Robust ellipse extended object tracking method based on variable center maximum correlation entropy criterion

Abstract

The application discloses a robust elliptical extended target tracking method based on a variable center maximum correlation entropy criterion, and is used for solving the problem of insufficient tracking precision when abnormal values exist in radar measurement data in the prior art. The method models the extended target as an ellipse, estimates kernel parameters based on the variable center maximum correlation entropy criterion, and then updates the motion state, so that the robust estimation of the motion state of the extended target is realized. The shape feature is represented by a covariance matrix of radar measurement data, initial estimation of the shape feature is obtained, and then recursive updating is performed under the Kalman filtering framework. The method innovatively combines the variable center maximum correlation entropy criterion with the Kalman filtering, effectively suppresses the influence of abnormal values in the radar measurement data by using the adaptive kernel center adjustment mechanism of the variable center maximum correlation entropy criterion, and shows good robustness.

Description

Technical Field

[0001] This invention relates to a target tracking technology, and more particularly to a robust elliptic extended target tracking method based on the variable center maximum correlation entropy criterion. Background Technology

[0002] Target tracking technology is a fundamental and crucial technology in numerous military and civilian fields, including national defense, autonomous driving, intelligent transportation, and disaster relief. In traditional target tracking methods, targets are typically simplified to point masses, ignoring their extended shape features. The motion state, such as position and velocity, is estimated solely based on measurement data collected at different times, using techniques like Kalman filtering (KF). However, with the widespread application of modern high-precision sensors, such as millimeter-wave radar, lidar, and high-resolution cameras, multiple measurements of a target can be acquired in a single scan. These measurements can not only estimate the target's motion state but also further deduce its shape features, such as size, attitude, and geometric contours. In many applications, the extended shape features of a target play a vital role in accurate perception and decision-making. For example, in autonomous driving systems, accurately estimating the vehicle's length, width, and heading angle can significantly improve the accuracy of driving intention prediction; in military reconnaissance, identifying the geometric features of a target can effectively support target classification and threat assessment. Furthermore, in scenarios where targets form dense formations, such as aerial refueling formations, sensors may be unable to distinguish individual targets, making it difficult to establish a one-to-one correspondence between targets and measurement data. In this context, viewing the target as an extended target possessing both motion and shape features is a more reasonable choice. Therefore, developing an extended target tracking (EOT) method based on multiple measurements to achieve simultaneous estimation of the target's motion and shape features is particularly necessary.

[0003] Over the past few decades, the EOT method has been extensively studied. However, this method still faces the following technical challenges:

[0004] Measurement data sparsity and outlier interference: Sensors such as millimeter-wave radar and lidar may acquire only a small number of measurements in a single scan, and the number and spatial distribution of these measurements change dynamically over time. Furthermore, due to noise, occlusion, or multipath effects, measurement data often contains outliers. Traditional EOT methods based on least squares or Gaussian assumptions (such as the stochastic matrix method) are sensitive to outliers, which can lead to biases in shape feature estimation.

[0005] The contradiction between the complexity of shape modeling and the real-time requirements of algorithms: The geometry of extended targets is usually approximated by models such as ellipses, rectangles, or star-shaped convex bodies. However, in dynamic environments, targets may deform, such as the contour changes when a vehicle turns. Existing methods, such as particle filtering, can handle complex extended shape features, but their high computational complexity makes it difficult to meet real-time requirements.

[0006] Therefore, there is an urgent need to develop an extended target tracking scheme that balances robustness, accuracy, and computational efficiency. Among various shape modeling methods, the elliptical / ellipsoidal approximation is widely adopted due to its broad applicability and computational efficiency. Based on the elliptical approximation and different physical extension modeling methods, existing extended target tracking methods based on the elliptical assumption mainly include particle filtering methods, stochastic hypersurface model methods, stochastic matrix methods, and other derived methods. Although these methods have made significant progress in the field of extended target tracking, they still have some technical shortcomings, as follows:

[0007] Particle filtering methods use a large number of particles to represent the state distribution of the target, resulting in high computational complexity and difficulty in meeting real-time requirements. In practical applications, particle filtering is prone to sample degradation, where the weights of most particles approach zero, and only a few particles have effective weights, leading to a decrease in tracking accuracy. Particle filtering methods typically assume that the measurement error is centered at zero, and their adaptability is poor for measurement errors with non-zero centered distributions, which can easily lead to tracking deviations.

[0008] The stochastic hypersurface model method requires complex modeling of the target geometry, resulting in high computational complexity and difficulty in real-time processing. In dynamic environments, the target geometry may change (such as the contour change when a vehicle turns), and the stochastic hypersurface model method has difficulty adapting to these changes quickly, leading to a decrease in tracking accuracy. The stochastic hypersurface model method usually assumes that the measurement error is centered at zero. For measurement errors that are not centered at zero, the tracking accuracy will be affected.

[0009] The random matrix method is based on the least squares or Gaussian assumptions, which are sensitive to outliers in the measurement data and can easily lead to deviations in shape feature estimation. The random matrix method usually assumes that the measurement error is centered at zero. For measurement errors with non-zero central distribution, its adaptability is poor and can easily lead to a decrease in tracking accuracy.

[0010] While other derivative methods perform well in certain specific scenarios, they lack a unified framework and struggle to maintain consistent performance across a variety of complex scenarios. Many derivative methods perform poorly when dealing with dynamic changes in target shape, failing to adapt quickly to these changes and resulting in decreased tracking accuracy. Furthermore, derivative methods typically assume that the measurement error is centered at zero, which makes them less adaptable to measurement errors with non-zero centers, easily leading to tracking deviations.

[0011] In summary, most existing methods assume that the measurement error is centered at zero, which is not always true in practical applications. Measurement errors with non-zero center distribution can lead to a decrease in tracking accuracy or even tracking failure. Existing methods lack the ability to dynamically adjust the error center and cannot effectively handle measurement errors with non-zero center distribution, thus affecting tracking accuracy and robustness. Many existing methods have high computational complexity, making it difficult to meet real-time requirements, especially when dealing with high-dimensional data. Existing methods are sensitive to outliers in measurement data, which can easily lead to deviations in shape feature estimation, thus affecting tracking accuracy. In dynamic environments, the shape of the target may change, and existing methods cannot quickly adapt to these changes, resulting in a decrease in tracking accuracy. Summary of the Invention

[0012] The technical problem to be solved by the present invention is to provide a robust elliptical extended target tracking method based on the variable center maximum correlation entropy criterion. Based on the variable center maximum correlation entropy criterion, by jointly estimating the kernel bandwidth and kernel center, it can better adapt to measurement errors with non-zero center distribution, thereby improving tracking accuracy and robustness.

[0013] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a robust elliptical extended target tracking method based on the variable center maximum correlation entropy criterion, characterized by including the following steps:

[0014] Step 1: In the extended target tracking system, for an extended target with an approximately elliptical shape, its tracking model consists of three parts: unknown parameterization, measurement model, and dynamic model, wherein the extended target is deployed in a two-dimensional coordinate system;

[0015] Unknown parameterization: extending the target's motion state r at time k k From position u k and speed v k Composition, expanding the shape features p of the target at time k k The angle α of counterclockwise rotation about the x-axis of the two-dimensional coordinate system k and the length vector of the major and minor semi-axes Composition, where the initial value of k is 1;

[0016] Measurement Model: At time k, the radar obtains a set of two-dimensional Cartesian coordinates of reflection points on the extended target. These coordinates are used as measurement values, and the j-th measurement value obtained at time k is represented as... and establish The measurement model, where j = 1, ..., J k J k This represents the number of measurements obtained at time k;

[0017] Dynamic model: Assuming the extended target moves at a constant velocity in a straight line within a short observation period, the dynamic model is described as follows: Among them, A k Let k represent the transition matrix at time k. t represents the sampling interval, λ k and ψ k All are process noise at time k, λ k It follows a Gaussian distribution with zero mean and covariance matrix Λ, ψ k r follows a Gaussian distribution with zero mean and covariance matrix Ψ, when k=1 k-1 Represents the initial motion state of the extended target, p k-1 This represents the initial shape features of the expanded target; when k > 1, r k-1 p represents the motion state of the extended target at time k-1. k-1 This represents the shape characteristics of the extended target at time k-1;

[0018] Step 2: Based on the dynamic model, for r k and p k Perform a prediction step to obtain r k One-step prediction value and p k One-step prediction value thereby obtaining Prediction error covariance matrix and Prediction error covariance matrix Then, the prediction error was analyzed. and The measurement error in the measurement model is whitened, and the corresponding whitened prediction error ξ is obtained. k Measurement error after whitening Among them, prediction error The whitening process used The measurement error whitening process in the measurement model used and

[0019] Step 3: Assume that when k > 1, r k-1 The estimated value As an unbiased estimate, based on this assumption, ξ k The estimated value of the core center is set to zero; ξ is set to zero. k The estimated value of the kernel bandwidth is set as ξ. k Standard deviation;

[0020] Step 4: Based on kernel density estimation theory, construct... The nth component kernel bandwidth σ k，(n)and the core center c k，(n) The joint estimation optimization problem is given by the expression $\mathbf{a}$, where $n \in {1, 2}$. The joint estimation optimization problem is decomposed into a kernel bandwidth $σ$. k，(n) The original problem and kernel center c of the estimation subproblem k，(n) Estimate the original problem of the subproblem; then calculate the kernel bandwidth σ. k，(n) The original problem of estimating the subproblem is transformed into kernel bandwidth σ. k，(n) Estimating the convexity of the subproblems, with the kernel center c k，(n) The original problem of estimating subproblems is transformed into the core-center problem c. k，(n) The estimation of the augmented optimization problem of the subproblem, wherein the augmented optimization problem includes... The weight is the center error weight. express The estimated value; then the core center c k，(n) The augmented optimization problem of estimating the subproblem is decomposed into a subproblem concerning the kernel center and a subproblem concerning the center error weights;

[0021] Step 5: Propose a criterion for r based on the maximum correlation entropy criterion of the variable center. k The cost function, and the known σ k，(n) and c k，(n) Substitute about r k The cost function is obtained by knowing σ. k，(n) and c k，(n) The optimization problem based on the maximum correlation entropy criterion with varying center is then categorized. This problem is then equivalently transformed into an augmented optimization problem, which includes prediction error weights and measurement error weights. Finally, the augmented optimization problem is decomposed into a function relating r. k Sub-problems concerning prediction error weights and measurement error weights;

[0022] Step 6: Obtain the results using an alternating iterative strategy. The nth component kernel bandwidth σ k，(n) The estimated value and the core center c k，(n) The estimated value and r k The estimated value Specifically, in each outer iteration, for σ... k，(n) Directly solve for the kernel bandwidth σ k，(n) Estimate the convexity of the subproblems to obtain σ at each outer iteration. k，(n) The optimal solution for c; k，(n) During the inner iteration process, the subproblem concerning the kernel center and the subproblem concerning the center error weight are solved alternately. When the first inner iteration condition is satisfied, the value of c in each outer iteration is obtained. k，(n) The optimal solution for r; kDuring the inner iteration process, solutions for r are solved alternately. k The subproblems concerning prediction error weights and measurement error weights, when satisfying the second inner-layer iteration condition, yield r for each outer-layer iteration. k The optimal solution, and r k The estimation error covariance matrix of the optimal solution; σ is obtained when the outer iteration conditions are satisfied. k，(n) The estimated value and c k，(n) The estimated value and r k The estimated value And thus obtain The estimation error covariance matrix R k Then, through the state transition equation, and R k Convert to r respectively k+1 One-step prediction value and its prediction error covariance matrix

[0023] Step 7: Based on the expanded target and Corresponding measurement source The corresponding random vector z k covariance matrix approximation Obtain α k rough estimate Extend the length of the semi-major axis of the target at time k rough estimate Extend the length of the minor semi-axis of the target at time k rough estimate Then obtain p k rough estimate Then calculate The estimation error covariance matrix Then, within the framework of Kalman filtering, update and obtain p. k The estimated value The Kalman gain corresponding to the Kalman filter equation includes...

[0024] Step 8: Following the process of Step 6 and Step 7, obtain the estimated values ​​of the motion state and shape features of the extended target at different times to achieve extended target tracking, where the different times are multiple consecutive times.

[0025] In step 1, Where, r k The dimension is 4×1, p k The dimension is 3×1. A vector consisting of the lengths of the major and minor axes of the extended target at time k, with the superscript "T" indicating the transpose of the vector or matrix; The measurement model is described as follows: in, Indicates the extension target and Time-response measurement source, u k =Hr k H represents from r k Extract u k The selection matrix is ​​H = [I2, 0], where I2 represents the 2-dimensional identity matrix and 0 represents the zero matrix with dimension 2×2. and The corresponding symbols represent the lengths of the major and minor axes of the extended target at time k. express The corresponding multiplicative noise vector follows a property with zero mean and a covariance matrix of... Gaussian distribution, for The first element, for The second element, and All are used for control The corresponding reflection points are random quantities that are uniformly distributed within the extended target range. express The measurement noise in the data follows a zero-mean pattern and has a noise covariance matrix of C. n Gaussian distribution, for Measurement errors in the measurement model.

[0026] In step 2, Where k=1 That is, r k-1 When k > 1 Indicates r k-1 The estimated value when k=1 That is, p k-1 When k > 1 p k-1 The estimated value, R represents the desired operation. k-1 express The estimated error covariance matrix, Ξ k-1 express The estimation error covariance matrix;

[0027] ξ k The acquisition process is as follows: Perform Cholesky decomposition to obtain And thus obtain Where, ξ k The dimension is 4×1;

[0028] The acquisition process is as follows: exist Perform a first-order Taylor expansion at this point: in, Indicates will Substitute into S k V was obtained from 1，k Indicates according to S k The first line S k，(1，：) The calculated Jacobian matrix, Indicates will Substitute into V 1，k V was obtained from 2，k Indicates according to S k The second line S k，(2，：) The calculated Jacobian matrix, Indicates will Substitute into V 2，k Obtain from; then The covariance matrix is ​​represented as M k , Will The covariance matrix is ​​represented as F k , Among them, F k The element F with index (i, t) (i,t) pass We calculate that i, t∈{1, 2}, and tr{·} represents finding the trace of the matrix; then we obtain... The relevant measurement error covariance matrix Q k , Then Q k Perform Cholesky decomposition to obtain And thus obtain The nth component is in, The dimension is 2×1, Π k，(n，：) Represents Π k The nth line.

[0029] In step 4, the joint estimation optimization problem is described as follows: in, express The estimated value, after obtaining r kThe estimated value Under the premise Π k，(n，：) Represents Π k The nth line, Q k express The relevant measurement error covariance matrix, H represents the variance from r k Extract u k The selection matrix;

[0030] In step 4, the kernel bandwidth σ k，(n) The process of obtaining the convex problem of estimating subproblems is as follows: fix the kernel center c. k，(n) The value, use this value as And let The joint estimation optimization problem is transformed into a kernel bandwidth σ problem. k，(n) The original problem for estimating subproblems is described as follows: Then, regarding the kernel bandwidth σ k，(n) The original problem of estimating the subproblem is subjected to a Taylor expansion, and its third-order terms are preserved to ensure the accuracy of the approximation, resulting in the Taylor expansion, which is used as the kernel bandwidth σ. k，(n) The convex problem of estimating subproblems is described as follows: in,

[0031] In step 4, the core center c k，(n) The process of obtaining the augmented optimization problem for estimating subproblems is as follows: fix the kernel bandwidth σ k，(n) The value, use this value as The joint estimation optimization problem is transformed into a kernel-centric c problem. k，(n) The original problem for estimating subproblems is described as follows: Then, based on the properties of convex conjugate functions, the kernel center c is... k，(n) The original problem of estimating subproblems is transformed into the core-center problem c. k，(n) The augmented optimization problem for estimating subproblems is described as follows: in, express The weights are the center error weights, and φ(·) represents the convex conjugate function of the exponential function;

[0032] In step 4, the process of obtaining the sub-problem concerning the kernel center is as follows: [Fixed] The value, denoted as The augmented optimization problem is transformed into a subproblem concerning the kernel center, described as follows:

[0033]

[0034] In step 4, the process of obtaining the sub-problem regarding the center error weight is as follows: fix the kernel center c. k，(n) The value, denoted as The augmentation optimization problem is transformed into a subproblem concerning the center error weights, described as follows:

[0035]

[0036] The specific process of step 5 is as follows:

[0037] Step 5.1: Fix the core bandwidth σ k，(n) The value, use this value as And fix the core center c k，(n) The value, use this value as Then, based on the maximum correlation entropy criterion of the variable center, a proposal is made regarding r. k The cost function is described as follows: in, Indicates about r k The cost function, The kernel function in the equation is a Gaussian kernel function, L = 4 + 2J. k ||·|| denotes the 2-norm, and G1 denotes a kernel function with a kernel bandwidth of 1. Indicates the kernel bandwidth is The kernel function, b k，(i) Indicates the relationship with r k The relevant zero center error vector b k The i-th element in

[0038] Step 5.2: Let Regarding r k The cost function is transformed into a known σ k，(n) and c k，(n) The cost function is described as follows: in, Indicates that σ is known k，(n) and c k，(n) The cost function, Indicates the kernel bandwidth is Gaussian kernel function, ξ k，(m) Indicates ξ k The m-th element, Γ k，(m，：) Indicates Γ k The m-th line;

[0039] Step 5.3: [The sentence is incomplete and requires more context to be translated accurately.] and Substitution In the middle, construct a known σ k，(n) and c k，(n)The optimization problem based on the maximum correlation entropy criterion with varying centers is described as follows:

[0040]

[0041] Step 5.4: Transform the optimization problem into an augmenting optimization problem, described as follows: Among them, κ m For prediction error weights, To measure the error weights, φ(·) denotes the convex conjugate function of the exponential function.

[0042] Step 5.5: Fix κ m and The values ​​are denoted as and these two values ​​are recorded accordingly. and The augmentation optimization problem is transformed into a problem concerning r. k The subproblems are described as follows: Regarding r k The subproblem is equivalently transformed into a problem concerning r. k The linear least squares problem is described as follows:

[0043] Fixed r k The value, denoted as The augmentation optimization problem is transformed into a subproblem concerning the prediction error weights and the measurement error weights, described as follows: in,

[0044] The process of step 6 is as follows:

[0045] Step 6.1: Let s represent the number of outer iterations, and initialize s to 1;

[0046] Step 6.2: During the s-th outer iteration, and Substitute kernel bandwidth σ k，(n) In the convex problem of estimating subproblems, the solution yields μ at the s-th outer iteration. k，(n) The optimal solution, that is, the solution obtained when σ is obtained in the s-th outer iteration. k，(n) optimal solution Where s = 1 For c k，(n) initial value For r k initial value Set to 0, To pass through c k，(n) Set to 0, σ k，(n) Let it be 1, κ m and Set all to -1 and substitute them into Solving for s, we find that when s>1 c represents the value of c in the (s-1)th outer iteration. k，(n) The optimal solution In the (s-1)th outer iteration, r k The optimal solution;

[0047] Step 6.3: During the s-th outer iteration, for c k，(n) Perform inner layer iterations as follows:

[0048] Step 6.3.1: Let q represent the number of inner iterations, and initialize q to 1;

[0049] Step 6.3.2: During the q-th inner iteration within the s-th outer iteration, ... and Substituting into the subproblem concerning the kernel center, we can obtain the value of c in the q-th inner iteration within the s-th outer iteration. k，(n) optimal solution Where q = 1 When the inner iteration begins during the s-th outer iteration... initial value Set to -1, when q > 1 This indicates the time of the (q-1)th inner iteration within the s-th outer iteration. The optimal solution. To pass Substitution Obtained from;

[0050] During the q-th inner iteration within the s-th outer iteration, and Substituting into the subproblem concerning the center error weights, we can obtain the result of the inner iteration q within the outer iteration s-th iteration. optimal solution

[0051] Step 6.3.3: Determine the first inner layer iteration condition Is it true? If it is true, then... When c is the outermost iteration of the s-th time k，(n) optimal solution Then execute step 6.4. If it fails, set q = q + 1, and then return to step 6.3.2 to continue execution. Here, when q = 1... When c starts during the s-th outer iteration... k，(n) initial value equal hour c represents the value of c in the (q-1)th inner iteration within the s-th outer iteration. k，(n) The optimal solution;

[0052] Step 6.4: During the s-th outer iteration, for r k Perform inner layer iterations as follows:

[0053] Step 6.4.1: Let q represent the number of inner iterations, and initialize q to 1;

[0054] Step 6.4.2: During the q-th inner iteration within the s-th outer iteration, ... and Substitute about r k In the linear least squares problem, the solution yields the value of r during the q-th inner iteration within the s-th outer iteration. k optimal solution Where q = 1 κ is the value at the start of the inner iteration during the s-th outer iteration. m initial value When the inner iteration begins during the s-th outer iteration... initial value and All are set to -1, when q > 1 κ represents the value of κ in the (q-1)th inner iteration within the s-th outer iteration. m The optimal solution This indicates the time of the (q-1)th inner iteration within the s-th outer iteration. The optimal solution. Indicates Kalman gain, Then calculate The estimation error covariance matrix Where I represents the identity matrix;

[0055] During the q-th inner iteration within the s-th outer iteration, Substituting these into the subproblem concerning the prediction error weight and the measurement error weight, we can solve for κ in the q-th inner iteration within the s-th outer iteration. m optimal solution and optimal solution in,

[0056] Step 6.4.3: Determine the second inner layer iteration condition Is it true? If it is true, then... When r is the s-th outer iteration k optimal solution Will As The estimation error covariance matrix Then execute step 6.5. If it fails, set q = q + 1, and then return to step 6.4.2 to continue execution. Here, when q = 1... When r starts during the s-th outer iteration... k initial value equal hour This indicates that when r is in the (q-1)th inner iteration within the s-th outer iteration... k The optimal solution;

[0057] Step 6.5: Determine if the outer iteration condition is true. If it is true, then... Corresponding as σ k，(n) The estimated value c k，(n) The estimated value r k The estimated value Then As The estimation error covariance matrix R k Then, through the state transition equation, and R k Convert to r respectively k+1 One-step prediction value and its prediction error covariance matrix If the condition is not met, let s = s + 1, and then return to step 6.2 to continue execution. The outer iteration condition is whether s is less than or equal to the preset number of iterations.

[0058] The specific process of step 7 is as follows:

[0059] Step 7.1: Let z k express The corresponding random vector, let y k express The corresponding random vector, let Indicate z k Let the covariance matrix be... Indicates y k The covariance matrix, and The relationship is as follows: Where, n k Represents a set The corresponding random vector; then calculate approximation in, express The mean, And calculate approximation in, It is positive definite;

[0060] Step 7.2: According to Obtain α k rough estimate rough estimate rough estimate in, express The element in the first row and first column, express The element in the 1st row and 2nd column, express The element in the second row and second column; thus, obtain p. k rough estimate

[0061] Step 7.3: Calculation The estimation error covariance matrix Specifically as follows:

[0062] Step 7.3.1: Definition The estimation error vector Δp k ,

[0063] Step 7.3.2: Let

[0064] Step 7.3.3: Definition in, Corresponding representation The element in the first row and first column, the element in the first row and second column, and the element in the second row and second column. Corresponding representation The element in the first row and first column, the element in the first row and second column, and the element in the second row and second column. S k,(1,：) S represents k The first row vector, S k,(2,：) S represents k The second row vector, express The first element, express The second element, Cn,(1,1) Indicate C n The element in the first row and first column, C n，(1,2) Indicate C n The element in the 1st row and 2nd column, C n，(2，2) Indicate C n The element in the 2nd row and 2nd column;

[0065] Step 7.3.4: Calculate the covariance matrix C of Δσ σ C σ The element in the first row and first column is C σ The element in the first row and second column is C σ The element in the second row and second column is C σ The element in the 1st row and 3rd column is C σ The element in the 2nd row and 3rd column is C σ The element in the 3rd row and 3rd column is

[0066] Step 7.3.5: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] Substitution In the middle, and on Performing a first-order Taylor expansion at σ yields: Δp k =DΔσ, where the first row of D The second line of D D's third line

[0067] Step 7.3.6: Calculation

[0068] Step 7.4: Update and obtain p within the framework of Kalman filtering k The estimated value Among them, K p This represents the Kalman gain corresponding to the Kalman filter equation. Then calculate The estimation error covariance matrix Ξ k ,

[0069] Compared with the prior art, the advantages of the present invention are as follows:

[0070] 1) Propose a robust extended target tracking framework based on MCC-VC: The MCC-VC criterion is innovatively introduced into the extended target tracking (EOT) problem. By estimating the error center, the robustness of the method of this invention to measurement outliers is significantly improved.

[0071] 2) Design an alternating iterative strategy under the MCC-VC framework: First, whiten the prediction error and measurement error to make them compatible with the MCC-VC framework. Then, through alternating optimization between the kernel bandwidth estimated by the kernel density estimation theory and the kernel center and motion state, a robust estimation of the motion state of the extended target can be achieved.

[0072] 3) The Kalman filter recursive formula is reconstructed based on MCC-VC theory, which effectively suppresses the influence of the non-zero center distribution of measurement error and improves the tracking accuracy and robustness of extended targets.

[0073] 4) Establish a pseudo-measurement update mechanism for the shape features of the extended target: Develop a two-step strategy of "initial estimation + Kalman filtering", take the initial estimate of the shape features as the pseudo-measurement value, calculate its estimation error covariance matrix, and then perform update optimization within the Kalman filtering framework. Attached Figure Description

[0074] Figure 1 This is a block diagram illustrating the overall implementation of the method of the present invention;

[0075] Figure 2 This is a graph showing the root mean square error (RMSE) of the estimation of the major and minor semi-axis lengths of the extended target using the method of the present invention under low noise conditions, as a function of the sampling time (sample index).

[0076] Figure 3 This is a graph showing the variation of the root mean square error (RMSE) of the position estimation of the extended target by the method of the present invention under low noise conditions with the sampling time (sample index);

[0077] Figure 4 This is a graph showing the variation of the root mean square error (RMSE) of the method of the present invention for estimating the angle of counterclockwise rotation of the extended target around the x-axis of the two-dimensional coordinate system under low noise conditions with the sampling time (sample index);

[0078] Figure 5 This is a graph showing the variation of the root mean square error (RMSE) of the velocity estimation of the extended target by the method of the present invention under low noise conditions with the sampling time (sample index);

[0079] Figure 6This is a graph showing the variation of the average Gauss-Wasestein distance (GWD) of the method of the present invention for all parameter estimates of the extended target under low noise conditions with the sampling time (sample index);

[0080] Figure 7 This is a graph showing the root mean square error (RMSE) of the estimation of the major and minor semi-axis lengths of the extended target under high noise conditions as a function of the sampling time (sample index).

[0081] Figure 8 This is a graph showing the variation of the root mean square error (RMSE) of the position estimation of the extended target by the method of the present invention under high noise conditions with the sampling time (sample index);

[0082] Figure 9 This is a graph showing the variation of the root mean square error (RMSE) of the method of the present invention for estimating the angle of counterclockwise rotation of the extended target around the x-axis of the two-dimensional coordinate system under high noise conditions with the sampling time (sample index);

[0083] Figure 10 This is a graph showing the root mean square error (RMSE) of the velocity estimation of the extended target by the method of the present invention under high noise conditions as a function of sampling time (sample index);

[0084] Figure 11 This is a graph showing the variation of the average Gauss-Wasestein distance (GWD) of the method of the present invention for all parameter estimates of the extended target under high noise conditions with the sampling time (sample index);

[0085] Figure 12 This is a schematic diagram of the trajectory for tracking extended targets in an autonomous driving multimodal dataset using the method of the present invention, where x direction represents the x-direction and y direction represents the y-direction;

[0086] Figure 13 This is a graph showing the variation of the Gauss-Warsworth-Stokes distance (GWD) of the extended target estimated by the method of this invention with the (sample index) in an autonomous driving multimodal dataset. Detailed Implementation

[0087] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0088] The present invention proposes a robust elliptic extended target tracking method based on the variable center maximum correlation entropy criterion, the overall implementation block diagram of which is shown below. Figure 1 As shown, it includes the following steps:

[0089] Step 1: In the extended target tracking system, for an extended target with an approximately elliptical shape, its tracking model consists of three parts: unknown parameterization, measurement model, and dynamic model. These parts together constitute a complete tracking framework for estimating the motion state and shape characteristics of the extended target, which is deployed in a two-dimensional coordinate system.

[0090] Unknown parameterization: extending the target's motion state r at time k k From position u k and speed v k Composition, expanding the shape features p of the target at time k k The angle α of counterclockwise rotation about the x-axis of the two-dimensional coordinate system k and the length vector of the major and minor semi-axes The composition is given by the initial value of k being 1.

[0091] Measurement Model: At time k, the radar obtains a set of two-dimensional Cartesian coordinates of reflection points on the extended target. These coordinates are used as measurement values, and the j-th measurement value obtained at time k is represented as... and establish The measurement model, where j = 1, ..., J k J k This represents the number of measurements obtained at time k.

[0092] Dynamic Model: Generally speaking, the dynamic model of the extended target's motion state and shape characteristics is not subject to specific restrictions. To simplify the analysis, this invention assumes that the extended target moves at a constant velocity in a straight line within a short observation period. The dynamic model is then described as follows: Among them, A k Let k represent the transition matrix at time k. t represents the sampling interval, λ k and ψ k All are process noise at time k, λ k It follows a Gaussian distribution with zero mean and covariance matrix Λ, ψ k r follows a Gaussian distribution with zero mean and covariance matrix Ψ, when k=1 k-1 Represents the initial motion state of the extended target, p k-1 This represents the initial shape features of the expanded target; when k > 1, r k-1 p represents the motion state of the extended target at time k-1. k-1 This represents the shape characteristics of the extended target at time k-1.

[0093] In this embodiment, in step 1, Where, r k The dimension is 4×1, p k The dimension is 3×1. A vector consisting of the lengths of the major and minor axes of the extended target at time k, with the superscript "T" indicating the transpose of the vector or matrix; The measurement model is described as follows: in, Indicates the extension target and The corresponding measurement source, i.e., the true two-dimensional Cartesian coordinates of the reflection point, is used for modeling. This invention utilizes multiplicative noise vectors Will Related to the shape characteristics of the extended target at time k: u k =Hr k H represents from r k Extract u k The selection matrix is ​​H = [I2, 0], where I2 represents the 2-dimensional identity matrix and 0 represents the zero matrix with dimension 2×2. and The corresponding symbols represent the lengths of the major and minor axes of the extended target at time k. express The corresponding multiplicative noise vector follows a property with zero mean and a covariance matrix of... Gaussian distribution, for The first element, for The second element, and All are used for control The corresponding reflection points are random quantities that are uniformly distributed within the extended target range. In this invention, a widely used spatial distribution model is used to represent the extended target range. express The measurement noise in the data follows a zero-mean pattern and has a noise covariance matrix of C. n Gaussian distribution, for Measurement errors in the measurement model.

[0094] Step 2: Based on the dynamic model, for r k and p k Perform a prediction step to obtain r k One-step prediction value and p k One-step prediction value thereby obtaining Prediction error covariance matrix and Prediction error covariance matrix For the estimation of the motion state of an extended target, there are two types of errors: prediction error and measurement error. To ensure that the estimation of the motion state of the extended target is compatible with the maximum correlation entropy criterion of the variable center (MCC-VC), the prediction error is addressed. and Measurement error in the measurement model Whitening is performed, and the corresponding prediction error ξ after whitening is obtained. k Measurement error after whitening Among them, prediction error The whitening process used The measurement error whitening process in the measurement model used and

[0095] In this embodiment, in step 2, Where k=1 That is, r k-1 When k > 1 Indicates r k-1 The estimated value when k=1 That is, p k-1 When k > 1 p k-1 The estimated value, R represents the desired operation. k-1 express The estimated error covariance matrix, Ξ k-1 express The estimated error covariance matrix. ξ k The acquisition process is as follows: Perform Cholesky decomposition to obtain And thus obtain Where, ξ k The dimension is 4×1. The acquisition process is as follows: due to in In the measurement model, the shape features are not linear, therefore... exist Perform a first-order Taylor expansion at this point: in, Indicates will Substitute into S k V was obtained from 1，k Indicates according to S k The first line S k，(1,：) The calculated Jacobian matrix, Indicates will Substitute into V 1，k V was obtained from 2，k Indicates according to S k The second line Sk，(2，：) The calculated Jacobian matrix, Indicates will Substitute into V 2，k Obtain from; then The covariance matrix is ​​represented as M k , Will The covariance matrix is ​​represented as F k , Among them, F k The element F with index (i, t) (i，t) pass We calculate that i, t∈{1, 2}, and tr{·} represents finding the trace of the matrix; then we obtain... The relevant measurement error covariance matrix Q k , Then Q k Perform Cholesky decomposition to obtain And thus obtain The nth component is in, The dimension is 2×1, Π k，(n,；) Represents Π k The nth line.

[0096] Step 3: Assume that when k > 1, r k-1 The estimated value As an unbiased estimate, based on this assumption, it is easy to know that ξ k It has the property of zero mean, therefore ξ k Setting the estimated value of the core center to zero is reasonable; because A single sample is insufficient to perform ξ analysis. k The kernel bandwidth estimate, therefore ξ k The estimated value of the kernel bandwidth is set as ξ. k Standard deviation, ξ k The standard deviation is 1.

[0097] Step 4: Due to the influence of multiplicative error, Since the mean of the kernel is not zero, its kernel bandwidth and kernel center need to be estimated. Therefore, a joint estimation optimization problem needs to be constructed. Based on the kernel density estimation (KDE) theory, a joint estimation optimization problem is constructed. The nth component kernel bandwidth σ k，(n) and the core center c k，(n)The joint estimation optimization problem is given by n∈{1,2}. The joint estimation of kernel bandwidth and kernel center in the joint estimation optimization problem may lead to local convergence due to the non-convexity of the problem. To solve this problem, this invention decomposes the joint estimation optimization problem into two sub-problems, estimating a parameter for each sub-problem. Specifically, the joint estimation optimization problem is decomposed into kernel bandwidth σ. k，(n) The original problem and kernel center c of the estimation subproblem k，(n) Estimate the original problem of the subproblem; then calculate the kernel bandwidth σ. k，(n) The original problem of estimating the subproblem is transformed into kernel bandwidth σ. k，(n) Estimating the convexity of the subproblems, with the kernel center c k，(n) The original problem of estimating subproblems is transformed into the core-center problem c. k，(n) The estimation of the augmented optimization problem of the subproblem, wherein the augmented optimization problem includes... The weight is the center error weight. express The estimated value; then the core center c k，(n) The augmented optimization problem of the estimation subproblem is decomposed into a subproblem concerning the kernel center and a subproblem concerning the center error weight.

[0098] In this embodiment, the Maximum Correlation Entropy (MCC) criterion has been widely applied to nonlinear non-Gaussian signal processing problems involving impulse noise. Its core idea is to assign appropriate weights to each measurement value, thus reducing the impact of outliers by assigning them smaller weights. Compared to the traditional MCC method (assuming a zero kernel center and calculating the kernel bandwidth using specific rules such as the Silverman criterion), the Variable Center Maximum Correlation Entropy (MCC-VC) criterion, based on kernel density estimation (KDE) theory, achieves joint optimization of kernel bandwidth and kernel center. When the kernel bandwidth and kernel center are accurately estimated, MCC-VC typically exhibits superior performance. Since the actual errors in real-world engineering problems often have non-zero center characteristics, a more precise estimation method is needed to estimate the Gaussian kernel function. Given the kernel center and kernel bandwidth, based on kernel density estimation theory, the following optimization problem can be constructed: in, and These represent the kernel bandwidth and kernel center, respectively. and These represent the optimal estimates of kernel bandwidth and kernel center, respectively. This represents the whitening measurement error of the j-th measurement, where J represents the number of measurements. Indicates the kernel bandwidth is The Gaussian kernel function. Therefore, in step 4, the joint estimation optimization problem is described as: in, Expressing the requirement to make When σ is at its minimum k，(n) and ck，(n) The value of exp(·) represents an exponential function with the natural constant as the base, where the natural constant is 2.71... express The estimated value, after obtaining r k The estimated value Under the premise Π k，(n，：) Represents Π k The nth line, Q k express The relevant measurement error covariance matrix, H represents the variance from r k Extract u k The selection matrix.

[0099] In this embodiment, in step 4, the kernel bandwidth σ k，(n) The process of obtaining the convex problem of estimating subproblems is as follows: fix the kernel center c. k，(n) The value, use this value as And let The joint estimation optimization problem is transformed into a kernel bandwidth σ problem. k，(n) The original problem for estimating subproblems is described as follows: Where min is the minimum function, the original problem is non-convex; then, the kernel bandwidth σ k，(n) The original problem of estimating the subproblem is subjected to a Taylor expansion, and its third-order terms are preserved to ensure the accuracy of the approximation, resulting in the Taylor expansion, which is used as the kernel bandwidth σ. k，(n) The convex problem of estimating subproblems is described as follows: in, The Taylor expansion has been proven to be strictly convex in (0 to +∞), thus yielding the global optimal solution, σ. k，(n) By adjusting μ k，(n) The estimate is obtained by taking the reciprocal. μ k，(n) cubed.

[0100] In this embodiment, in step 4, the core center c k，(n) The process of obtaining the augmented optimization problem for estimating subproblems is as follows: fix the kernel bandwidth σ k，(n) The value, use this value as The joint estimation optimization problem is transformed into a kernel-centric c problem. k，(n) The original problem for estimating subproblems is described as follows: The original problem is nonconvex; then, based on the properties of convex conjugate functions, the kernel center c is... k，(n) The original problem of estimating subproblems is transformed into the core-center problem c. k，(n) The augmented optimization problem for estimating subproblems is described as follows: Where max is the function for finding the maximum value. express The weights are the center error weights, and φ(·) represents the exponential function e -y convex conjugate function.

[0101] As can be seen from the augmented optimization problem, by utilizing the properties of convex conjugate functions, the problem can be transformed from one unknown quantity c into a single unknown quantity c. k，(n) The original problem is transformed into a problem concerning an unknown quantity c. k，(n) and J k The augmented optimization problem of unknown center error weights, although increasing the number of unknowns, is easier to handle and can be solved by iteratively solving two subproblems. Therefore, the kernel center c is further... k，(n) The augmented optimization problem of the estimation subproblem is decomposed into a subproblem concerning the kernel center and a subproblem concerning the center error weight.

[0102] In this embodiment, step 4, the process of obtaining the sub-problem concerning the kernel center, is as follows: [Fixed] The value, denoted as The augmented optimization problem is transformed into a subproblem concerning the kernel center, described as follows: The sub-question is about the nuclear center c. k，(n) The linear least squares problem can be easily solved by setting the derivative to zero.

[0103] In this embodiment, the process of obtaining the sub-problem of the center error weight in step 4 is as follows: fix the kernel center c k，(n) The value, denoted as The augmentation optimization problem is transformed into a subproblem concerning the center error weights, described as follows: Based on the properties of convex conjugate functions, for a fixed... when At that time, the subproblem reaches its maximum value. express The weight.

[0104] Step 5: Propose a criterion for r based on the maximum correlation entropy criterion with varying center (MCC-VC). k The cost function, and the known σ k，(n) and c k，(n) Substitute about r k The cost function is obtained by knowing σ. k，(n) and c k，(n) The optimization problem based on the maximum correlation entropy criterion with varying center is then categorized. This problem is then equivalently transformed into an augmented optimization problem, which includes prediction error weights and measurement error weights. Finally, the augmented optimization problem is decomposed into a function relating r. kSub-problems concerning prediction error weights and measurement error weights.

[0105] In this embodiment, the specific process of step 5 is as follows:

[0106] Step 5.1: Fix the core bandwidth σ k，(n) The value, use this value as And fix the core center c k，(n) The value, use this value as Then, based on the maximum correlation entropy criterion of variable center (MCC-VC), a proposal is made regarding r. k The cost function is described as follows: in, Indicates about r k The cost function, The kernel function in the equation is a Gaussian kernel function, L = 4 + 2J. k ||·|| denotes the 2-norm, and G1 denotes a kernel function with a kernel bandwidth of 1. Indicates the kernel bandwidth is The kernel function, b k，(i) Indicates the relationship with r k The relevant zero center error vector b k The i-th element in

[0107] Step 5.2: Let Regarding r k The cost function is transformed into a known σ k，(n) and c k，(n) The cost function is described as follows: in, Indicates that σ is known k，(n) and c k，(n) The cost function, Indicates the kernel bandwidth is Gaussian kernel function, ξ k，(m) Indicates ξ k The m-th element, Γ k，(m，：) Indicates Γ k The m-th line.

[0108] Step 5.3: [The sentence is incomplete and requires more context to be translated accurately.] and Substitution In the middle, construct a known σ k，(n) and c k，(n) The optimization problem based on the maximum correlation entropy criterion with varying centers is described as follows:

[0109]

[0110] Step 5.4: Due to the non-convexity of the optimization problem, direct solution is quite challenging. Observation reveals that the objective function of the optimization problem contains an exponential function term. Therefore, we can refer to the kernel center c. k，(n) Estimation of subproblem handling methods. The optimization problem is equivalently transformed into an augmented optimization problem, described as: Among them, κ m For prediction error weights, For the measurement error weights, φ(·) represents the exponential function e -y convex conjugate function,

[0111] Step 5.5: As can be seen from the augmented optimization problem, by utilizing the properties of the convex conjugate function, the problem can be transformed from one unknown vector r to a single unknown vector r. k The optimization problem is transformed into an optimization problem involving an unknown vector r. k and 4+2J k This is an augmented optimization problem with unknown error weights (including prediction error weights and measurement error weights). Note that although the number of unknowns increases, this augmented optimization problem is easier to handle and can be solved by iteratively solving two subproblems.

[0112] Fixed κ m and The values ​​are denoted as and these two values ​​are recorded accordingly. and The augmentation optimization problem is transformed into a problem concerning r. k The subproblems are described as follows: because and With r k It is irrelevant, therefore we can consider r k The subproblem is equivalently transformed into a problem concerning r. k The linear least squares problem is described as follows: The solution can be easily obtained by setting the derivative to zero.

[0113] Fixed r k The value, denoted as The augmentation optimization problem is transformed into a subproblem concerning the prediction error weights and the measurement error weights, described as follows: in, According to the properties of convex conjugate functions, when At that point, the subproblem reaches its maximum value.

[0114] Step 6: Obtain the results using an alternating iterative strategy. The nth component kernel bandwidth σ k，(n) The estimated value and the core center c k，(n)The estimated value and r k The estimated value Specifically, in each outer iteration, for σ... k，(n) Directly solve for the kernel bandwidth σ k，(n) Estimate the convexity of the subproblems to obtain σ at each outer iteration. k，(n) The optimal solution for c; k，(n) During the inner iteration process, the subproblem concerning the kernel center and the subproblem concerning the center error weight are solved alternately. When the first inner iteration condition is satisfied, the value of c in each outer iteration is obtained. k，(n) The optimal solution for r; k During the inner iteration process, solutions for r are solved alternately. k The subproblems concerning prediction error weights and measurement error weights, when satisfying the second inner-layer iteration condition, yield r for each outer-layer iteration. k The optimal solution, and r k The estimation error covariance matrix of the optimal solution; σ is obtained when the outer iteration conditions are satisfied. k，(n) The estimated value and c k，(n) The estimated value and r k The estimated value And thus obtain The estimation error covariance matrix R k Then, through the state transition equation, and R k Convert to r respectively k+1 One-step prediction value and its prediction error covariance matrix

[0115] In this embodiment, step 6 is as follows:

[0116] Step 6.1: Let s represent the number of outer iterations, and the initial value of s is 1.

[0117] Step 6.2: During the s-th outer iteration, and Substitute kernel bandwidth σ k，(n) Convex problems for estimating subproblems In the solution, μ is obtained at the s-th outer iteration. k，(n) The optimal solution, that is, the solution obtained when σ is obtained in the s-th outer iteration. k，(n) optimal solution Where s = 1 For c k，(n) initial value For r k initial value Set to 0, To pass through c k，(n) Set to 0, σ k，(n) Let it be 1, κ m and Set all to -1 and substitute them into Solving for s, we find that when s>1 c represents the value of c in the (s-1)th outer iteration. k，(n) The optimal solution In the (s-1)th outer iteration, r k The optimal solution.

[0118] Step 6.3: During the s-th outer iteration, for c k，(n) Perform inner layer iterations as follows:

[0119] Step 6.3.1: Let q represent the number of inner iterations, and the initial value of q is 1.

[0120] Step 6.3.2: During the q-th inner iteration within the s-th outer iteration, ... and Substitute the subproblem concerning the nuclear center In the solution, we obtain c when the inner iteration is q within the outer iteration of the s-th iteration. k，(n) optimal solution Where q = 1 When the inner iteration begins during the s-th outer iteration... initial value Set to -1, when q>1 This indicates the time of the (q-1)th inner iteration within the s-th outer iteration. The optimal solution. To pass Substitution It was obtained from the middle.

[0121] During the q-th inner iteration within the s-th outer iteration, and Substitute into the subproblem concerning the weight of the center error. In the solution, the q-th inner iteration within the s-th outer iteration is obtained. optimal solution

[0122] Step 6.3.3: Determine the first inner layer iteration condition Is it true? If it is true, then... When c is the outermost iteration of the s-th time k，(n) optimal solution Then execute step 6.4. If it fails, set q = q + 1, and then return to step 6.3.2 to continue execution. Here, when q = 1... When c starts during the s-th outer iteration... k，(n) initial value equal hour c represents the value of c in the (q-1)th inner iteration within the s-th outer iteration. k，(n) The optimal solution.

[0123] Step 6.4: During the s-th outer iteration, for r k Perform inner layer iterations as follows:

[0124] Step 6.4.1: Let q represent the number of inner iterations, and the initial value of q is 1.

[0125] Step 6.4.2: During the q-th inner iteration within the s-th outer iteration, ... and Substitute about r k Linear least squares problem In the solution, we obtain the value of r during the q-th inner iteration within the s-th outer iteration. k optimal solution Where q = 1 κ is the value at the start of the inner iteration during the s-th outer iteration. m initial value When the inner iteration begins during the s-th outer iteration... initial value and All are set to -1, when q>1 κ represents the value of κ in the (q-1)th inner iteration within the s-th outer iteration. m The optimal solution This indicates the time of the (q-1)th inner iteration within the s-th outer iteration. The optimal solution. Indicates Kalman gain, Then calculate The estimation error covariance matrix Where I represents the identity matrix.

[0126] During the q-th inner iteration within the s-th outer iteration, Substitute the subproblems concerning prediction error weights and measurement error weights. In the solution, we obtain κ when the inner iteration is q within the outer iteration of the s-th iteration. m optimal solution and optimal solution in,

[0127] Step 6.4.3: Determine the second inner layer iteration condition Is it true? If it is true, then... When r is the s-th outer iteration k optimal solution Will As The estimation error covariance matrix Then execute step 6.5. If it fails, set q = q + 1, and then return to step 6.4.2 to continue execution. Here, when q = 1... When r starts during the s-th outer iteration... k initial value equal hour This indicates that when r is in the (q-1)th inner iteration within the s-th outer iteration... k The optimal solution.

[0128] Step 6.5: Determine if the outer iteration condition is true. If it is true, then... Corresponding as σ k，(n) The estimated value c k，(n) The estimated value r k The estimated value Then As The estimation error covariance matrix R k Then, through the state transition equation, and R k Convert to r respectively k+1 One-step prediction value and its prediction error covariance matrix If the condition is not met, then let s = s + 1, and return to step 6.2 to continue execution. The outer iteration condition is whether s is less than or equal to a preset number of iterations, such as 2.

[0129] Step 7: For shape feature estimation, given a dataset in a two-dimensional plane, the covariance matrix is ​​naturally considered to characterize the data dispersion and thus estimate the shape features. In statistics and data analysis, the covariance matrix is ​​a fundamental tool for describing data distribution and variability. The eigenvalues ​​and eigenvectors of the covariance matrix can reveal the geometric characteristics of data points, specifically: by quantifying the variability of data in different directions, the main direction of the data and its corresponding shape features can be determined. In this invention, measured values ​​are used. The shape features are estimated and then updated based on Kalman filtering theory. As mentioned earlier, estimating the shape features requires calculating the covariance matrix of the data points.

[0130] Based on the expanded target and Corresponding measurement source The corresponding random vector z k covariance matrix approximation Obtain α k rough estimate Extend the length of the semi-major axis of the target at time k rough estimate Extend the length of the minor semi-axis of the target at time k rough estimate Then obtain p k rough estimate Then calculate The estimation error covariance matrix Then, within the framework of Kalman filtering, update and obtain p. k The estimated value The Kalman gain corresponding to the Kalman filter equation includes...

[0131] In this embodiment, the specific process of step 7 is as follows:

[0132] Step 7.1: Let z k Represents a set of data points The corresponding random vector, let y k Represents a set of data points The corresponding random vector, let Indicate z k Let the covariance matrix be... Indicates y k The covariance matrix, and The relationship is as follows: Where, n k Represents a set The corresponding random vector; in practice It can be approximated by the sample covariance, and then calculated. approximation in, Represents a set of data points The mean, And calculate approximation in, It is positive definite, note. It must be positive definite, but this requirement may not be met when the measurement is particularly sparse. In this case, it can be directly used. To approximate

[0133] Step 7.2: According to Obtain α k rough estimate rough estimate rough estimate in, express The element in the first row and first column, express The element in the 1st row and 2nd column, express The element in the second row and second column; thus, obtain p. k rough estimate

[0134] Step 7.3: You can Consider it as p k A single measurement, or pseudo-measurement, has a covariance matrix. The approximate result can be obtained through calculation as follows: Calculation The estimation error covariance matrix Specifically as follows:

[0135] Step 7.3.1: Definition The estimation error vector Δp k ,

[0136] Step 7.3.2: Let

[0137] Step 7.3.3: Definition in, Corresponding representation The element in the first row and first column, the element in the first row and second column, and the element in the second row and second column. Corresponding representation The element in the first row and first column, the element in the first row and second column, and the element in the second row and second column. S k,(1,：) S represents k The first row vector, S k，(2， : ) S represents kThe second row vector, express The first element, express The second element, C n,(1,1) Indicate C n The element in the first row and first column, C n，(1，2) Indicate C n The element in the 1st row and 2nd column, C n，(2，2) Indicate C n The element in the second row and second column.

[0138] Step 7.3.4: Calculate the covariance matrix C of Δσ σ C σ C is a symmetric matrix. σ The element in the first row and first column is C σ The element in the first row and second column is C σ The element in the second row and second column is C σ The element in the 1st row and 3rd column is C σ The element in the 2nd row and 3rd column is C σ The element in the 3rd row and 3rd column is

[0139] Step 7.3.5: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] Substitution In the middle, and on Performing a first-order Taylor expansion at σ yields: Δp k =DΔσ, where the first row of D The second line of D D's third line

[0140] Step 7.3.6: Calculation

[0141] Step 7.4: Update and obtain p within the framework of Kalman filtering k The estimated value Among them, K p This represents the Kalman gain corresponding to the Kalman filter equation. Then calculate The estimation error covariance matrix Ξ k ,

[0142] Step 8: Following the process of Step 6 and Step 7, obtain the estimated values ​​of the motion state and shape features of the extended target at different times to achieve extended target tracking, where the different times are multiple consecutive times.

[0143] To verify the feasibility and effectiveness of the method of the present invention, simulation experiments were conducted on the method of the present invention under low noise and high noise conditions, and the method of the present invention was tested in practice using the existing autonomous driving multimodal dataset (nuScenes dataset).

[0144] Simulation experiment:

[0145] The actual trajectory of the extended target is set in the same way as the MEM-EKF method proposed in existing literature, with the major and minor axes of the ellipse being 170 meters and 40 meters, respectively. During the motion, the lengths of the major and minor axes of the extended target remain constant, but the angle of counterclockwise rotation around the x-axis of the two-dimensional coordinate system changes dynamically with time. The extended target moves at a constant speed of 50 km / h along the -π / 4 direction from the origin of the coordinate system at the initial moment. Measurement data are generated by sampling at 10-second intervals, for a total of 103 samplings. The measurement points at each moment are uniformly distributed within the elliptical region, and the number of measurement points at a single moment follows a Poisson distribution with a mean of 30. The actual initial motion state is r0 = [0m, 0m, 50 / 3.6×coS(-π / 4)m / s, 50 / 3.6×sin(-π / 4)m / s]. t The actual initial shape characteristics are p0 = [-π / 4 rad, 170 m, 40 m]. T The covariance matrix of r0 is R0 = diag{900m} 2 900m 2 16 (m / s) 2 16 (m / s) 2}, the covariance matrix of p0 is Ξ0=diag{0.2rad 2 400m 2 400m 2}, where diag{} denotes constructing a diagonal matrix. The estimated initial motion state. According to Gaussian distribution Randomly generated, estimated initial shape features According to Gaussian distribution Randomly generated. Multiplicative noise vector. Assume that the following expression follows a mean of zero and a covariance matrix of... The Gaussian distribution of λ. Furthermore, the process noise λ k The covariance matrix Λ is set as Λ=diag{100m 2 100m 2 , 1 (m / s) 2, 1 (m / s) 2}, process noise ψ k The covariance matrix Ψ is set as Ψ = diag{0.01rad}. 2 0.001m 2 0.001m 2 The noise covariance matrix of small noise is set as C. n =diag{200m 2 80m 2 Let the noise covariance matrix of large noise be C. n =diag{1000m 2 200m 2}

[0146] Based on the above parameter settings, simulation experiments were conducted to test the tracking performance of the extended target under different measurement noise powers. The tracking performance was evaluated using the root mean square error (RMSE) of the extended target's velocity, position, semi-major and minor axis lengths, and counterclockwise rotation angle around the x-axis of the two-dimensional coordinate system, as well as the average Gauss-Wasestein distance (GWD), obtained from 1000 Monte Carlo experiments. GWD is defined as: Where, Φ k Represents a symmetric positive definite shape matrix. Indicate u k The estimated value, Φ k The estimated value.

[0147] Figure 2 The graph shows the root mean square error (RMSE) of the estimation of the major and minor semi-axis lengths of the extended target using the method of the present invention under low noise conditions, as a function of the sampling time (sample index). Figure 3 The graph shows the variation of the root mean square error (RMSE) of the position estimation of the extended target using the method of the present invention with the sampling time (sample index) under low noise conditions. Figure 4 The graph shows the root mean square error (RMSE) of the method of the present invention for estimating the angle of counterclockwise rotation of the extended target around the x-axis of the two-dimensional coordinate system under low noise conditions, as a function of sampling time (sample index). Figure 5 The graph shows the root mean square error (RMSE) of the velocity estimation of the extended target using the method of this invention under low noise conditions, as a function of the sampling time (sample index). From... Figures 2 to 5As can be seen from the data, when the sampling time changes, the method of the present invention can accurately estimate the position, velocity, major and minor axis lengths, and counterclockwise rotation angle of the extended target under the condition of low measurement noise power. Except for the estimation of the major and minor axis, the tracking performance of other parameters will be slightly worse when the extended target turns.

[0148] Figure 6 The graph shows the variation of the average Gauss-Wasestein distance (GWD) for all parameter estimates of the extended target using the method of this invention under low noise conditions, as a function of the sampling index. Figure 6 As can be seen, when the noise power is low, the average Gauss-Wasestein distance (GWD) estimated for all parameters of the extended target by the method of the present invention will reach the best tracking accuracy in a short time, and the tracking performance will deteriorate slightly when the extended target turns.

[0149] Figure 7 The graph shows the root mean square error (RMSE) of the estimation of the major and minor semi-axis lengths of the extended target using the method of the present invention under high noise conditions, as a function of the sampling time (sample index). Figure 8 The graph shows the variation of the root mean square error (RMSE) of the method of the present invention for the position estimation of the extended target under high noise conditions with the sampling time (sample index). Figure 9 The graph shows the root mean square error (RMSE) of the method of the present invention for estimating the angle of counterclockwise rotation of the extended target around the x-axis of the two-dimensional coordinate system under high noise conditions, as a function of sampling time (sample index). Figure 10 The graph shows the root mean square error (RMSE) of the velocity estimation of the extended target using the method of this invention under high noise conditions, as a function of the sampling time (sample index). From... Figures 7 to 10 As can be seen from the data, when the sampling time changes, the method of the present invention can accurately estimate the position, velocity, major and minor axis lengths, and counterclockwise rotation angle of the extended target when the measurement noise power is large. Except for the estimation of the major and minor axis, the tracking performance of other parameters will be slightly worse when the extended target turns.

[0150] Figure 11 The graph shows the variation of the average Gauss-Wasestein distance (GWD) for all parameter estimates of the extended target under high noise conditions using the method of this invention, as a function of the sampling index. Figure 11As can be seen, when the noise power is low, the average Gauss-Wasestein distance (GWD) estimated for all parameters of the extended target by the method of the present invention will reach the best tracking accuracy in a short time, and the tracking performance will deteriorate slightly when the extended target turns.

[0151] Experimental test:

[0152] In the experiment using the autonomous driving multimodal dataset, this invention selected scene-0757 from the "mini" subset of the nuScenes dataset. This scene contains the reflection points generated when a bus measuring 13.818m × 3.132m turns right at an intersection, as shown by radar illumination of the vehicle. Radar measurement data for 11 time points was extracted from this scene from the "mini" subset, collected every 0.5 seconds by the forward-facing radar. The measurement noise covariance matrix was set as C. n =diag{0.5 2 m 2 0.5 2 m 2 The actual initial motion state is r0 = [300m] 2 600m 2 The actual initial shape characteristics are p0 = [-π / 3rad], -0.5m / s, 1m / s]. 2 7m 2 1m 2 The covariance matrix of r0 is R0 = diag{100m}. 2 100m 2 , 1 (m / s) 2 , 1 (m / s) 2}, the covariance matrix of p0 is Ξ0=diag{0.1rad 2 1m 2 1m 2}, estimated value of the initial motion state According to Gaussian distribution Randomly generated, estimated initial shape features According to Gaussian distribution Randomly generated. Based on the above parameter settings, the tracking performance of the method of the present invention was evaluated by experimentally testing the velocity, position, semi-major and semi-minor axis lengths, and the average Gauss-Warsworth-Stokes distance (GWD) of the extended target obtained through 1000 Monte Carlo experiments.

[0153] Figure 12 A trajectory diagram illustrating the tracking of extended targets using the method of this invention in an autonomous driving multimodal dataset is provided, where x direction represents the x-direction and y direction represents the y-direction. Figure 13 The Gauss-Wasestein distance (GWD) for all parameter estimates of the extended target using the method of this invention is shown as a function of (sampleindex) in an autonomous driving multimodal dataset. Figure 12 As can be seen, the method of the present invention achieves high consistency between the tracked trajectory and the actual position of the extended target. From... Figure 13 As can be seen, as the sampling time changes, the number of data points obtained by the extended target sampling decreases, so the Gauss-Wasestein distance (GWD) increases with the change of sampling time, but its estimation is still reliable.

Claims

1. A robust elliptic extended target tracking method based on the variable center maximum correlation entropy criterion, characterized in that... Includes the following steps: Step 1: In the extended target tracking system, for an extended target with an approximately elliptical shape, its tracking model consists of three parts: unknown parameterization, measurement model, and dynamic model, wherein the extended target is deployed in a two-dimensional coordinate system; Unknown parameterization: extending the target's motion state r at time k k From position u k and speed v k Composition, expanding the shape features p of the target at time k k The angle α of counterclockwise rotation about the x-axis of the two-dimensional coordinate system k and the length vector of the major and minor semi-axes l k Composition, where the initial value of k is 1; Measurement Model: At time k, the radar obtains a set of two-dimensional Cartesian coordinates of reflection points on the extended target. These coordinates are used as measurement values, and the j-th measurement value obtained at time k is represented as... and establish The measurement model, where j = 1, ..., J k J k This represents the number of measurements obtained at time k; Dynamic model: Assuming the extended target moves at a constant velocity in a straight line within a short observation period, the dynamic model is described as follows: Among them, A k Let k represent the transition matrix at time k. t represents the sampling interval, λ k and ψ k All are process noise at time k, λ k It follows a Gaussian distribution with zero mean and covariance matrix Λ, ψ k r follows a Gaussian distribution with zero mean and covariance matrix Ψ, when k=1 k-1 Represents the initial motion state of the extended target, p k-1 This represents the initial shape features of the expanded target; when k > 1, r k-1 p represents the motion state of the extended target at time k-1. k-1 This represents the shape characteristics of the extended target at time k-1; Step 2: Based on the dynamic model, for r k and p k Perform a prediction step to obtain r k One-step prediction value and p k One-step prediction value thereby obtaining Prediction error covariance matrix and Prediction error covariance matrix Then, the prediction error was analyzed. and The measurement error in the measurement model is whitened, and the corresponding whitened prediction error ξ is obtained. k Measurement error after whitening Among them, prediction error The whitening process used The measurement error whitening process in the measurement model used and Step 3: Assume that when k > 1, r k-1 The estimated value As an unbiased estimate, based on this assumption, ξ k The estimated value of the core center is set to zero; ξ is set to zero. k The estimated value of the kernel bandwidth is set as ξ. k Standard deviation; Step 4: Based on kernel density estimation theory, construct... The nth component kernel bandwidth σ k，(n) and the core center c k，(n) The joint estimation optimization problem is given by the expression $\mathbf{a}$, where $n \in {1, 2}$. The joint estimation optimization problem is decomposed into a kernel bandwidth $σ$. k，(n) The original problem and kernel center c of the estimation subproblem k，(n) Estimate the original problem of the subproblem; then calculate the kernel bandwidth σ. k，(n) The original problem of estimating the subproblem is transformed into kernel bandwidth σ. k，(n) Estimating the convexity of the subproblems, with the kernel center c k，(n) The original problem of estimating subproblems is transformed into the core-center problem c. k，(n) The estimation of the augmented optimization problem of the subproblem, wherein the augmented optimization problem includes... The weight is the center error weight. express The estimated value; then the core center c k，(n) The augmented optimization problem of estimating the subproblem is decomposed into a subproblem concerning the kernel center and a subproblem concerning the center error weights; Step 5: Propose a criterion for r based on the maximum correlation entropy criterion of the variable center. k The cost function, and the known σ k，(n) and c k，(n) Substitute about r k The cost function is obtained by knowing σ. k，(n) and c k，(n) The optimization problem based on the maximum correlation entropy criterion with varying center is then categorized. This problem is then equivalently transformed into an augmented optimization problem, which includes prediction error weights and measurement error weights. Finally, the augmented optimization problem is decomposed into a function relating r. k Sub-problems concerning prediction error weights and measurement error weights; Step 6: Obtain the results using an alternating iterative strategy. The nth component kernel bandwidth σ k，(n) The estimated value and the core center c k，(n) The estimated value and r k The estimated value Specifically, in each outer iteration, for σ... k，(n) Directly solve for the kernel bandwidth σ k，(n) Estimate the convexity of the subproblems to obtain σ at each outer iteration. k，(n) The optimal solution for c; k，(n) During the inner iteration process, the subproblem concerning the kernel center and the subproblem concerning the center error weight are solved alternately. When the first inner iteration condition is satisfied, the value of c in each outer iteration is obtained. k，(n) The optimal solution for r; k During the inner iteration process, solutions for r are solved alternately. k The subproblems concerning prediction error weights and measurement error weights, when satisfying the second inner-layer iteration condition, yield r for each outer-layer iteration. k The optimal solution, and r k The estimation error covariance matrix of the optimal solution; σ is obtained when the outer iteration conditions are satisfied. k，(n) The estimated value and c k，(n) The estimated value and r k The estimated value And thus obtain The estimation error covariance matrix R k Then, through the state transition equation, and R k Convert to r respectively k+1 One-step prediction value and its prediction error covariance matrix Step 7: Based on the expanded target and Corresponding measurement source The corresponding random vector z k covariance matrix approximation Obtain α k rough estimate The length l of the major semi-axis of the extended target at time k k,(1) rough estimate The length l of the minor semi-axis of the extended target at time k k，(2) rough estimate Then obtain p k rough estimate Then calculate The estimation error covariance matrix Then, within the framework of Kalman filtering, update and obtain p. k The estimated value The Kalman gain corresponding to the Kalman filter equation includes... Step 8: Following the process of Step 6 and Step 7, obtain the estimated values ​​of the motion state and shape features of the extended target at different times to achieve extended target tracking, where the different times are multiple consecutive times.

2. The robust elliptic extended target tracking method based on the variable center maximum correlation entropy criterion according to claim 1, characterized in that... In step 1, Where, r k The dimension is 4×1, p k The dimension is 3×1, l k A vector consisting of the lengths of the major and minor axes of the extended target at time k, with the superscript "T" indicating the transpose of the vector or matrix; The measurement model is described as follows: in, Indicates the extension target and The corresponding measurement source, u k =Hr k H represents from r k Extract u k The selection matrix, H = [I2, 0], where I2 represents the 2x2 identity matrix, 0 represents the zero matrix of dimension 2×2, and l k，(1) and l k，(2) The corresponding symbols represent the lengths of the major and minor axes of the extended target at time k. express The corresponding multiplicative noise vector follows a property with zero mean and a covariance matrix of... Gaussian distribution, for The first element, for The second element, and All are used for control The corresponding reflection points are random quantities that are uniformly distributed within the extended target range. express The measurement noise in the data follows a zero-mean pattern and has a noise covariance matrix of C. n Gaussian distribution, for Measurement errors in the measurement model.

3. The robust elliptic extended target tracking method based on the variable center maximum correlation entropy criterion according to claim 2, characterized in that... In step 2, Where k=1 That is, r k-1 When k > 1 Indicates r k-1 The estimated value when k=1 That is, p k-1 When k > 1 p k-1 The estimated value, R represents the desired operation. k-1 express The estimated error covariance matrix, Ξ k-1 express The estimation error covariance matrix; ξ k The acquisition process is as follows: Perform Cholesky decomposition to obtain And thus obtain Where, ξ k The dimension is 4×1; The acquisition process is as follows: exist Perform a first-order Taylor expansion at this point: in, Indicates will Substitute into S k V was obtained from l，k Indicates according to S k The first line S k，(1，：) The calculated Jacobian matrix, Indicates will Substitute into V 1，k V was obtained from 2，k Indicates according to S k The second line S k，(2，：) The calculated Jacobian matrix, Indicates will Substitute into V 2，k Obtain from; then The covariance matrix is ​​represented as M k , Will The covariance matrix is ​​represented as F k , Among them, F k The element F with index (i, t) (i，t) pass We calculate that i, t∈{1, 2}, and tr{·} represents finding the trace of the matrix; then we obtain... The relevant measurement error covariance matrix Q k , Then Q k Perform Cholesky decomposition to obtain And thus obtain The nth component is in, The dimension is 2×1, Π k，(n,；) Represents Π k The nth line.

4. The robust elliptic extended target tracking method based on the variable center maximum correlation entropy criterion according to claim 3, characterized in that... In step 4, the joint estimation optimization problem is described as follows: in, express The estimated value, after obtaining r k The estimated value Under the premise Π k，(n，：) Represents Π k The nth line, Q k express The relevant measurement error covariance matrix, H represents the variance from r k Extract u k The selection matrix; In step 4, the kernel bandwidth σ k，(n) The process of obtaining the convex problem of estimating subproblems is as follows: fix the kernel center c. k，(n) The value, use this value as And let The joint estimation optimization problem is transformed into a kernel bandwidth σ problem. k，(n) The original problem for estimating subproblems is described as follows: Then, regarding the kernel bandwidth σ k，(n) The original problem of estimating the subproblem is subjected to a Taylor expansion, and its third-order terms are preserved to ensure the accuracy of the approximation, resulting in the Taylor expansion, which is used as the kernel bandwidth σ. k，(n) The convex problem of estimating subproblems is described as follows: in, In step 4, the core center c k，(n) The process of obtaining the augmented optimization problem for estimating subproblems is as follows: fix the kernel bandwidth σ k，(n) The value, use this value as The joint estimation optimization problem is transformed into a kernel-centric c problem. k，(n) The original problem for estimating subproblems is described as follows: Then, based on the properties of convex conjugate functions, the kernel center c is... k，(n) The original problem of estimating subproblems is transformed into the core-center problem c. k，(n) The augmented optimization problem for estimating subproblems is described as follows: in, express The weights are the center error weights, and φ(·) represents the convex conjugate function of the exponential function; In step 4, the process of obtaining the sub-problem concerning the kernel center is as follows: [Fixed] The value, denoted as The augmented optimization problem is transformed into a subproblem concerning the kernel center, described as follows: In step 4, the process of obtaining the sub-problem regarding the center error weight is as follows: fix the kernel center c. k，(n) The value, denoted as The augmentation optimization problem is transformed into a subproblem concerning the center error weights, described as follows:

5. The robust elliptic extended target tracking method based on the variable center maximum correlation entropy criterion according to claim 4, characterized in that... The specific process of step 5 is as follows: Step 5.1: Fix the core bandwidth σ k，(n) The value, use this value as And fix the core center c k，(n) The value, use this value as Then, based on the maximum correlation entropy criterion of the variable center, a proposal is made regarding r. k The cost function is described as follows: in, Indicates about r k The cost function, The kernel function in the equation is a Gaussian kernel function, L = 4 + 2J. k ||·|| denotes the 2-norm, and G1 denotes a kernel function with a kernel bandwidth of 1. Indicates the kernel bandwidth is The kernel function, b k，(i) Indicates the relationship with r k The relevant zero center error vector b k The i-th element in Step 5.2: Let Regarding r k The cost function is transformed into a known σ k，(n) and c k，(n) The cost function is described as follows: in, Indicates that σ is known k，(n) and c k，(n) The cost function, Indicates the kernel bandwidth is Gaussian kernel function, ξ k，(m) Indicates ξ k The m-th element, Γ k，(m，：) Indicates Γ k The m-th line; Step 5.3: [The sentence is incomplete and requires more context to be translated accurately.] and Substitution In the middle, construct a known σ k，(n) and c k，(n) The optimization problem based on the maximum correlation entropy criterion with varying centers is described as follows: Step 5.4: Transform the optimization problem into an augmenting optimization problem, described as follows: Among them, κ m For prediction error weights, To measure the error weights, φ(·) denotes the convex conjugate function of the exponential function. Step 5.5: Fix κ m and The values ​​are denoted as and these two values ​​are recorded accordingly. and The augmentation optimization problem is transformed into a problem concerning r. k The subproblems are described as follows: Regarding r k The subproblem is equivalently transformed into a problem concerning r. k The linear least squares problem is described as follows: Fixed r k The value, denoted as The augmentation optimization problem is transformed into a subproblem concerning the prediction error weights and the measurement error weights, described as follows: in, 6. The robust elliptic extended target tracking method based on the variable center maximum correlation entropy criterion according to claim 5, characterized in that... The process of step 6 is as follows: Step 6.1: Let s represent the number of outer iterations, and initialize s to 1; Step 6.2: During the s-th outer iteration, and Substitute kernel bandwidth σ k，(n) In the convex problem of estimating subproblems, the solution yields μ at the s-th outer iteration. k，(n) The optimal solution, that is, the solution obtained when σ is obtained in the s-th outer iteration. k，(n) optimal solution Where s = 1 For c k，(n) initial value For r k initial value Set to 0, To pass through c k，(n) Set to 0, σ k，(n) Let it be 1, κ m and Set all to -1 and substitute them into Solving for s, we find that when s>1 c represents the value of c in the (s-1)th outer iteration. k，(n) The optimal solution In the (s-1)th outer iteration, r k The optimal solution; Step 6.3: During the s-th outer iteration, for c k，(n) Perform inner layer iterations as follows: Step 6.3.1: Let q represent the number of inner iterations, and initialize q to 1; Step 6.3.2: During the q-th inner iteration within the s-th outer iteration, ... and Substituting into the subproblem concerning the kernel center, we can obtain the value of c in the q-th inner iteration within the s-th outer iteration. k，(n) optimal solution Where q = 1 When the inner iteration begins during the s-th outer iteration... initial value Set to -1, when q>1 This indicates the time of the (q-1)th inner iteration within the s-th outer iteration. The optimal solution. To pass Substitution Obtained from; During the q-th inner iteration within the s-th outer iteration, and Substituting into the subproblem concerning the center error weights, we can obtain the result of the inner iteration q within the outer iteration s-th iteration. optimal solution Step 6.3.3: Determine the first inner layer iteration condition Is it true? If it is true, then... When c is the outermost iteration of the s-th time k，(n) optimal solution Then execute step 6.

4. If it fails, set q = q + 1, and then return to step 6.3.2 to continue execution. Here, when q = 1... When c starts during the s-th outer iteration... k，(n) initial value equal When q > 1 c represents the value of c in the (q-1)th inner iteration within the s-th outer iteration. k，(n) The optimal solution; Step 6.4: During the s-th outer iteration, for r k Perform inner layer iterations as follows: Step 6.4.1: Let q represent the number of inner iterations, and initialize q to 1; Step 6.4.2: During the q-th inner iteration within the s-th outer iteration, ... and Substitute about r k In the linear least squares problem, the solution yields the value of r during the q-th inner iteration within the s-th outer iteration. k optimal solution Where q = 1 κ is the value at the start of the inner iteration during the s-th outer iteration. m initial value When the inner iteration begins during the s-th outer iteration... initial value and All are set to -1, when q>1 κ represents the value of κ in the (q-1)th inner iteration within the s-th outer iteration. m The optimal solution This indicates the time of the (q-1)th inner iteration within the s-th outer iteration. The optimal solution. Indicates Kalman gain, Then calculate The estimation error covariance matrix Where I represents the identity matrix; During the q-th inner iteration within the s-th outer iteration, Substituting these into the subproblem concerning the prediction error weight and the measurement error weight, we can solve for κ in the q-th inner iteration within the s-th outer iteration. m optimal solution and optimal solution in, Step 6.4.3: Determine the second inner layer iteration condition Is it true? If it is true, then... When r is the s-th outer iteration k optimal solution Will As The estimation error covariance matrix Then execute step 6.

5. If it fails, set q = q + 1, and then return to step 6.4.2 to continue execution. Here, when q = 1... When r starts during the s-th outer iteration... k initial value equal When q > 1 This indicates that when r is in the (q-1)th inner iteration within the s-th outer iteration... k The optimal solution; Step 6.5: Determine if the outer iteration condition is true. If it is true, then... Corresponding as σ k，(n) The estimated value c k，(n) The estimated value r k The estimated value Then As The estimation error covariance matrix R k Then, through the state transition equation, and R k Convert to r respectively k+1 One-step prediction value and its prediction error covariance matrix If the condition is not met, let s = s + 1, and then return to step 6.2 to continue execution. The outer iteration condition is whether s is less than or equal to the preset number of iterations.

7. The robust elliptic extended target tracking method based on the variable center maximum correlation entropy criterion according to claim 6, characterized in that... The specific process of step 7 is as follows: Step 7.1: Let z k express The corresponding random vector, let y k express The corresponding random vector, let Indicate z k Let the covariance matrix be... Indicates y k The covariance matrix, and The relationship is as follows: Where, n k Represents a set The corresponding random vector; then calculate approximation in, express The mean, And calculate approximation in, It is positive definite; Step 7.2: According to Obtain α k rough estimate l k，(1) rough estimate l k，(2) rough estimate in, express The element in the first row and first column, express The element in the 1st row and 2nd column, express The element in the second row and second column; thus, obtain p. k rough estimate Step 7.3: Calculation The estimation error covariance matrix Specifically as follows: Step 7.3.1: Definition The estimation error vector Δp k , Step 7.3.2: Let Step 7.3.3: Definition in, Corresponding representation The element in the first row and first column, the element in the first row and second column, and the element in the second row and second column. Corresponding representation The element in the first row and first column, the element in the first row and second column, and the element in the second row and second column. S k，(1，：) S represents k The first row vector, S k，(2，：) S represents k The second row vector, express The first element, express The second element, C n,(1,1) Indicate C n The element in the first row and first column, C n，(1，2) Indicate C n The element in the 1st row and 2nd column, Cn ，(2,2) Indicate C n The element in the 2nd row and 2nd column; Step 7.3.4: Calculate the covariance matrix Cσ of Δσ. The element in the first row and first column of Cσ is... The element in the first row and second column of Cσ is The element in the 2nd row and 2nd column of Cσ is The element in the 1st row and 3rd column of Cσ is The element in the 2nd row and 3rd column of Cσ is The element in the 3rd row and 3rd column of Cσ is Step 7.3.5: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] Substitution In the middle, and on Performing a first-order Taylor expansion at σ yields: Δp k =DΔσ, where the first row of D The second line of D D's third line Step 7.3.6: Calculation Step 7.4: Update and obtain p within the framework of Kalman filtering k The estimated value Among them, K p This represents the Kalman gain corresponding to the Kalman filter equation. Then calculate The estimation error covariance matrix Ξ k ,

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