ∝ means proportional to.

[0212] Step 10 updates the model probability in step 9 Combine the following formula to perform multi-sensor consistency fusion processing:

[0213]

[0214] Step 11: Update the value based on the target motion model probability and the state estimation covariance matrix

[0215]

[0216] in Represents the model probability update value after the Lth fusion.

[0217] In summary, the state estimation values ​​of each sensor and the state estimation covariance matrix of the target at the current moment are obtained to complete the state update.

[0218] The practicability of the present invention is demonstrated by the following simulation examples:

[0219] 1. Simulation conditions and parameters

[0220] The simulation scenario is a single target tracking scenario, and the sensor location distribution diagram is as follows: Figure 2 As shown in the figure, the model numbers are marked as 1, 2, and 3 respectively. The model transfer process is: {1, 2, 3, 2, 1, 3, 1}. The duration of each model is 1→30s, 2→40s, and 3→40s. The process noise variance is q=1, and the measurement noise variance is [σ R ,σ θ ]=[10m,0.2°], the total simulation time is 250s, the process noise outlier ratio is 10%, and the corresponding process noise variance is 100; the measurement noise outlier ratio is 10%, and the corresponding measurement noise variance is 40×[σ R ,σ θ ], number of fusions L = 5.

[0221] 2. Simulation content and result analysis

[0222] Figure 1 It is a flowchart of the algorithm processing corresponding to the method of the present invention;

[0223] Figure 2 The invention adopts the sensor distribution diagram and the target motion trajectory change diagram in the method of the invention.

[0224] Figure 3 This is the statistical diagram of the root mean square error of distance and speed under different methods

[0225] The curve of the root mean square error changing with time, where the number of Monte Carlo times is 100, can be seen from the figure that the distance estimation error of the method of the present invention is significantly reduced after parameter estimation combined with multi-sensor fusion compared with the single sensor parameter estimation method, which proves the effectiveness of the method of the present invention.

[0226] Figure 4Comparison of single sensor estimation results and distributed estimation results in the method of the present invention

[0227] The number of Monte Carlo simulations is 100. It can be seen from the figure that the estimation error of the method of the present invention by combining variational estimation with multi-sensor parameter fusion is significantly reduced compared with that without multi-sensor fusion, which proves the effectiveness of the method of the present invention.

[0228] Figure 5 This is a curve diagram of the root mean square error of the model probability estimation changing with time when the method of the present invention is used, wherein the number of Monte Carlo times is 100. It can be seen from the figure that the method of the present invention has a good model convergence probability.

Claims

1. A distributed state estimation method for maneuvering targets in the background of trailing noise, It is characterized in that The following steps are involved: S1. Initialize system parameters. Initialize sensor network parameters: define the sensor network The sensor node S represents the node that receives and processes data, the communication node C represents the node that completes data transmission, and the connection link Represents the communication link between communicable nodes, and initializes the adjacent node set of the sth sensor as Where p represents the neighboring node of sensor s, and the initial sensor consistency weight coefficient is w; Initialize the discrete time state space transfer model: define the set of target motion models at time k as Where M represents the number of motion models included in the target motion process, and the motion state of the sth sensor at time k is defined as Then we have: in Indicates that the model at the kth moment is i, f i (·) represents the state transfer function of the i-th motion model; process noise Follow tailing distribution where p(·) represents the probability density function, St(x|μ,Σ,v) represents the Student's-t distribution with mean μ, scale matrix Σ, and degrees of freedom v; Initialize the measurement space transfer model: in Indicates the measured value, h s,i (·) represents the measurement transfer function corresponding to the i-th motion model in the s-th sensor, and the measurement noise Follow tailing distribution S2. Perform model interaction on the motion state of each target model: Combine the following formula to calculate the model prediction probability of the sth sensor target model j: Probability of interacting with the model in represents the probability update value of model i at time k-1 (obtained from the previous moment), represents the Markov transition probability matrix (TPM) at time k, where Pr(·) represents the probability value; Combine the following formula to calculate the motion state interaction result of the target i-th model: Interaction results with state covariance in, and They represent the state estimation value and state estimation covariance matrix of model j at time k-1 (obtained from the previous time), and ∑· represents the summation operation; S3, perform one-step prediction calculation on the motion state value and motion state covariance matrix of each target model: Combine the following formula to calculate the one-step prediction value of the motion state of the target's sth sensor's ith model: and the one-step forecast covariance matrix where F i (·) represents the state transition function f i The Jacobian matrix of (·), represents the process noise covariance matrix of model i at time k, (·) T Indicates the transpose operation; S4. Decompose the target motion state distribution and measurement distribution into the following probability density function: The target motion state distribution is decomposed as follows: in, represents the set of sensor measurements of the target from the initial moment to the k-1 moment, N(x|μ,Σ) represents a Gaussian distribution with a mean of μ and a variance of Σ; Obey the scale matrix The degrees of freedom are The inverse-Wishart distribution, that is G(x; a, b) represents the gamma distribution with shape parameter a and scale parameter b; ∫· represents the integral operation; The target measurement distribution is decomposed as follows: in Obey the scale matrix The degrees of freedom are The inverse-Wishart distribution, that is S5. Model interaction is performed on the distribution prior parameters of each sensor of the target and each motion model, including: Combine the following formula to calculate the inverse-Wishart distribution of the motion state and measurement-related parameters of the target i model in step S4: and Parameter Degree of Freedom Interaction Results Interaction results with the scale matrix in and They represent the inverse-Wishart distribution at time k-1 respectively. and degrees of freedom, and They represent the inverse-Wishart distribution at time k-1 respectively. and The scale matrix of Combine the following formula to calculate the gamma distribution of the i-th motion model and Shape parameter interaction results Parameter interaction results Interaction results with scale parameters S6. Perform one-step prediction calculation on the target model latent variable parameters, including: Combine the following formula to calculate the inverse-Wishart distribution of the i-th model and Parameter degrees of freedom predicted value Predicted values ​​with scale matrix Where n x represents the dimension of the motion state vector, represents the dimension of the measurement state vector, ρ represents the forgetting factor; Combine the following formula to calculate the gamma distribution and Shape parameter prediction results Prediction results with scale parameters S7, combining the variational Bayesian algorithm to solve the target state update method of each sensor and the hyperparameter update method of the related parameter distribution, Set the target motion state and distribution parameter set of each sensor at time k Combine the following formula to solve the joint probability density function corresponding to the above distribution parameter set: Combined with the joint probability density function, the marginal probability density of the target distribution parameters of each sensor is calculated and the corresponding hyperparameter update method is determined. Combine the following formula to calculate the motion state of the sth sensor target: Marginal log-likelihood, in E(·) represents the expected operation, E q(x) (x) = ∫xq(x)dx, where (·) -1 represents the inverse operation, Representation and The irrelevant constant term, combined with the above formula, can obtain the state update value corresponding to the target i-th model and the state update covariance Among them, H s,i h represents the transfer function of the ith model measurement of the sth sensor s,i The Jacobian matrix of (·), represents the innovation covariance matrix; Combine the following formula to calculate Marginal likelihood, Among them, det(·) represents the determinant operation, Represents the joint probability density function with irrelevant expected constant term; and: In summary, we can get The corresponding hyperparameter update step is, Combine the following formula to calculate Marginal likelihood, in Representation and Irrelevant constant term; assuming Combine the following formula to calculate Hyperparameter update step, Combine the following formula to calculate Marginal likelihood, Sure Hyperparameter update step, in Ψ(·) represents a two-parameter gamma distribution; Get the hyperparameter update steps corresponding to the measurement-related distribution: Sure Hyperparameter update step, in, assumed Sure Hyperparameter update step, in Sure Hyperparameter update step: in S8, the process noise correlation distribution in step S7 is combined with the inverse Wishart distribution and the gamma distribution parameters to perform multi-sensor consistency fusion processing according to the following formula: Where w represents the fusion weight coefficient, and L represents the number of consistent fusions; S9, calculate the pseudo-likelihood value corresponding to each target sensor and each motion model and the model probability update value corresponding to time k, The pseudo-likelihood result is obtained by combining the variational Bayes principle with the following formula: Where D KL (p||q) represents the KL divergence between function p and function q. Combining the results of S7, we can solve the above equation to obtain the following pseudo-likelihood value: According to the obtained pseudo-likelihood results, the model probability update value of the i-th model at time k is obtained by combining the following formula: Where ∝ means proportional to; S10, updating the model probability value in step S9 Combine the following formula to perform multi-sensor consistency fusion processing: S11, based on the target motion model probability update value and the state estimation covariance matrix in Represents the model probability update value after the Lth fusion; Obtain the state estimation value of each sensor and the state estimation covariance matrix of the target at the current moment to complete the state update.

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