Maneuvering target tracking method based on maximum correlation entropy extended Kalman filter

Abstract

This invention provides a maneuvering target tracking method based on maximum correlation entropy extended Kalman filtering, comprising: establishing a model set, target state equation, and measurement equation for an interactive multi-model algorithm; initializing the model probabilities, target state vector, covariance matrix, and Markov state transition matrix; performing input interaction between models and linearizing the nonlinear models using an extended Kalman filter; performing one-step prediction for each model and designing a cost function based on the maximum entropy criterion; obtaining the posterior update values ​​of the target in each model at time k+1 through an iterative method; updating the model probabilities, correcting the transition probabilities, and finally fusing the tracking results. Through the above methods, this invention can solve the problem of nonlinear maneuvering target tracking under non-Gaussian noise and improve the accuracy of target estimation.

Description

Technical Field

[0001] This invention belongs to the technical field of radar target tracking methods, specifically relating to a maneuvering target tracking method based on maximum correlation entropy extended Kalman filtering. Background Technology

[0002] Maneuvering target tracking is a process of estimating the state of a maneuvering object based on sensor information. This tracking technology has wide applications in defense science and technology and the national economy. A challenging problem in maneuvering target tracking is the uncertainty of the maneuvering target. Since a single model is insufficient to describe the target's motion state, multiple models are often used. Interactive multi-model algorithms (IMMAs) are a commonly used multi-model estimation strategy. Within the IMA framework, when the estimated target state or sensor measurement vector is nonlinear, nonlinear filters such as the Extended Kalman filter (EKF) can be used to track the maneuvering target. However, these traditional nonlinear filters are derived based on the minimum mean square error criterion and only contain second-order information of the tracking error. Therefore, they achieve good tracking results under Gaussian noise conditions but poor results under non-Gaussian noise conditions. To address this problem, this invention combines the EKF algorithm based on the maximum correlation entropy criterion with the IMA. Because it uses the maximum correlation entropy criterion instead of the minimum mean square error criterion, it can retain the higher-order moment information of the error. Compared to traditional nonlinear maneuvering target tracking algorithms, this algorithm achieves better tracking results under non-Gaussian noise conditions. Summary of the Invention

[0003] The purpose of this invention is to provide a maneuvering target tracking method based on maximum correlation entropy extended Kalman filter, which solves the problem of poor tracking performance of existing nonlinear filters under non-Gaussian noise conditions; and optimizes the tracking performance to make it more accurate.

[0004] The technical solution adopted in this invention is a maneuvering target tracking method based on maximum correlation entropy extended Kalman filtering, and the specific operation steps are as follows:

[0005] Step 1: Establish the model set, target state equation, and measurement equation for the interactive multi-model algorithm;

[0006] Step 2, Initialize parameters: Initialize the model probabilities, target state vectors, covariance matrices, and Markov state transition matrices for each model at time k=1;

[0007] Step 3, Input Interaction: Based on the model probabilities, target state vector, covariance matrix and Markov state transition matrix of each model at time k, calculate the mixing probability between models at time k, and obtain the estimated value of the target in the mixed state of each model and the mixing covariance matrix at time k.

[0008] Step 4, prior estimation of the filter: Since the measurement equation is linear, the nonlinearity of the system is relatively small. Therefore, the nonlinear models in the model set are linearized using the extended Kalman filter with low computational cost. One-step prediction is performed on each model to obtain the prior prediction value of the target at time k+1 in each model.

[0009] Step 5, posterior update of the filter: Based on the target state equation, measurement equation obtained in step 1 and the prior prediction value obtained in step 4, design a cost function based on the maximum entropy criterion, and obtain the posterior update value of the target in each model at time k+1 through the iterative method.

[0010] Step 6, Model Probability Update: By calculating the likelihood function of each model, the probability update value of each model is obtained according to the Bayesian probability formula. A correction function is constructed using the model probability change rate to correct the transition probabilities between models.

[0011] Step 7, Fuse the output results: Fuse the posterior update values ​​and covariance of each model to output the target's state vector at time k+1. The covariance matrix P k+1 ;

[0012] Step 8: Repeat steps 3-7 until the target tracking process is complete.

[0013] The invention is further characterized by:

[0014] Step 1 is as follows:

[0015] Step 1.1, the target state at time k is represented as: A linear CV model simulating uniform linear motion of the target is used to construct the target state equation as follows:

[0016] x k+1 =F k x k +G k w k (1)

[0017]

[0018] Wherein, the state vector x k In the , x and y represent the position of the target along the x-direction and the position along the y-direction, respectively; These are the target's velocity along the x-direction and velocity along the y-direction; T represents the sampling interval, w k F represents Gaussian white noise with a mean of 0 and a covariance of Q. k Let G represent the state transition matrix. k Represents the noise driving matrix;

[0019] Step 1.2, with Let k represent the target state at time k. A nonlinear CT model simulating a coordinated turning motion of the target with unknown angular velocity is used to construct the target state equation:

[0020] x k+1 =f(x) k )+G k w k (3)

[0021]

[0022] Wherein, angular velocity ω k It is not a constant;

[0023] Step 1.3: Using the x-direction position and y-direction position as observations, establish the measurement equation with non-Gaussian noise:

[0024] z k =H k x k +v k (5)

[0025]

[0026] Among them, z k This represents the observation vector at time k, and the measurement noise v. k It is non-Gaussian noise that follows a mixture of Gaussian distributions, specifically manifested as: v k ~(1-α)N(0,R 1k )+αN(0,R 2k ), where α represents the weight, ranging from 0 to 1, N(·,·) represents a normal distribution, and R 1k To measure the noise covariance, R 2k This is used to measure the covariance of noise when it is subjected to abnormal disturbances.

[0027] Step 2 shall be implemented in the following manner:

[0028] Initialize parameter values, including determining the probability that the target is in model i at time k=1. State estimation covariance matrix and Markov state transition matrix Π k ={π ij,k} M×M , where each element π ij,k Let M represent the transition probability of the system from model i to model j at time k, and M represent the total number of models.

[0029] Step 3 is as follows:

[0030] Step 3.1, based on the model probability and Markov state transition matrix Π k The mixing probability between models at time k is calculated using formulas (7) and (8).

[0031]

[0032]

[0033] in, This represents the probability that the target is in model j after the input interaction;

[0034] Step 3.2, based on the target state at time k covariance matrix The mixture probability between the models obtained in step 3.1 The mixed state estimates of the target at time k under each model are obtained using formulas (9) and (10), respectively. and mixed covariance matrix

[0035]

[0036]

[0037] in, It is the estimated mixed state of the target under various models at time k. It is the mixed covariance of the target at time k across all models.

[0038] Step 4 shall be implemented in the following manner:

[0039] Step 4.1: Calculate the Jacobian matrix of the nonlinear system state equation according to formulas (11) and (12), and linearize the nonlinear state equation (3):

[0040]

[0041] The partial derivatives of each state variable with respect to the angular velocity are:

[0042]

[0043] Where, ω k Angular velocity, T is the sampling interval. These are the velocities in the x-direction and the velocities in the y-direction, respectively.

[0044] Step 4.2: Use the mixture state estimate of the target at time k obtained in Step 3.2 to determine the model. and mixed covariance matrix Depending on whether the state equation is linear, the filtered prior prediction value is obtained using formula (13) or (14) respectively. Use formula (15) to obtain the prior covariance estimate.

[0045]

[0046]

[0047]

[0048] Step 5 is as follows:

[0049] Step 5.1: Based on the target state equations (1) and (3), the measurement equation (5), and the filtered prior predictions obtained in step 4.2... and The system equations are extended as follows:

[0050]

[0051] in,

[0052]

[0053] The covariance matrix is:

[0054]

[0055] in, For the prior prediction covariance matrix The lower triangular matrix obtained by performing Cholesky decomposition. The measurement covariance matrix R k+1 The lower triangular matrix obtained by performing Cholesky decomposition;

[0056] Multiply both sides of formula (16) by the left side. The following extended equation is obtained:

[0057]

[0058] in

[0059]

[0060] Where I represents the identity matrix;

[0061] Step 5.2, design the cost function based on maximum entropy:

[0062]

[0063] Among them, G σ Let L represent the Gaussian kernel function. The dimensions are given by L = n + m, where n represents the state dimension and m represents the measurement dimension. express The r-th element in express The rth line;

[0064] The optimal estimate of the target state is:

[0065]

[0066] in, for Line r:

[0067]

[0068] Taking the derivative of formula (21), the optimal objective state is:

[0069]

[0070] in, And there are:

[0071]

[0072]

[0073] in, This represents a diagonal matrix constructed from the kernel functions related to the prediction of the target's motion state. This represents a diagonal matrix constructed from kernel functions related to target measurements. for The first to the nth lines, for Lines n+1 to n+m;

[0074] Step 5.3: Let the iteration number t = 1, and use the prior prediction value obtained in step 4.2 as the initial value for the iteration process: And determine the kernel bandwidth value σ and the threshold ε;

[0075] Step 5.4: Calculate the state estimate obtained in the t-th iteration using the following formula.

[0076]

[0077] in,

[0078]

[0079]

[0080]

[0081] Step 5.5: Compare the estimated values ​​of the t-th iteration and the (t-1)-th iteration obtained from step 5.4 to see if they satisfy equation (31). If they do not satisfy, repeat step 5.4; if they do satisfy, end the iteration process and record the result of the t-th iteration. As the filtered posterior update value The covariance matrix is ​​updated using formula (32).

[0082]

[0083]

[0084] Step 6 shall be implemented in the following manner:

[0085] Step 6.1, based on the filtered prior prediction values ​​obtained in step 4.2 Covariance Matrix Calculate the likelihood function for each model:

[0086]

[0087] Step 6.2, according to the Bayesian probability formula, update the probability of each model using the following formula:

[0088]

[0089] Step 6.3, construct the transition probability correction function for model j:

[0090]

[0091]

[0092] in, This represents the rate of change of the model probability;

[0093] Step 6.4: Use the correction function of model j to correct the transition probabilities of other models transitioning to this model.

[0094]

[0095] Normalize the transition probabilities:

[0096]

[0097] Step 7 is as follows:

[0098] Step 7.1, update the filtered posterior value obtained in step 5.5. Combine the updated probabilities of each model obtained in step 6.2 with the state estimates of each model:

[0099]

[0100] Step 7.2: Update the values ​​based on the covariance matrix obtained in step 5.5. Integrate the covariance of each model:

[0101]

[0102] The beneficial effects of this invention are:

[0103] 1. This invention proposes a maneuvering target tracking algorithm based on maximum correlation entropy extended Kalman filter, which can solve the tracking problem of maneuvering targets under nonlinear and non-Gaussian noise conditions.

[0104] 2. Within the framework of the interactive multi-model algorithm, an extended Kalman filter based on maximum entropy is adopted. Since the maximum correlation entropy is used instead of the minimum mean square error criterion, the higher-order moment information of the error can be preserved. Under non-Gaussian noise conditions, its tracking results are better than those of the traditional interactive multi-model algorithm based on the extended Kalman filter. Attached Figure Description

[0105] Figure 1 This is a global flowchart of the maneuvering target tracking method based on maximum correlation entropy extended Kalman filtering of the present invention;

[0106] Figure 2 This is a target tracking trajectory diagram in Embodiment 1 of the maneuvering target tracking method based on maximum correlation entropy extended Kalman filtering of the present invention;

[0107] Figure 3(a) is a comparison of the position mean square error between Embodiment 1 of the maneuvering target tracking method based on maximum correlation entropy extended Kalman filtering of the present invention and the traditional method;

[0108] Figure 3(b) is a comparison of the velocity mean square error between Embodiment 1 of the maneuvering target tracking method based on maximum correlation entropy extended Kalman filtering of the present invention and the traditional method. Detailed Implementation

[0109] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments, so that the advantages and features of the present invention can be more readily understood by those skilled in the art.

[0110] Example 1

[0111] To verify the effectiveness of this invention, a maneuvering target was tracked. The radar sampling period was 0.1s, and the Monte Carlo simulation was performed 100 times. The specific motion process of the target was as follows: starting from the origin, it moved in a uniform straight line at a speed of 5m / s along the x-direction. After 3 seconds, the target began to make a 30° left turn. After 5 seconds, the target stopped turning and continued to move in a uniform straight line at a speed of 5m / s along the x-direction. After 4 seconds, the target began to make a 30° right turn. After 6 seconds, the target stopped turning and continued to move in a uniform straight line at a speed of 5m / s along the x-direction. After 2 seconds, the target stopped moving. The specific implementation was carried out according to the following steps:

[0112] Perform step 1 to establish the model set, target state equation, and measurement equation for the interactive multi-model algorithm.

[0113] The specific steps are as follows:

[0114] Step 1.1, the target state at time k is represented as: A linear CV model simulating uniform linear motion of the target is used to construct the target state equation as follows:

[0115] x k+1 =F k x k +G k w k (1)

[0116]

[0117] Wherein, the state vector x k In the , x and y represent the position of the target along the x-direction and the position along the y-direction, respectively; These are the target's velocity along the x-direction and velocity along the y-direction; T represents the sampling interval, w k F represents Gaussian white noise with a mean of 0 and a covariance of Q. k Let G represent the state transition matrix. k Represents the noise driving matrix;

[0118] Step 1.2, with Let k represent the target state at time k. A nonlinear CT model simulating a coordinated turning motion of the target with unknown angular velocity is used to construct the target state equation:

[0119] x k+1 =f(x) k )+G k w k (3)

[0120]

[0121] Wherein, angular velocity ωk It is not a constant;

[0122] Step 1.3: Using the x-direction position and y-direction position as observations, establish the measurement equation with non-Gaussian noise:

[0123] z k =H k x k +v k (5)

[0124]

[0125] Among them, z k This represents the observation vector at time k, and the measurement noise v. k It is non-Gaussian noise that follows a mixture of Gaussian distributions, specifically manifested as: v k ~(1-α)N(0,R 1k )+αN(0,R 2k ), where α represents the weight, ranging from 0 to 1, N(·,·) represents a normal distribution, and R 1k To measure the noise covariance, R 2k This is used to measure the covariance of noise when it is subjected to abnormal disturbances.

[0126] Step 2, Initialize parameters: Initialize the model probability, target state vector, covariance matrix and Markov state transition matrix for each model (total number of models is M) at time k=1;

[0127]

[0128] Step 3, Input Interaction: Based on the model probabilities, target state vector, covariance matrix and Markov state transition matrix of each model at time k, calculate the mixture probability between models at time k, and obtain the estimated value of the target in the mixture state of each model and the mixture covariance matrix at time k.

[0129] The specific steps are as follows:

[0130] Step 3.1, based on the model probability and Markov state transition matrix Π k The mixing probability between models at time k is calculated using formulas (7) and (8).

[0131]

[0132]

[0133] in, This represents the probability that the target is in model j after the input interaction;

[0134] Step 3.2, based on the target state at time k covariance matrix The mixture probability between the models obtained in step 3.1 The mixed state estimates of the target at time k under each model are obtained using formulas (9) and (10), respectively. and mixed covariance matrix

[0135]

[0136]

[0137] in, It is the estimated mixed state of the target under various models at time k. It is the mixed covariance of the target at time k across all models.

[0138] Step 4, prior estimation of the filter: Since the measurement equation is linear, the nonlinearity of the system is relatively small. Therefore, the extended Kalman filter with low computational cost is used to linearize the nonlinear models in the model set, and a one-step prediction is performed on each model to obtain the prior prediction value of the target at time k+1 in each model.

[0139] The specific steps are as follows:

[0140] Step 4.1: Calculate the Jacobian matrix of the nonlinear system state equation according to formulas (11) and (12), and linearize the nonlinear state equation (3):

[0141]

[0142] The partial derivatives of each state variable with respect to the angular velocity are:

[0143]

[0144] Where, ω k Angular velocity, T is the sampling interval. These are the velocities in the x-direction and the velocities in the y-direction, respectively.

[0145] Step 4.2: Use the mixture state estimate of the target at time k obtained in Step 3.2 to determine the model. and mixed covariance matrix Depending on whether the state equation is linear, the filtered prior prediction value is obtained using formula (13) or (14) respectively. Use formula (15) to obtain the prior covariance estimate.

[0146]

[0147]

[0148]

[0149] Step 5, posterior update of the filter: Based on the target state equation, measurement equation obtained in Step 1 and the prior prediction value obtained in Step 4, design a cost function based on the maximum entropy criterion, and obtain the posterior update value of the target in each model at time k+1 through an iterative method.

[0150] The specific steps are as follows:

[0151] Step 5.1: Based on the target state equations (1) and (3), the measurement equation (5), and the filtered prior predictions obtained in step 4.2... and The system equations are extended as follows:

[0152]

[0153] in,

[0154]

[0155] The covariance matrix is:

[0156]

[0157] in, For the prior prediction covariance matrix The lower triangular matrix obtained by performing Cholesky decomposition. The measurement covariance matrix R k+1 The lower triangular matrix obtained by performing Cholesky decomposition;

[0158] Multiply both sides of formula (16) by the left side. The following extended equation is obtained:

[0159]

[0160] in

[0161]

[0162] Where I represents the identity matrix;

[0163] Step 5.2, design the cost function based on maximum entropy:

[0164]

[0165] Among them, G σ Let L represent the Gaussian kernel function. The dimensions are given by L = n + m, where n represents the state dimension and m represents the measurement dimension. express The r-th element in express The rth line;

[0166] The optimal estimate of the target state is:

[0167]

[0168] in, for Line r:

[0169]

[0170] Taking the derivative of formula (21), the optimal objective state is:

[0171]

[0172] in, And there are:

[0173]

[0174]

[0175] in, This represents a diagonal matrix constructed from the kernel functions related to the prediction of the target's motion state. This represents a diagonal matrix constructed from kernel functions related to target measurements. for The first to the nth lines, for Lines n+1 to n+m;

[0176] Step 5.3: Let the iteration number t = 1, and use the prior prediction value obtained in step 4.2 as the initial value for the iteration process: And determine the kernel bandwidth value σ and the threshold ε;

[0177] Step 5.4: Calculate the state estimate obtained in the t-th iteration using the following formula.

[0178]

[0179] in,

[0180]

[0181]

[0182]

[0183] Step 5.5: Compare the estimated values ​​of the t-th iteration and the (t-1)-th iteration obtained from step 5.4 to see if they satisfy equation (31). If they do not satisfy, repeat step 5.4; if they do satisfy, end the iteration process and record the result of the t-th iteration. As the filtered posterior update value The covariance matrix is ​​updated using formula (32).

[0184]

[0185]

[0186] Step 6, Model Probability Update: By calculating the likelihood function of each model, and using Bayes' probability formula, the probability update value of each model is obtained. A correction function is constructed using the model probability change rate to correct the transition probabilities between models. This is implemented specifically according to the following steps:

[0187] Step 6.1, based on the filtered prior prediction values ​​obtained in step 4.2 Covariance Matrix Calculate the likelihood function for each model:

[0188]

[0189] Step 6.2, according to the Bayesian probability formula, update the probability of each model using the following formula:

[0190]

[0191] Step 6.3, construct the transition probability correction function for model j:

[0192]

[0193]

[0194] in, This represents the rate of change of the model probability;

[0195] Step 6.4: Use the correction function of model j to correct the transition probabilities of other models transitioning to this model.

[0196]

[0197] Normalize the transition probabilities:

[0198]

[0199] Step 7, Fuse the output results: Fuse the posterior update values ​​and covariance of each model to output the target's state vector at time k+1. The covariance matrix P k+1 .

[0200] The specific steps are as follows:

[0201] Step 7.1, update the filtered posterior value obtained in step 5.5. Combine the updated probabilities of each model obtained in step 6.2 with the state estimates of each model:

[0202]

[0203] Step 7.2: Update the values ​​based on the covariance matrix obtained in step 5.5. Integrate the covariance of each model:

[0204]

[0205] Step 8: Repeat steps 3-7 until target tracking is complete, obtaining the final target tracking result as shown below. Figure 2 and Figures 3(a)-3(b) As shown.

[0206] Depend on Figure 2 It can be seen that under non-Gaussian noise conditions, the maximum entropy extended Kalman filter algorithm based on the interactive multi-model is close to the true state of the target, indicating that the algorithm can track maneuvering targets well. As shown in Figures 3(a) and 3(b), the root mean square error of position and root mean square error of velocity of the maximum entropy extended Kalman filter algorithm based on the interactive multi-model are smaller than the corresponding error values ​​of the extended Kalman filter algorithm based on the interactive multi-model, indicating that the maximum entropy extended Kalman filter algorithm based on the interactive multi-model has higher accuracy and better tracking effect.

Claims

1. A maneuvering target tracking method based on maximum correlation entropy extended Kalman filter, characterized in that, The specific steps are as follows: Step 1: Establish the model set, target state equation, and measurement equation for the interactive multi-model algorithm; Step 2, Initialize parameters: Initialize the model probabilities, target state vectors, covariance matrices, and Markov state transition matrices for each model at time k=1; Step 3, Input Interaction: Based on the model probabilities, target state vector, covariance matrix and Markov state transition matrix of each model at time k, calculate the mixing probability between models at time k, and obtain the estimated value of the target in the mixed state of each model and the mixing covariance matrix at time k. Step 4, Filter Prior Estimation: The nonlinear models in the model set are linearized using an extended Kalman filter, and a one-step prediction is made for each model to obtain the prior prediction value of the target at time k+1 in each model. Step 5, posterior update of the filter: Based on the target state equation, measurement equation obtained in step 1 and the prior prediction value obtained in step 4, design a cost function based on the maximum entropy criterion, and obtain the posterior update value of the target in each model at time k+1 through the iterative method. Step 6, Model Probability Update: By calculating the likelihood function of each model, the probability update value of each model is obtained according to the Bayesian probability formula. A correction function is constructed using the model probability change rate to correct the transition probabilities between models. Step 7, Fuse the output results: Fuse the posterior update values ​​and covariance of each model to output the target's state vector at time k+1. Covariance Matrix ; Step 8: Repeat steps 3-7 until the target tracking process is complete.

2. The maneuvering target tracking method based on maximum correlation entropy extended Kalman filter according to claim 1, characterized in that, Step 1 is as follows: Step 1.1, the target state at time k is represented as: A linear CV model simulating uniform linear motion of the target is constructed, and the target state equation is as follows: (1) (2) Wherein, the state vector in They represent the target along The position of direction, along The position of direction; , Is the target along velocity in direction, along The velocity in the direction; T represents the sampling interval. This indicates that the mean is 0 and the covariance is... Gaussian white noise, Represents the state transition matrix. Represents the noise driving matrix; Step 1.2, with Let k represent the target state at time k. A nonlinear CT model simulating a coordinated turning motion of the target with unknown angular velocity is used to construct the target state equation: (3) (4) Among them, angular velocity It is not a constant; Step 1.3, with Direction and position As the orientation and position are observed, a measurement equation with non-Gaussian noise is established: (5) (6) in, Represents the observation vector at time k, measuring noise. It is non-Gaussian noise that follows a mixture of Gaussian distributions, specifically manifested as: ,in This represents the weight, with a value ranging from 0 to 1. Indicates a normal distribution. To measure the noise covariance, This is used to measure the covariance of noise when it is subjected to abnormal disturbances.

3. The maneuvering target tracking method based on maximum correlation entropy extended Kalman filter according to claim 2, characterized in that, Step 2 shall be implemented in the following manner: Initialize parameter values, including determining the target's position in the model at time k=1. probability State estimation Covariance matrix and Markov state transition matrix Each element express Time system from model Transfer to model The transition probability, This indicates the total number of models.

4. The maneuvering target tracking method based on maximum correlation entropy extended Kalman filter according to claim 3, characterized in that, Step 3 is as follows: Step 3.1, based on the model probability and Markov state transition matrix The mixing probability between models at time k is calculated using formulas (7) and (8). : (7) (8) in, This indicates that after input interaction, the target is in the model. The probability of; Step 3.2, based on the target state at time k Covariance matrix The mixture probabilities between the models obtained in step 3.1 The mixed state estimates of the target at time k under each model are obtained by formulas (9) and (10), respectively. and mixed covariance matrix : (9) (10) in, It is the estimated mixed state of the target under various models at time k. It is the mixed covariance of the target at time k across all models.

5. The maneuvering target tracking method based on maximum correlation entropy extended Kalman filter according to claim 4, characterized in that, Step 4 shall be implemented in the following manner: Step 4.1: Calculate the Jacobian matrix of the nonlinear system state equation according to formulas (11) and (12), and linearize the nonlinear state equation (3): (11) The partial derivatives of each state variable with respect to the angular velocity are: (12) in, Angular velocity, For sampling interval, , These are the velocities in the x-direction and the velocities in the y-direction, respectively. Step 4.2: Use the mixture state estimate of the target at time k obtained in Step 3.2 to determine the model. and mixed covariance matrix Depending on whether the state equation is linear, the filtered prior prediction value is obtained using formula (13) or (14) respectively. The prior covariance estimate is obtained using formula (15). (13) (14) (15)。 6. The maneuvering target tracking method based on maximum correlation entropy extended Kalman filter according to claim 5, characterized in that, Step 5 is as follows: Step 5.1, based on the target state equation (1) and (3), the measurement equation (5), and the filtered prior prediction value obtained in step 4.

2. and The system equations are extended as follows: (16) in, (17) The covariance matrix is: (18) in, For the prior prediction covariance matrix The lower triangular matrix obtained by performing Cholesky decomposition. For the measurement covariance matrix The lower triangular matrix obtained by performing Cholesky decomposition; Multiply both sides of formula (16) by the left side. The following extended equation is obtained: (19) in (20) in, Represents the identity matrix; Step 5.2, design the cost function based on maximum entropy: (21) in, Represents the Gaussian kernel function. yes Dimension and 'n' represents the state dimension, and 'm' represents the measurement dimension. express The first in One element, express The OK; The optimal estimate of the target state is: (22) in, for The OK; (23) Taking the derivative of formula (21), the optimal objective state is: (24) in, And there are: (25) (26) in, This represents a diagonal matrix constructed from the kernel functions related to the prediction of the target's motion state. This represents a diagonal matrix constructed from kernel functions related to target measurements. … for The first to the nth lines, … for Lines n+1 to n+m; Step 5.3: Let the iteration number t=1, and use the prior prediction value obtained in step 4.2 as the initial value for the iteration process: And determine the kernel bandwidth value. and threshold ; Step 5.4: Calculate the state estimate obtained in the t-th iteration using the following formula. : (27) in, (28) (29) (30) Step 5.5: Compare the estimated values ​​of the t-th iteration and the (t-1)-th iteration obtained from step 5.4 to see if they satisfy equation (31). If they do not, repeat step 5.4; if they do, end the iteration process and record the result of the t-th iteration. As the filtered posterior update value The covariance matrix is ​​updated using formula (32). : (31) (32)。 7. The maneuvering target tracking method based on maximum correlation entropy extended Kalman filter according to claim 6, characterized in that, Step 6 shall be implemented in the following manner: Step 6.1, based on the filtered prior prediction values ​​obtained in step 4.2 Covariance Matrix Calculate the likelihood function for each model: (33) Step 6.2, according to the Bayesian probability formula, update the probability of each model using the following formula: (34) Step 6.3, construct the transition probability correction function for model j: (35) (36) in, This represents the rate of change of the model probability; Step 6.4: Use the correction function of model j to correct the transition probabilities of other models transitioning to this model. (37) Normalize the transition probabilities: (38)。 8. The maneuvering target tracking method based on maximum correlation entropy extended Kalman filter according to claim 7, characterized in that, Step 7 is as follows: Step 7.1, update the filtered posterior value obtained in step 5.

5. Combine the updated probabilities of each model obtained in step 6.2 with the state estimates of each model: (39) Step 7.2: Update the values ​​based on the covariance matrix obtained in step 5.

5. By integrating the covariance of each model: (40)。

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