A Star-Convex Maneuvering Extended Target Tracking Method Based on Improved Expectation Mode Augmentation

Abstract

This invention relates to a star-convex maneuvering extended target tracking method based on improved expectation pattern augmentation. It models the target motion state within a variable structure multi-model algorithm framework, improving upon the EMA algorithm in existing model set design methods. First, an adaptive threshold is obtained using the OTSU algorithm to rationally partition the basic model set. Second, possible model subsets are retained, models adjacent to the model with the highest prediction probability are reactivated, and impossible models are eliminated, simultaneously obtaining the extended expectation pattern. The proposed method can achieve joint estimation of the target motion state and extended form in uniform acceleration scenarios, and still achieves high tracking performance even in strong maneuvering scenarios.

Description

Technical Field

[0001] This invention relates to the field of target tracking technology, and specifically to a star-convex maneuvering extended target tracking method. Background Technology

[0002] This invention focuses on extended targets detected by radar sensing, which can be understood as targets whose shape is not negligible relative to point targets. The aim is to jointly estimate the motion state (including position, velocity, etc.) and extended shape of targets within the observation area based on measurement data acquired by radar and other sensors. Any target tracking algorithm is built upon a tracking model, and selecting a suitable model is crucial to the final tracking result. This invention primarily addresses the establishment of motion models.

[0003] In modern target tracking, target motion patterns are complex and variable. Especially in high-maneuver scenarios, the target's motion state at the next moment is often unpredictable, making it difficult for a single, fixed mathematical model to describe the complex motion behavior. Based on a single model, Interactive Multiple Models (IMM) has been proposed, belonging to a type of Fixed Structure Multiple Model (FSMM) algorithm. At any given moment, several fixed models are used to filter the target state in parallel, and then the outputs of each filter are weighted according to the model probabilities. For this type of fixed-structure multiple model algorithm, it is difficult to fully utilize the system's real-time information; optimal estimation can only be achieved when the pattern space composed of the entire model set matches the real pattern. If the target's real pattern deviates from the current pattern space, tracking may fail. To improve tracking accuracy, the number of models is usually increased to achieve maximum coverage of the target's real pattern. This increases the computational burden, and competition between models may actually reduce tracking accuracy.

[0004] The Variable Structure Multiple Model (VSMM) algorithm helps overcome this challenge. Compared to the FSMM algorithm, it adds a model set design step, which can be understood as a model set adaptive module. This module determines which models in the entire model set will be selected at each time step to perform subsequent multi-model estimation operations. Thus, a smaller number of models can more closely approximate the true motion pattern of the target. The two main tasks completed in one recursive process of the VSMM algorithm can be summarized as follows:

[0005] (1) Model Set Adaptation (MSA): This function utilizes prior and posterior information to determine the model set at each time step. Its main functions include activating new models and terminating a subset of the current model set. Activating a new model aims to find a "better" model and add it to the existing model set to form a new model set for state estimation. "Better" means that the activated new model better describes the true system pattern. Conversely, terminating a model aims to remove models that deviate significantly from the system pattern from the original model set, reducing unnecessary competition between models and lowering computational costs.

[0006] (2) Multiple-model (MM) sequence condition estimation: It is responsible for making the best possible estimate of the target state under the given model set conditions using interactive multiple-model estimation methods.

[0007] The difference between various variable structure multi-model algorithms lies in their different model set adaptation methods. When using variable structure multi-model algorithms to model the motion state of extended targets, the model set adaptation (MSA) process, i.e., model set design, is the core step, and the quality of the model set design largely determines the performance of the algorithm. The Expectation Mode Augmentation (EMA) algorithm is a relatively classic algorithm among existing model set design methods.

[0008] Expected Mode Augmentation (EMA) is a model activation method that extends the base model set with a modified model to find a model that more closely approximates the system's true motion patterns. Typically, this extended model is a probability-weighted sum of the base models, hence the name "expected mode." EMA significantly outperforms IMM in tracking performance, but its base model set remains unchanged, limiting the ability of the extended expected mode to correct the base model set. Ideally, the model should change in real-time based on the target's potential motion behavior.

[0009] One pressing technical problem that needs to be addressed by those skilled in the art is how to improve the EMA algorithm in existing model set design methods to enable adaptive changes in the basic model set, thereby further improving the tracking accuracy of targets in maneuvering scenarios. Summary of the Invention

[0010] To address the shortcomings of existing technologies, this invention utilizes the OTSU algorithm (maximum inter-class variance method) to derive an improved EMA algorithm. By employing strategies such as basic model set partitioning and model set adaptation, the basic model set is made time-varying, thereby further improving the tracking accuracy of star-convex extended targets in maneuvering scenarios.

[0011] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0012] A method for tracking star-convex maneuvers based on improved expectation pattern augmentation includes the following steps:

[0013] S1. Model Set Partitioning: Based on the model prediction probabilities and the threshold τ obtained using the OTSU algorithm (maximum inter-class variance method), the basic model set at time k-1 is partitioned. Divided into a set of possible models M l and the set of impossible models M u ,in: The threshold τ is adaptively implemented using the OTSU algorithm. The partitioning process ensures that the total value in the two subsets is the model's predicted probability. The difference is greatest in the subset and smallest in the subset, where b represents the number of models in the basic model set at time k-1, and p and q represent the possible model sets M after partitioning. l and the set of impossible models M u The number of models in the model is p + q = b;

[0014] S2. Based on the model set partitioning results of step S1, formulate an adaptive strategy for the model set, delete mismatched models, retain only possible models, and calculate the extended expected pattern to ensure that the basic model set is variable.

[0015] S3. Based on the model set determined in step S2, perform the multi-model sequence conditional estimation step to obtain the overall estimate, the estimation error covariance matrix, and the updated model probability.

[0016] Furthermore, in step S1, the model set partitioning uses the OTSU algorithm to automatically select a threshold τ to binarize the probability set of the predicted models. Then, the minimum probability value in the major class is used as the threshold value for "keeping the model" and "removing the model", resulting in two different model subsets M. l and M u The specific method is as follows:

[0017] Assume the basic model set at time k-1. The number of models is r, and the set of possible models is M. l The proportion of the number of models in the middle range to the total number is λ1, and their numerical average is ρ1; the set of impossible models is M.u Let λ0 be the proportion of the number of models in the middle class to the total number, and ρ0 be their numerical average; let g be the variance between classes; then we have

[0018] λ1=p / r, λ o =q / r, λ1+λ0=1;

[0019] λ1ρ1+λ0ρ0=1;

[0020] g = λ1λ0*(λ1-λ0) 2 ;

[0021] Then, the threshold τ that maximizes the inter-class variance is obtained by traversing the class.

[0022] Furthermore, step S2 specifically includes the following operations:

[0023] (1) Retention of possible models: Retain the set of possible models M l All models in;

[0024] (2) Activation of the new model: Activation and the most likely model Adjacent model set M a ;

[0025] (3) Deletion of impossible models: Deleting the set of impossible models M u If all models are not activated, then the set of basic models at time k is:

[0026] (4) Extension of expected patterns: utilizing the newly generated set of basic models and its prediction probability Obtain the extended expected pattern In the formula, e represents the number of models in the basic model set at time k;

[0027] Finally, according to the formula Obtain the basic model set M at the current time. k .

[0028] Furthermore, in step S3, the IMM algorithm is used to estimate the target state, and the calculation loop for one sampling period is as follows:

[0029] (1) Model condition reinitialization: Under the assumption that the j-th model is valid at the current time, the input of the filter matched with it is a mixture of the estimates of each filter at the previous time; that is, the previous overall state estimate is used to reinitialize the model. And the covariance matrix P of the estimation error k-1|k-1 As a public initial condition;

[0030]

[0031]

[0032] Assume the matching model at time k-1 is The matching model at time k is Under the premise of information Z k-1 The mixed probability under the condition is:

[0033]

[0034] in

[0035] (2) Model Conditional Filtering: Given the re-initialized state and covariance matrix, state estimation is updated after obtaining new measurements; assuming the model is used at time k-1. The model used at time k Then and As the initial value, use with The matched models, according to the corresponding filtering equations, are used to calculate the state estimates. and the covariance matrix of the estimation error

[0036] (3) Model probability update: That is, for j = 1, 2, ..., r, calculate the updated model probability.

[0037]

[0038] In the formula Representation and Model The likelihood function of the match;

[0039] (4) Estimation fusion: This involves providing the overall estimate and estimation error covariance matrix at time k. When synthesizing the estimation results of each model, the weighting is based on the values ​​of each model. The model probability updated at time k Then the population estimate and the population estimate error covariance matrix at time k are respectively:

[0040]

[0041]

[0042] That is, the overall state estimate is the probability-weighted sum of the filter state estimates of all filters; where This is the updated result of the j-th model filter state estimate. It is the corresponding state estimation update error covariance matrix.

[0043] Furthermore, the specific steps of model conditional filtering include:

[0044] 1): State prediction, i.e., for j = 1, 2, ..., r, calculate respectively:

[0045]

[0046]

[0047] 2) Measurement prediction residuals and its covariance matrix That is, for j = 1, 2, ..., r, calculate respectively:

[0048]

[0049]

[0050] In the formula and All are independent Gaussian process noises;

[0051] Simultaneously calculate and The likelihood function for matching:

[0052]

[0053] 3) Filtering update: For j = 1, 2, ..., r, calculate the filtering gain matrix, state estimation update matrix, and state estimation update error covariance matrix respectively:

[0054]

[0055]

[0056]

[0057] In the formula It is the Kalman gain.

[0058] Beneficial Effects: This invention studies the target motion state modeling problem within the framework of a variable structure multi-model algorithm. It improves upon the EMA algorithm in existing model set design methods using the OTSU algorithm. First, based on the model prediction probabilities and an adaptive threshold obtained using the OTSU algorithm, the basic model set is rationally partitioned. Then, based on the partitioning results, an adaptive strategy for the model set is formulated: possible model subsets are retained, models adjacent to the model with the highest prediction probability are reactivated, and impossible models are eliminated. Simultaneously, an extended expected pattern is obtained. Based on the determined model set, state estimation is performed using a multi-model sequence conditional estimation step. The improved algorithm achieves time-varying basic model sets, further enhancing the ability of the extended expected pattern to correct the basic model set while reducing computational burden. The proposed method can achieve joint estimation of target motion state and extended morphology, achieving high tracking performance even in highly maneuverable scenarios. Attached Figure Description

[0059] Figure 1 This is a comparison chart of Hausdorff distances for the target during the entire maneuver in the simulation experiment using three algorithms (fixed structure IMM algorithm, original EMA algorithm, and improved EMA algorithm);

[0060] Figure 2 This is a comparison chart of the root mean square errors of the target's position using the three methods during the entire maneuvering process in the simulation experiment;

[0061] Figure 3 This is a comparison chart of the root mean square error of the target's velocity using the three methods during the entire maneuvering process in the simulation experiment;

[0062] Note: Hausdorff distance is a metric used to measure shape estimation performance in extended target tracking; the smaller the value, the better the estimation performance. Root mean square error of position and root mean square error of velocity are used to evaluate the estimation effect of the center of mass motion state; the smaller the value, the better the estimation effect of the center of mass motion state. Detailed Implementation

[0063] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0064] A star-convex maneuvering extended target tracking method based on an improved expectation pattern augmentation algorithm includes three steps: model set partitioning, model set adaptation, and multi-model sequence conditional estimation.

[0065] Step S1, Model Set Partitioning: Using the OTSU algorithm, a threshold τ is automatically selected to binarize the probability set of the predicted models, thus dividing the basic model set at time k-1. Divided into a set of possible models and the set of impossible models Where b represents the number of models in the basic model set at time k-1, and p and q represent the possible model sets M after partitioning. l and the set of impossible models M u The number of models in the model is p+q=b.

[0066] The threshold τ is adaptively determined using the Otsu's method (Otsu's method), which finds a suitable numerical level τ by calculating the variance to encompass the entire set. The elements in the set are divided into two subsets M. l and M u This results in two distinct model subsets; the partitioning process ensures that the overall values ​​(i.e., model prediction probabilities) within the two subsets are equal. The difference is greatest in the subset and smallest in the subset.

[0067] In step S1, at any given time, the OTSU algorithm is used to automatically select a threshold τ to binarize the probability set of the predicted models. Then, the minimum probability value in the major class is used as the threshold value for "keeping the model" and "removing the model", resulting in two different model subsets. The specific steps are as follows:

[0068] Assuming a basic model set The number of models is r, and the set of possible models is M. l The proportion of the number of models in the middle range to the total number is λ1, and their numerical average is ρ1; the set of impossible models is M. u Let λ0 be the proportion of the number of models in the middle class to the total number, and ρ0 be their numerical average; let g be the variance between classes; then we have

[0069] λ1=p / r, λ o =q / r, λ1+λ0=1;

[0070] λ1ρ1+λ0ρ0=1;

[0071] g = λ1λ0*(λ1-λ0) 2 ;

[0072] Then, the threshold τ that maximizes the inter-class variance is obtained by traversing the class.

[0073] The advantages of using the OTSU algorithm for model set partitioning can be summarized as follows:

[0074] (1) It is simple to calculate and can effectively divide the model set when the numerical differences in the probabilities of the models in the set are not large.

[0075] (2) Compared with the method of dividing by a fixed threshold, the threshold can be variable, which can be adapted according to the distribution of elements in the set, making the division process more reasonable.

[0076] Step S2, Model Set Adaptation: Remove mismatched models, retain only possible models, and simultaneously calculate the expanded expected pattern; according to the formula Obtain the basic model set M at the current time. k .

[0077] Specifically, step S2 mainly includes the following operations:

[0078] (1) Retention of possible models: Retain the set of possible models M l All models in it.

[0079] (2) Activation of the new model: Activation and the most likely model Adjacent model set M a .

[0080] (3) Deletion of impossible models: Deleting the set of impossible models M u If all models are not activated, then the set of basic models at time k is:

[0081] (4) Extension of expected patterns: utilizing the newly generated set of basic models and its prediction probability Obtain the extended expected pattern In the formula, e represents the number of models in the basic model set at time k.

[0082] The basic model set at the current moment

[0083] Step S3: After determining the model set at the current time, begin the interactive multiple model (IMM) sequence condition estimation operation. The specific steps for state estimation using the IMM algorithm include the following:

[0084] S3.1: Model Condition Reinitialization. When calculating the target state estimate using the multi-model method, since each model filter can potentially be the currently effective system model filter, only the previous overall state estimate and the covariance matrix of the estimation error are used as common initial conditions. Then, each model performs its own state estimation using the basic unscented Kalman filter algorithm, while simultaneously calculating the probabilities of each model. After reinitialization, the input to the j-th model filter is:

[0085]

[0086]

[0087]

[0088] In the formula This indicates that the matching model at time k-1 is assumed to be The matching model at time k is Under the premise of information Z k-1 Let be the conditional mixture probability. Let π be the matching probability between model i and the actual motion pattern of the system at time k-1; ij This represents the transition probability between models; the transition between models follows a first-order Markov process. When the Markov chain is homogeneous, if at time k-1 and mode s... i The matched model is m i k time and pattern s j The matched model is m j So from model m i To model m j The transition probability is denoted as π. ij ,Right now

[0089] P(m k =m j |m k-1 =m i ) = π ij , k∈N, i,j=1,2,…,r.

[0090] S3.2: Model Conditional Filtering. This involves updating the state estimate of each filter based on the new measurement data obtained at time k. In other words, given the re-initialized state and covariance matrix, the new measurement z is used to update the state estimate. k Then, the state estimation is updated.

[0091] Assuming the model is used at time k-1 The model used at time k Then and As the initial value, use with The matched models, according to the corresponding filtering equations, are used to calculate the state estimates. and the covariance matrix of the estimation error Specifically, it includes:

[0092] S3.2.1: State prediction. That is, for j = 1, 2, ..., r, calculate respectively.

[0093]

[0094]

[0095] S3.2.2: Measurement Prediction Residual and its covariance matrix That is, for j = 1, 2, ..., r, calculate respectively:

[0096]

[0097]

[0098] In the formula and All are independent Gaussian process noises;

[0099] Simultaneously calculate and The likelihood function for matching:

[0100]

[0101] Under the Gauss assumption, the likelihood function can be calculated as follows:

[0102]

[0103] S3.2.3: Filtering Update; that is, for j = 1, 2, ..., r, calculate the filtering gain matrix, state estimation update matrix, and state estimation update error covariance matrix respectively:

[0104]

[0105]

[0106]

[0107] In the formula It is the Kalman gain.

[0108] S3.3: Calculate the likelihood function matching each model and update the model probabilities. That is, for j = 1, 2, ..., r, calculate the model probabilities:

[0109]

[0110] In the formula Representation and Model The likelihood function for matching.

[0111] S3.4: Estimation Fusion; this involves providing the overall estimate and the estimation error covariance matrix at time k. When synthesizing the estimation results from each model, the weighting is based on the values ​​of each model. The model probability updated at time k Then the population estimate and the population estimate error covariance matrix at time k are respectively:

[0112]

[0113]

[0114] That is, the overall state estimate is obtained by weighting the probability of the filter state estimates of all filters, where This is the updated result of the j-th model filter state estimate. This is the corresponding state estimation update error covariance matrix; at this point, one iteration process ends.

[0115] The effectiveness of this invention is verified through simulation experiments conducted in a uniform acceleration scenario. To demonstrate the effectiveness of the proposed method, a relatively fair simulation environment was set up, in which the target's acceleration in both the horizontal and vertical directions is random, and the time τ spent at a certain acceleration is... T It's also random. The relevant parameters are set as follows:

[0116] Let the acceleration of the target in the horizontal direction be a. x =a max *cosβ, the acceleration in the numerical direction is a x =a max *sinβ. Wherein... β∈(0°,135°), five β values ​​within this angle range will be randomly generated during a single program execution. The simulation program executes 50 steps per run, corresponding to a certain acceleration (a). x ,a y The time spent on τ T It is a satisfaction Random numbers.

[0117] In the above scenario, the effectiveness of the MEMA algorithm (i.e. the improved EMA algorithm) proposed in this invention is verified by simulation using the fixed-structure IMM algorithm and the original EMA algorithm as comparison algorithms.

[0118] Appendix Figure 1-3 The estimation performance of three algorithms (the fixed-structure IMM algorithm, the original EMA algorithm, and the improved EMA algorithm) is presented. Hausdorff distance is a metric used to measure the performance of extended shape estimation during extended target tracking; a smaller value indicates that the estimated shape is closer to the actual extended shape of the target. The root mean square error of velocity and position can determine the accuracy of the tracking algorithm in estimating the target's motion transitions (including position and velocity); similarly, smaller values ​​indicate better algorithm performance.

[0119] In this simulation scenario, the target's maneuvering behavior at each moment is random, posing a significant challenge to the tracking algorithm. Overall, the IMM algorithm tends to exhibit higher peak errors when the target undergoes sudden maneuvers (i.e., sudden changes in acceleration). This is primarily because its model set is fixed, making it unable to quickly estimate the target's position at the moment of strong maneuvering. EMA, by extending an expected model, avoids large peak errors and exhibits relatively better tracking performance. The MEMA algorithm proposed in this invention, by setting the basic model set to be non-fixed and using a variable threshold to rationally partition the model set, eliminates some impossible models and reduces unnecessary competition between models. Compared to the EMA algorithm, MEMA improves tracking accuracy while reducing computational load. Furthermore, the performance of the MEMA algorithm remains relatively stable throughout the tracking process compared to the other two algorithms, indicating strong robustness.

[0120] In summary, this invention models the target motion state within the framework of a variable structure multi-model algorithm. It improves upon the EMA algorithm in existing model set design methods, proposing a novel model set design method—the MEMA algorithm. The first step involves using the OTSU algorithm to obtain an adaptive threshold for rationally partitioning the basic model set. The second step involves developing an adaptive model set strategy. At each time step, possible model subsets are retained, models adjacent to the model with the highest prediction probability are reactivated, impossible models are eliminated, and an extended expected pattern is obtained. The improved algorithm achieves time-varying basic model set, further enhancing the ability of the extended expected pattern to correct the basic model set while reducing computational burden. The proposed method can achieve joint estimation of target motion state and extended morphology, achieving high tracking performance even in highly maneuverable scenarios.

[0121] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for tracking a star-convex maneuvering extended target based on improved expected pattern augmentation, characterized in that, Includes the following steps: S1. Model Set Partitioning: Based on the model prediction probabilities and the threshold τ obtained using the OTSU algorithm (maximum inter-class variance method), the basic model set at time k-1 is partitioned. Divided into a set of possible models M l and the set of impossible models M u ,in: b represents the number of models in the basic model set at time k-1, and p and q represent the possible model sets M after partitioning. l and the set of impossible models M u The number of models in the dataset is p+q=b; the threshold τ is adaptively implemented based on the OTSU algorithm, and the partitioning process makes the total value in the two subsets, i.e., the model prediction probability, equal to the total value in the subsets. The difference is greatest, and the difference between values ​​in each subset is smallest; S2. Based on the model set partitioning results of step S1, formulate an adaptive strategy for the model set, delete mismatched models, retain only possible models, and calculate the extended expected pattern to ensure that the basic model set is variable. S3. Based on the model set determined in step S2, perform the multi-model sequence conditional estimation step to obtain the overall estimate, the estimation error covariance matrix, and the updated model probability.

2. The method for tracking a star-convex maneuvering extended target based on improved expected pattern augmentation according to claim 1, characterized in that, In step S1, the model set partitioning uses the OTSU algorithm to automatically select a threshold τ to binarize the probability set of the predicted models. Then, the minimum probability value in the major class is used as the threshold value for "keeping the model" and "removing the model", resulting in two different model subsets M. l and M u The specific method is as follows: Assume the basic model set at time k-1. The number of models is r, and the set of possible models is M. l The proportion of the number of models in the middle range to the total number is λ1, and their numerical average is ρ1; the set of impossible models is M. u Let λ0 be the proportion of the number of models in the middle class to the total number, and ρ0 be their numerical average; let g be the variance between classes; then we have λ1=p / r,λ o =q / r,λ1+λ0=1; λ1ρ1+λ0ρ0=1; g=λ1λ0*(λ1-λ0) 2 ; Then, the threshold τ that maximizes the inter-class variance is obtained by traversing the class.

3. The method for tracking a star-convex maneuvering extended target based on improved expected pattern augmentation according to claim 1, characterized in that, Step S2 specifically includes the following operations: (1) Retention of possible models: Retain the set of possible models M l All models in; (2) Activation of the new model: Activation and the most likely model Adjacent model set M a ; (3) Deletion of impossible models: Deleting the set of impossible models M u If all models are not activated, then the set of basic models at time k is: (4) Extension of expected patterns: utilizing the newly generated set of basic models and its prediction probability Obtain the extended expected pattern In the formula, e represents the number of models in the basic model set at time k; Finally, according to the formula Obtain the basic model set M at the current time. k .

4. The method for tracking a star-convex maneuvering extended target based on improved expected pattern augmentation according to claim 1, characterized in that, In step S3, the IMM algorithm is used to estimate the target state. The calculation loop for one sampling period is as follows: (1) Model condition reinitialization: Under the assumption that the j-th model is valid at the current time, the input of the filter matched with it is a mixture of the estimates of each filter at the previous time; that is, the previous global state estimate is used to reinitialize the model. And the covariance matrix P of the estimation error k-1|k-1 As a public initial condition; Assume the matching model at time k-1 is The matching model at time k is Under the premise of information Z k-1 The mixed probability under the condition is: in (2) Model Conditional Filtering: Given the re-initialized state and covariance matrix, state estimation is updated after obtaining new measurements; assuming the model is used at time k-1. The model used at time k Then and As the initial value, use with The matched models, according to the corresponding filtering equations, are used to calculate the state estimates. and the covariance matrix of the estimation error (3) Model probability update: That is, for j = 1, 2, ..., r, calculate the updated model probability. In the formula Representation and Model The likelihood function of the match; (4) Estimation fusion: This involves providing the overall estimate and estimation error covariance matrix at time k. When synthesizing the estimation results of each model, the weighting is based on the values ​​of each model. The model probability updated at time k Then the population estimate and the population estimate error covariance matrix at time k are respectively: That is, the overall state estimate is the probability-weighted sum of the filter state estimates of all filters; where This is the updated result of the j-th model filter state estimate. It is the corresponding state estimation update error covariance matrix.

5. The method for tracking a star-convex maneuvering extended target based on improved expected pattern augmentation according to claim 4, characterized in that: The specific steps of model conditional filtering include: 1): State prediction, i.e., for j = 1, 2, ..., r, calculate respectively: 2) Measurement prediction residuals and its covariance matrix That is, for j = 1, 2, ..., r, calculate respectively: In the formula and All are independent Gaussian process noises; Simultaneously calculate and The likelihood function for matching: 3) Filtering update: For j = 1, 2, ..., r, calculate the filtering gain matrix, state estimation update matrix, and state estimation update error covariance matrix respectively: In the formula It is the Kalman gain.

Images