Method for carrying out extended target tracking by using random matrix and partial normal distribution

Abstract

The invention discloses a method for performing extended target tracking by using a random matrix and partial normal distribution, which comprises the following steps of: establishing an evolution model and a partial normal distribution measurement model, and performing prior prediction on a prior target motion state, an extended form and a measurement deflection variable; carrying out posteriori estimation on a target motion state, an expansion form and a measurement skew variable, and obtaining a skew constraint vector estimation value; re-modeling based on an IT-IMM framework: obtaining an optimal solution of a prior probability density function of a target motion state, an extension form and a measurement skew variable through a weighted KLA algorithm; the posterior probability density of the corresponding mode is obtained through a variational Bayesian algorithm, and mode probability updating is carried out; and through weighted KLA approximation, final estimation of the motion state and the expansion form of the target is obtained. According to the method, accurate tracking of the target motion state and accurate estimation of the expansion form can be realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of target tracking, in particular to a method for extended target tracking using random matrix and skew-normal distribution suitable for complex environment observation limitation and high maneuverability target. BACKGROUND

[0002] Target tracking technology is a key technology in modern automation and intelligent systems, widely used in military reconnaissance, intelligent traffic monitoring, aerospace and border security, etc. With the development of technology, target tracking technology has experienced a transition from point target to extended target. Point target tracking mainly focuses on the estimation of the position, velocity and acceleration of the target, while extended target tracking needs to estimate the physical extension of the target. With the advancement of radar and sensor technology, it is possible to distinguish multiple reflections of an object, and multiple measurements of each object can be made in one scan, which makes it possible to detect multiple scattering centers on the target, providing the possibility for extended target tracking.

[0003] The challenge of extended target tracking (EOT) technology lies in the accurate estimation and tracking of the physical characteristics of the target such as size, shape and direction, as well as the position and velocity state of the target. In addition, the target may exhibit high dynamic changes and uncertainties during maneuvering, which puts higher requirements on the adaptability and robustness of the tracking algorithm.

[0004] Existing EOT methods usually use random matrices to handle the extended characteristics of the target, but most of them ignore the asymmetry of the scattering center distribution on the target, i.e. the skewness of the measurement distribution.

[0005] In practical applications, due to the interaction between the physical characteristics of the target and the radar signal, such as the incidence angle, reflection angle and uneven surface material, the measurement distribution of the target often shows skewness, which cannot be effectively described in existing random matrix methods based on the assumption of symmetric distribution, making the measurement model not realistic in describing the measurement data distribution, resulting in limited tracking estimation performance of the algorithm.

[0006] Specific problems include: 1. Insufficient capture of skewed measurement distribution: existing methods fail to fully capture the skewness of the target measurement distribution, which is particularly evident when the target is moving at high speed or the surface characteristics are complex and variable, resulting in a significant decrease in tracking accuracy.

[0007] 2. Insufficient adaptability to dynamic model and measurement model mutations: the target may experience rapid state changes during maneuvering, and existing algorithms often lack effective mechanisms to adapt to these mutations, thereby affecting the continuity and accuracy of tracking.

[0008] 3. Multi-maneuver phase and complex motion mode processing problem: For extended targets with multiple maneuver phases and complex motion modes, existing algorithms are difficult to achieve high precision and robust tracking, especially in the case of rapid changes in target size, shape and motion characteristics.

[0009] Therefore, it is a technical problem to be solved to provide an extended target tracking algorithm capable of accurately capturing target measurement distribution skew characteristics, adapting to dynamic model and measurement model mutations in target maneuvering process, and effectively processing extended targets with multiple maneuver phases and complex motion modes. SUMMARY

[0010] To solve the above-mentioned defects in the prior art, the present application aims to provide a method for extended target tracking using random matrix and skew normal distribution, which describes the skew phenomenon of the measurement distribution on the target by introducing skew normal distribution, and quickly and accurately estimates the target state and the physical extension form of the target through variational Bayesian iteration. The present application also combines the information theory interactive multiple model (IT-IMM) framework to process the mutations of motion state, extension form and measurement distribution that may occur during target maneuvering.

[0011] The present application is realized by the following technical solutions.

[0012] In one aspect of the present application, a method for extended target tracking using random matrix and skew normal distribution is provided, comprising: establishing an evolution model and a measurement model of skew normal distribution according to the target motion state and the extension form, respectively; using the target motion state and the extension form to combine the evolution model to perform prior prediction of the prior target motion state, the extension form and the measurement skew variable; recursively updating using the variational Bayesian method to obtain the posterior estimation of the target motion state, the extension form and the measurement skew variable, and the skew constraint vector estimation value; based on the information theory interactive multiple model (IT-IMM) framework, remodeling the evolution model of the target motion state and the extension form and the measurement model of the skew normal distribution: obtaining the optimal solution of the prior probability density function of the target motion state, the extension form and the measurement skew variable through weighted Kullback-Leibler average (KLA) algorithm; based on the prior probability density function of the target motion state, the extension form and the measurement skew variable, obtaining the posterior probability density of the corresponding mode through the variational Bayesian algorithm to perform mode probability updating; according to each updated mode probability and the posterior probability density, obtaining the final estimation of the target motion state and the extension form through weighted KLA approximation.

[0013] As preferred, the evolution model and the measurement model of the skew-normal distribution are respectively established according to the target motion state and the extended shape, including: The evolution of the target motion state is determined by the state transition matrix and the Gaussian noise; The evolution distribution of the extended shape is determined by the Wishart distribution, and the evolution model is obtained; The measurement model is established based on the skew-normal distribution, which is used to represent the asymmetric distribution of the radar measurement on the target.

[0014] As preferred, the posterior estimates of the target motion state, the extended shape and the measurement skew variable, and the skew constraint vector estimate value are obtained, including: The posterior joint distribution density of the motion state, the extended shape and the skew variable at time k is assumed; The prior prediction is performed on the state variable, the extended shape and the measurement skew variable; The posterior estimate of the measurement skew variable is performed by the variational Bayesian method; The measurement point of the target distribution is obtained by the radar direction, and the prediction value of the skew constraint vector of the target is obtained, and then the posterior estimate value of the skew constraint vector of the target is obtained.

[0015] As preferred, the posterior estimate of the measurement skew variable is performed by the variational Bayesian method, including: The distribution functions of the motion state, the extended shape and the measurement skew variable are multiplied to approximate the real joint distribution density by the variational Bayesian method: The optimal solution for the distribution function of the estimation variable is obtained; The distribution parameters of the target motion state, the extended shape and the measurement skew variable are iteratively estimated by the variational Bayesian algorithm, the joint distribution probability density function is substituted into the optimal solution of the estimation variable distribution function, and the measurement data is obtained, and the posterior estimate value is obtained.

[0016] As preferred, the optimal solution of the prior probability density function of the target motion state, the extended shape and the measurement skew variable is obtained by the weighted Kullback-Leibler average KLA algorithm, including: When the target maneuvers, the IT-IMM framework is used to process the sudden changes of the target motion state, the extended shape and the measurement distribution, and a set of dynamic models is established at the same time k; The posterior joint distribution density function of the i th model at time k is reconstructed, which includes the distribution parameter assumption of the target motion state, the extended shape and the measurement skew variable; The evolution model and the measurement model of the target motion state and the extended shape at time k are reinitialized by using the total probability theorem: ​Based on the posterior probabilities of each model and the transition probabilities between models in the previous time step, calculate the mixing weights of the i-th model in the current time step, and integrate the posterior distributions of each model in the previous time step through the mixing weights to complete the initialization of the prior distribution of the current model. By using the weighted KLA algorithm, the initial multi-model mixture prior distribution is approximated as a single-mode distribution, thus obtaining the optimal solution of the prior probability density function of the target motion state, extended shape, and measurement skew variables.

[0017] As a preferred method, the variational Bayesian algorithm obtains the posterior probability density of the corresponding mode and performs mode probability updates, including: For the first The motion state model, measurement distribution model, and prior probability density of the ... The posterior probability density of each modality; Update the [number]th [item] according to Bayes' rule and the law of total probability. Modal probabilities of each mode.

[0018] Preferably, based on each updated modal probability and posterior probability density, a weighted KLA approximation is used to obtain the final estimate of the target's motion state and extended form, including: The overall probability density function is obtained by summing the modal probability of each mode and its posterior probability density. By using a weighted KLA method approximation, the final estimate of the motion state and extended morphology is obtained.

[0019] The present invention, by adopting the above technical solution, has the following beneficial effects: 1. The tracking method proposed in this invention establishes a new measurement model, which introduces a skewed distribution to describe the skewness of the target measurement distribution and uses variational Bayesian method for recursive estimation, thereby improving the accuracy and robustness of tracking.

[0020] 2. The method of this invention is applicable to situations where the target has multiple maneuvering phases and complex motion characteristics. Facing the abrupt changes in the motion state and measurement distribution that may occur during the maneuvering process, it combines the variational Bayesian method and the IT-IMM framework, and adopts the weighted Kullback-Leibler averaging (KLA) method to consider multiple possible dynamic states of the target and corresponding modal probability updates. It effectively integrates information from different models in the mixing and output phases, optimizes the comprehensive utilization of information, and provides a computationally efficient and highly adaptable extended target tracking solution that can achieve accurate tracking of the target's motion state and accurate estimation of its extended form.

[0021] 3. The application can effectively fuse information from different models in the mixing and output stages, thereby improving the adaptability and robustness of the tracking algorithm, and providing an effective solution for extended target tracking in complex environments.

[0022] 4. The application provides a method that can effectively estimate the motion state and physical extension of the target, and can adapt to the skew phenomenon of the measurement distribution that may occur during target maneuvering. In addition, the application also includes an information theory interacting multiple model framework for processing target motion state mutations, thereby improving the accuracy and robustness of target tracking.

[0023] 5. The technical solution of the application can be widely applied in fields requiring high-precision target tracking, such as military reconnaissance, intelligent traffic monitoring, etc. Through the application, the problems faced by existing technologies in handling extended targets with complex motion characteristics can be solved.

[0024] The method of the application can achieve high-precision and robust tracking in the case of rapid changes in target size, shape and motion characteristics, while overcoming the limitations of existing technologies under the assumption of symmetric distribution, to meet the growing demand for target tracking accuracy and reliability.

[0025] The method of the application for extended target tracking using random matrices and skew normal distribution can be applied in military reconnaissance, unmanned aerial vehicle management and control, and extended target identification and tracking in road traffic. BRIEF DESCRIPTION OF DRAWINGS

[0026] The drawings described herein are used to provide further understanding of the application, form part of the application, and do not constitute an improper limitation on the application. In the drawings: Figure 1 Flowchart of extended target tracking algorithm with skew random matrix; Figure 2 Schematic diagram of simulation scene; Fig. 3 (a) and (b) are target tracking estimation scene effect diagrams of different extended target tracking algorithms under two measured scene data; Fig. 3 (a) is a comparison diagram of the tracking effect of the VB-EOT-SN algorithm with skew random matrix and the EOT-Feldmann, MEM-EKF* and VB-EOT-G algorithms under the radar measurement data of the first measured scene; Fig. 3 (b) is a comparison diagram of the tracking effect of the VB-EOT-SN algorithm and the EOT-Feldmann, MEM-EKF* and VB-EOT-G algorithms under the radar measurement data of the second measured scene; Fig. 4 (a) is Figure 2Figure 2 (a) and (b) are the comparison chart of VB-EOT-SN algorithm and EOT-Feldmann algorithm in the simulation scene of the Wasserstein distance data of the simulation scene; Figure 4 (b) and (c) are the comparison chart of VB-EOT-SN algorithm and EOT-Feldmann algorithm, MEM-EKF* and VB-EOT-G algorithm in the measured scene of the Wasserstein distance data of the measured scene tracking results of the measured scene of Figure 3 (a) and (b). DETAILED DESCRIPTION

[0027] The present application will be described in detail below with reference to the accompanying drawings and specific embodiments, which are used to explain the present application, but not as a limitation of the present application.

[0028] As Figure 1 shown, the embodiment of the present application provides a method for extended target tracking using random matrix and skew normal distribution, comprising the following steps: S101: respectively establishing an evolution model and a measurement model of skew normal distribution according to the target motion state and the extended shape.

[0029] Considering the changes of the target motion state and the extended shape at each time in the tracking process, an evolution model is established for the target motion state and the extended shape; considering the physical action principle of radar and target, a measurement model of skew normal distribution is established according to the target motion state and the extended shape, which is used to describe the skew phenomenon of the radar target extended shape measurement distribution.

[0030] Establishment of target model: an evolution model is established for the target motion state and the extended shape, i.e. considering the changes of the target motion state and the extended shape at each time in the tracking process, the evolution of the target motion state is described by a state transition matrix and a Gaussian noise, and the evolution distribution of the extended shape is described by a Wishart distribution.

[0031] Establishment of measurement model: considering the physical action principle of radar and target, a new measurement model is established based on skew normal distribution according to the target motion state and the extended shape to describe the asymmetric distribution of the radar measurement on the target, i.e. the skew direction and skew range are described by a constraint vector and a latent variable, so that the physical characteristics of the target can be more accurately captured by using the measurement data.

[0032] Specifically, the following steps are included: 11) the evolution of the target motion state is determined by a state transition matrix and a Gaussian noise

[0033] The target motion state is as follows: ​

[0034] where, is the target motion state at last time, is the target motion state at current time, Gaussian noise with mean 0 and error covariance matrix ; 12) The evolution distribution of the extended shape is determined by the Wishart distribution, and the evolution model is obtained as follows:

[0035] where is the extended shape of the target at current time, is the extended shape of the target at last time, degree of freedom , is the dimension of the physical space, is the inverse matrix of the evolution model of the extended shape, which can be used to describe the dependence of the extended shape on the direction, size and shape, and for the evolution model of the Wishart distribution:

[0036] 13) A measurement model is established based on the skew normal distribution to represent the asymmetric distribution of the radar measurement on the target, and the measurement model is as follows:

[0037] where, is the radar measurement, is a known measurement matrix of dimension is the target motion state at current time, is the measurement noise subject to the skew Gaussian distribution, is the number of measurement points, is the measurement point. The measurement noise is obtained as follows: 131) There is a skew direction constraint vector of dimension , as follows: where is the angle of the skew direction, and is the approximate size describing the skew distribution, and the latent random variable of the truncated Gaussian distribution is expressed as follows:

[0038] where, for , the standard normal distribution is expressed as , and and are used to represent the position and scale of skew, respectively, is a random variable subject to the truncated normal distribution, the evolution is described as:

[0039] where, is a transition parameter, is process noise, is a random variable subject to the truncated normal distribution at the previous time, is subject to: .

[0040] 132)Based on the extended form and the measurement skew variable , the measurement noise distribution in the measurement model is described as a skew normal distribution:

[0041] is a skew direction constraint vector, when and / or , the measurement noise degenerates to an ordinary standard normal distribution, is an extended form measurement matrix.

[0042] S102: Use the target motion state and the extended form to combine the evolution model to make prior prediction of the prior target motion state, the extended form, and the measurement skew variable; recursively update using the variational Bayesian method to obtain the posterior estimation of the target motion state, the extended form, and the measurement skew variable, and the skew constraint vector estimation value.

[0043] Approximate the joint probability density function of the target motion state and the extended form and the skew variable of the measurement distribution, obtain the prior state and the prior form using the evolution model of the target motion state and the extended form at the previous time, recursively update using the variational Bayesian method to obtain the posterior estimation of the target motion state, the extended form, and the measurement skew variable. Then assume that the measurement distribution is biased towards the sensor direction to obtain the constraint vector estimation value of the skew distribution.

[0044] Specifically, the following steps are included: 21) In order to obtain a recursive algorithm, the posterior joint distribution density of the motion state, the extended form, and the skew variable at time k is assumed as follows:

[0045] where, is the measurement at time k-1, is the posterior estimation of the state variable, is the posterior estimation covariance matrix of the state variable, is the posterior degree of freedom parameter of the inverse Wishart distribution,​ posterior estimate of the target spread morphology, posterior mean and posterior variance of the truncated normal distribution, i.e., for the state variable posterior estimate parameters of the target spread morphology and the skew variable .

[0046] 22) Perform prior prediction for the target motion state variable, the target spread morphology, and the measurement skew variable.

[0047] 221) Perform prior prediction for the target motion state variable: based on the predicted state variable distribution density function:

[0048] The prior prediction value for the state variable and the state variable estimation error covariance matrix is given by:

[0049] where, is the current time motion state prior estimate, is the state transition matrix, is the previous time motion state posterior estimate, is the covariance matrix of the current time motion state prior estimate, is the covariance matrix of the previous time motion state posterior estimate, is the process noise matrix; 222) Perform prior prediction for the target spread morphology: based on the predicted spread morphology distribution density function:

[0050] where, is the prior degree of freedom; The prior prediction value for the spread morphology and the degree of freedom parameter is given by:

[0051] where, is the evolution coefficient of the spread morphology, is the spatial dimension, is the spread morphology transition matrix, and is the state transition related statistics, is obtained from the posterior of the previous time:

[0052] ​223) Prior prediction of the measurement skew variable: Based on the skew distribution density function:

[0053] where, is the prior mean of the truncated normal distribution, is the prior variance of the truncated normal distribution; The predicted estimate for the skew variable can be obtained as:

[0054] where, is the process noise variance, , is the posterior variance of the truncated normal distribution, posterior mean, , is the prior variance of the truncated normal distribution, prior mean, is the state transition coefficient.

[0055] 23) Perform variational Bayesian posterior estimation of the measurement skew variable.

[0056] 231) Multiply the distribution functions of the motion state, the spread shape, and the measurement skew variable to approximate the true joint distribution density using the variational Bayesian method:

[0057] where, is the measurement skew variable, , , are the distribution function values, respectively.

[0058] Obtain , , the distribution function values by minimizing the K-L divergence between the approximate distribution density and the true posterior distribution density: and The K-L divergence of the two functions

[0059] 232) The optimal solution for estimating the distribution function of the variable can be obtained as:

[0060] where, is the measurement at the current time, is the measurement at the previous time.

[0061] In the formula, the joint distribution probability density function can be calculated by the following probability distribution as follows:

[0062] 233)The motion state, the extended form and the measurement skew variable distribution parameter are iteratively estimated by the variational Bayesian algorithm, the joint distribution probability density function is substituted into the optimal solution of the approximate estimation function in turn respectively, and the obtained measurement data is combined to obtain the posterior estimation value thereof.

[0063] The processing mode of the measurement data is as follows:

[0064] Wherein, is a radar measurement data point, is the number of measurement points at the current moment, is a radar measurement point mean value, is a measurement deviation covariance matrix; The posterior estimation of the target motion state is represented as follows:

[0065] Wherein, is a position component of the target posterior estimation state, is the posterior estimation of the motion state at the current moment, is a radar measurement point mean value, is a known measurement matrix of dimension, is a posterior skew variable, is a skew constraint variable; In the formula:

[0066] The posterior estimation of the extended form is:

[0067] Wherein, is a posterior degree of freedom parameter, is a comprehensive deviation matrix, is an inverse matrix of the extended form measurement matrix, is a radar measurement point mean value.

[0068] The posterior estimation of the measurement skew variable is:

[0069] Wherein, and are the posterior estimation mean value and variance of the measurement skew variable, is a position component of the target posterior estimation state, is a prior mean value of the truncated normal distribution, To truncate the prior variance of the normal distribution, This refers to the measurement weighting coefficient.

[0070]

[0071] For the measurement skew parameter mean and error covariance The calculation method is as follows:

[0072] in, This is the truncation correction factor.

[0073] In the formula:

[0074] Iterate N times, substituting the variables into each other according to the algorithm to solve, and finally obtain the converged estimate; for The solution is as follows: 24) The motion state, extended form and measurement skewness variable distribution parameters are iteratively estimated using the variational Bayesian algorithm; by substituting the joint probability density function into the optimal solution of the approximate estimation function in turn, and combining it with the obtained measurement data, the posterior estimate of it is obtained.

[0075] For the skew constraint vector Since the distribution of measurement points on the target is usually biased towards the radar direction, that is, the skewness direction is used with respect to the target azimuth. The representation of: In the formula, the target azimuth angle Its predicted estimate is approximated as follows:

[0076] in, , It is the position component of the target's predicted state. , Is the goal again? The sensor position at any given time allows us to obtain the predicted value of the target's skew constraint vector.

[0077] in, This is a priori prediction estimate of the target azimuth at the current moment.

[0078] When the position component of the target's posterior estimated state is obtained , Then, the posterior estimate of the target skew constraint vector can be obtained: , wherein, .

[0079] S103: Based on the information theory interactive multiple model (IT-IMM) framework, the evolution model and the measurement model of the target motion state and the extended shape are remodeled; the optimal solution of the prior probability density function of the target motion state, the extended shape and the measurement skew variable is obtained through the weighted KLA algorithm.

[0080] When an extended object moves, all motion states, extensions and measurement distributions (especially skew) can be abrupt. For a maneuvering extended object, the skew of its motion and measurement (e.g., skew direction) can be complex. In order to more accurately describe the motion and measurement of the object, the motion state evolution model and the measurement model of the target are remodeled by considering a jump Markov system, and the weighted KLA is used to approximate the prior probability density function and obtain the optimal solution.

[0081] Specifically, the following steps are included: 31) First, a set of dynamic modes is established, M modes are established at the same time k, each mode represents a possible dynamic state of the target, and these modes can describe the motion characteristics of the target in different maneuvering stages.

[0082] When the target maneuvers, the abrupt changes of the motion state, the extended shape and the measurement distribution are adapted through the information theory interactive multiple model (IT-IMM) framework: the motion state model of each mode corresponds to a set of independent motion state parameters (including state transition matrix and process noise matrix ), the skew measurement noise matrix of the measurement distribution model of each mode corresponds to the measurement distribution parameters (including skew constraint vector and measurement distortion matrix ), and the models follow the Markov transition rule, which depends on the current mode , each mode is assumed to be a Markov chain with transition probability .

[0083] For the dynamic model, it is represented as follows:

[0084] wherein, is the i-th model effective at time k, is the motion state process noise, is the measurement noise, and the process noise in the motion state evolution model is described as follows:

[0085] in, Let be the noise covariance matrix of the i-model process.

[0086] Measurement noise in the measurement model The description is as follows:

[0087] Each skew constraint vector and measurement distortion matrix All with a mode Correspondingly, at the same time There are transition probabilities between the various modes. Markov chains, transition probabilities Right now: .

[0088] 32) To Time of the first The posterior joint probability density function of each model is reconstructed. This function includes distribution parameter assumptions for the target motion state, extended morphology, and measurement skew variables, as follows:

[0089] make:

[0090] Using the law of total probability The evolution model and measurement model of the target's motion state and extended form at each moment are re-initialized: Based on the posterior probabilities of each model and the transition probabilities between models at the previous time step, the mixing weights of the i-th model at the current time step are calculated. The posterior distributions of each model at the previous time step are integrated through the mixing weights to complete the initialization of the prior distribution of the current model.

[0091]

[0092] in, The weights are the combined weights of the previous time step i and the previous time step j. The set of states for the objective; Mixed weights in the formula It is obtained from the following calculations:

[0093] in, Current moment j Prior weights of components Components from the previous moment j The weight, for jState to i State transition probability; where the prediction weight is obtained by the following calculation:

[0094] where, is the posterior weight of component i at the previous time j.

[0095] For , the initialized multi-model mixture prior distribution is approximated as a single-modal distribution by the weighted KLA algorithm, and the optimal solution of the prior probability density function of the target motion state (prior mean, prior covariance), the extended shape (prior degree of freedom, prior scale matrix), and the measurement bias variable (prior mean, prior variance) is obtained: the effectiveness of the modeling and the optimal solution solving method described in this step is verified by simulation data and real experimental data to ensure the processing ability of model mutation and tracking accuracy when the target maneuvers.

[0096] The result of the weighted KLA algorithm approximation is:

[0097] The optimal solution is obtained as:

[0098] where, is the posterior motion state and the posterior motion state covariance matrix of component i at the previous time, is the target posterior extended shape degree of freedom and the extended shape matrix of component i at the previous time, is the truncated Gaussian distribution posterior mean and the posterior variance of component i at the previous time.

[0099] where:

[0100] where, is the posterior motion state and the posterior motion state covariance matrix of component j at the previous time, is the target posterior extended shape degree of freedom and the extended shape matrix of component j at the previous time, is the truncated Gaussian distribution posterior mean and the posterior variance of component j at the previous time.

[0101] S104: Based on the prior probability density function of the target motion state and the extended shape and the measurement bias variable, the posterior probability density of the corresponding mode is obtained by the variational Bayesian algorithm, and the mode probability is updated.

[0102] Model conditional filtering, based on the model, measurement and prior probability density of the mode, can obtain the posterior probability density of the corresponding mode through variational Bayes algorithm, and then update the mode probability. According to Bayes' rule and the total probability theorem, the predicted mode probability and likelihood function of each mode are used to update the mode probability.

[0103] Specifically, the steps include the following: 41) Based on the first Motion state model of each modality Measurement distribution model and prior probability density The first step can be obtained using a variational Bayesian algorithm consistent with that described in S102. The posterior probability density of each modality ; 42) According to Bayes' rule and the law of total probability, the... The modal probabilities of each modality can be updated as follows:

[0104] in, Let be the likelihood function of the i-th mode. Let be the likelihood function of the j-th mode. Where the likelihood function Obtained from the following formula:

[0105] in, Let be the covariance matrix of the likelihood function for the i-th mode. Let be the prior skewness variable for the i-th mode at the current time. The parameters in the equation are obtained by a variational Bayesian process.

[0106] S105: Based on each updated modal probability and its posterior probability density, the final estimate of the target motion state and extended form is obtained through weighted KLA approximation.

[0107] Specifically, the steps include the following: 51) Based on each mode modal probability and the posterior probability density obtained therefrom The probability density function of the population can be obtained by summing these values. :

[0108] 52) By applying an approximation using the weighted KLA method, the final estimates of the motion state and extended form are obtained as follows:

[0109] where, is the posterior estimated motion state and posterior estimated motion state covariance matrix of component i at current time, is the posterior estimated extended shape and posterior estimated extended shape matrix of component i at current time, is the posterior estimated truncated Gaussian distribution mean and posterior estimated variance of component i at current time.

[0110] The present application is further illustrated by specific examples.

[0111] (1) Considering the changes of the target motion state and the extended shape at each time in the tracking process, an evolution model is established for the motion state and the extended shape of the target, and a measurement model is established according to the physical action principle of the radar and the target, according to the motion state and the extended shape of the target.

[0112] In the nuScenes measured data set scene one (bus straight driving, with a slight turning) as shown in Fig. 3 (a), the motion state modeling is a constant speed motion model of the vehicle as the motion state transition matrix:

[0113] In the nuScenes measured data set scene two (car turning left, with few measurement values at each scan) as shown in Fig. 3 (b), the motion state modeling is a constant turning motion model of the vehicle as the motion state transition matrix:

[0114] wherein T=0.5 is the sampling interval time step, represent different steering angular velocities; the process noise is:

[0115] and the motion state is initialized by two-point difference method; The extended shape is modeled by an ellipse with a true axis length and the same direction as the initial speed direction, and the extended shape evolution matrix of the target is In scene one, it is set as:

[0116] In scene two, it is set as:

[0117] The measurement noise of the measured data is:

[0118] (2) For the target in the measured data scene one and scene two, at time to it Assumptions are made regarding the motion state, expansion pattern, and skewness variable's posterior joint probability density at each moment. Then, time updates are performed, and prior predictions are made for the state variable, expansion pattern, and skewness variable: based on the predicted state variable probability density function. We obtain its prior predictions for the state variables and the state variable estimation error covariance matrix: Based on the predicted extended morphological distribution density function We obtain its prior predictions for the extended form and degree-of-freedom parameters: Based on the skewed distribution density function Predictive estimates for skewed variables can be obtained. Then perform variational Bayesian measurement posterior estimation.

[0119] The motion state, expansion morphology, and measurement skewness distribution parameters are iteratively estimated using a variational Bayesian algorithm. By successively substituting the joint probability density function into the optimal solution of the approximate estimation function, and combining it with the obtained measurement data, the posterior estimates of the target's motion state, expansion morphology, and measurement skewness variables are obtained. For the moment skew constraint vector Since the distribution of measurement points on the target is usually biased towards the radar direction, the predicted value of the target's skew constraint vector can be obtained. When the position components of the target's posterior estimated state are obtained , Then, the posterior estimate of the target skew constraint vector can be obtained: .

[0120] (3) When the target has complex motion states and measurement conditions, consider a jumping Markov system to remodel the target's motion state model and measurement model, such as... Figure 2 The simulation scenario described involves a sensor monitoring an area near an intersection. Vehicles can enter the monitored area from points P1, P2, P3, and P4, travel straight on L1, L2, L3, and L4 respectively, and then proceed straight, turn right, or turn left at the intersection. For example, the vehicle shown in the diagram enters the area from P1, goes directly to L1, and then may turn left with a 1 / 3 probability.

[0121] The motion state model of the target vehicle is remodeled:

[0122] When the target is moving straight or turning, the vehicle's motion is described by a near-constant speed model or a constant turning model: The state transition matrix for the vehicle's constant-speed motion model is:

[0123] The constant turning model of the vehicle is:

[0124] where , is the sampling interval time step, represents different steering angular velocities:

[0125] The process noise is:

[0126] The measurement model of the target is re-modeled: assuming that the near end of the vehicle closer to the sensor produces more measurement values than the far end, the measurement noise is:

[0127] For , if the vehicle is driving straight on L1 and L4 (L2 and L3), then , denoted as D1 (D2); if the vehicle is turning, then , denoted as D3.

[0128] When a target maneuvers, all its dynamic models, extended models and measurement models can change. For example, if the vehicle shown in Figure 2 moves from L1 to L2, its dynamic mode sequence is {F1, F2, F1}, its measurement mode sequence is {D1, D3, D2}, and the algorithm establishes four modes:

[0129] Again, the weighted KLA is used to approximate the prior probability density function and to obtain the optimal solution, at time , the prior estimates of the motion state, the extended shape and the measurement bias variable of the target in the th mode are obtained: .

[0130] (4) Based on the motion state, the measurement distribution model and the prior probability density of the four modes, at time , the posterior probability density of the th mode is obtained by the variational Bayesian algorithm , and according to the Bayesian rule and the total probability theorem, the mode probability of the th mode is updated using the predicted mode probability of each mode and the likelihood function. ​

[0131] (5) Based on the time Modal probability of each mode and the posterior probability density obtained therefrom This allows us to obtain the overall probability density function. By using a weighted KLA approximation, the final estimate of the motion state and extended form is obtained.

[0132] As shown in Figure 4(a), in the case of Figure 2 The simulation scenario shown illustrates that when the target vehicle moves, all motion states, extensions, and measurement distributions (especially skewness) may undergo abrupt changes, resulting in complex motion states and measurement conditions for the target. The VB-EOT-SN algorithm, optimized within the IT-IMM framework and incorporating a skewness-based random matrix, is executed, and its tracking performance is compared with other commonly used algorithms. Using Wasserstein distance as the final evaluation metric, the Wasserstein distance is lower than other algorithms for most of the time, roughly within the range of 0s-8s and 11s-25s. Furthermore, its average tracking estimation accuracy is good, demonstrating excellent tracking performance even when multiple motion states exist at the target location and the target's dynamics and measurements are complex.

[0133] As shown in Figure 4(b), based on the measured data of Scenario 1, under the target tracking situation shown in Figure 3(a), the extended target tracking algorithm with skewness random matrix VB-EOT-SN is executed and its tracking performance is compared with other commonly used algorithms. The Wasserstein distance is used as the final evaluation index. At most times, in the approximate range of 5s-8s, 10s-34s, and 36s-40s, the Wasserstein distance is lower than that of other algorithms, and its average tracking estimation accuracy is good. It has excellent tracking performance when tracking the target vehicle in a straight line with slight turning.

[0134] As shown in Figure 4(c), based on the measured data of Scenario 2, under the target tracking situation shown in Figure 3(b), the extended target tracking algorithm with skewness random matrix VB-EOT-SN is executed and its tracking performance is compared with other commonly used algorithms. The Wasserstein distance is used as the final evaluation index. At most times, in the approximate range of 0s-5s, 7s-12s, and 12.5s-13.5s, the Wasserstein distance is lower than that of other algorithms, and its average tracking estimation accuracy is good. It has excellent tracking performance when tracking the turning motion of the target vehicle.

[0135] The above experimental results verify that the present invention improves the accuracy of target tracking and achieves accurate identification of targets with multiple motion characteristics, complex motion states, and measurement conditions, which has significant theoretical and practical value.

[0136] The present application is not limited to the above-mentioned embodiments, and on the basis of the technical solutions disclosed in the present application, those skilled in the art can make some substitutions and modifications to some technical features without creative labor on the basis of the disclosed technical content, and these substitutions and modifications are all within the protection scope of the present application.

Claims

1. A method for extended object tracking using random matrix and skew-normal distribution, characterized in that, Comprise: Establishing evolution model and measurement model of skew-normal distribution according to target motion state and extended shape respectively; Using target motion state and extended shape to combine evolution model to make prior prediction of target motion state, extended shape and measurement skew variable; Using variational Bayesian method to recursively update to obtain posterior estimation of target motion state, extended shape and measurement skew variable and skew constraint vector estimation value; Based on IT-IMM framework, re-modeling evolution model of target motion state and extended shape and measurement model of skew-normal distribution: Using weighted KLA algorithm to obtain optimal solution of prior probability density function of target motion state, extended shape and measurement skew variable; Based on prior probability density function of target motion state, extended shape and measurement skew variable, using variational Bayesian algorithm to obtain posterior probability density of corresponding mode to update mode probability; According to each updated mode probability and posterior probability density, using weighted KLA approximation to obtain final estimation of target motion state and extended shape.

2. The method of extended target tracking using random matrices and the power-normal distribution according to claim 1, characterized in that, Establishing evolution model and measurement model of skew-normal distribution according to target motion state and extended shape respectively, comprising: Determining evolution of target motion state through state transition matrix and Gaussian noise; Determining evolution distribution of extended shape through Wishart distribution to obtain evolution model; Based on skew-normal distribution, establishing measurement model to represent asymmetric distribution of radar measurement on target.

3. The method of extended target tracking using random matrices and the power-normal distribution according to claim 2, characterized in that, Evolution model is: wherein, is a random matrix, is a degree of freedom, is a scale matrix, is a normalization constant, is a dimension of the physical space; Measurement model is: wherein, is a radar measurement, is is a known measurement matrix of dimension N x M, is the target motion state at the current time instant, is a measurement noise that is subject to a skewed Gaussian distribution, is a measurement point, is the number of measurement points.

4. The method of extended target tracking using random matrices and the power-normal distribution according to claim 1, characterized in that, Obtaining posterior estimation of target motion state, extended shape and measurement skew variable and skew constraint vector estimation value, comprising: right Hypotheses are made regarding the motion state at any given time, the expansion pattern, and the posterior joint distribution density of the skewed variables; Making prior prediction of state variable, extended shape and measurement skew variable; Making posterior estimation of measurement skew variable through variational Bayesian algorithm; Obtaining target distribution deviating to measurement point of radar direction to obtain predicted value of target skew constraint vector and then obtaining posterior estimation value of target skew constraint vector.

5. The method of extended target tracking using random matrices and the power-normal distribution according to claim 4, characterized in that, Making posterior estimation of measurement skew variable through variational Bayesian algorithm, comprising: Using variational Bayesian method to multiply distribution functions of motion state, extended shape and measurement skew variable to approximate real joint distribution density: Obtaining optimal solution of estimation variable distribution function; Through variational Bayesian algorithm, iteratively estimating distribution parameters of target motion state, extended shape and measurement skew variable, substituting joint distribution probability density function into optimal solution of estimation variable distribution function and combining obtained measurement data to obtain posterior estimation value.

6. The method of extended target tracking using random matrices and the power-normal distribution according to claim 5, characterized in that, Posterior estimation of target motion state is as follows: wherein, is a position component of a target posterior estimate state, is a current time motion state posterior estimate, is a radar measurement point mean, is a is a known measurement matrix of dimension, is a skew constraint variable, is a posterior skew variable, is a Kalman gain, is a target motion state posterior estimate covariance matrix, is a target motion state prior estimate covariance matrix; Posterior estimation of extended shape is: wherein, is a posteriori degree of freedom, is a priori degree of freedom, is a posteriori extended shape matrix, is a priori extended shape matrix, is an inverse of the extended shape measurement matrix, is a number of measurement points at the current time, is a combined bias matrix, is a measurement bias covariance matrix; Posterior estimation of measurement skew variable is: wherein and are the posterior mean and variance of the bias variable, is the prior mean of the truncated normal distribution, is the prior variance of the truncated normal distribution, is the measurement weight coefficient.

7. The method of extended target tracking using random matrices and the power-normal distribution of claim 1, wherein, Using weighted KLA algorithm to obtain optimal solution of prior probability density function of target motion state, extended shape and measurement skew variable, comprising: When target maneuvers, using IT-IMM framework to process mutation of target motion state, extended shape and measurement distribution, establishing a group of dynamic models at the same time k; Reconstruct the posterior joint distribution density function of the i th model at time k, which contains the distribution parameter assumptions of the target motion state, extended shape and measurement bias variables; Reinitialize the evolution model of the target motion state and extended shape and the measurement model at time k using the total probability theorem: Based on the posterior probability of each model at the last time and the transition probability between models, calculate the mixing weight of the i th model at the current time, integrate the posterior distribution of each model at the last time through the mixing weight, and complete the prior distribution initialization of the current model; Approximate the initialized multi-model mixed prior distribution to a single modal distribution through the weighted KLA algorithm to obtain the optimal solution of the prior probability density function of the target motion state, extended shape and measurement bias variable.

8. The method of extended target tracking using random matrices and the power-normal distribution according to claim 1, characterized in that, The variational Bayesian algorithm obtains the posterior probability density corresponding to the modal, updates the modal probability, including: For the first The motion state model, measurement distribution model, and prior probability density of the ... The posterior probability density of each modality; update the modality probability of the first modality according to the Bayes rule and the total probability theorem. update the modality probability of the first modality according to the Bayes rule and the total probability theorem.

9. The method of extended target tracking using random matrices and the power-normal distribution according to claim 1, characterized in that, According to each updated modal probability and the posterior probability density, the final estimate of the target motion state and the extended shape is obtained through the weighted KLA approximation, including: According to the modal probability of each modal and the obtained posterior probability density, the total probability density function is obtained by summation; Through the weighted KLA method, the final estimate of the motion state and the extended shape is obtained.

10. A method for extended target tracking using random matrices and skew normal distribution according to any one of claims 1-9 is applied in military reconnaissance, unmanned aerial vehicle management, and extended target identification and tracking of road traffic.

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