A target track clustering and fitting method and system suitable for multiple motion patterns

Abstract

The application relates to the technical field of target trajectory, in particular to a target track clustering and fitting method and system suitable for multiple motion modes, which comprises the following steps: constructing a point track data set; establishing a unified vector motion state model suitable for uniform straight line motion, uniform acceleration straight line motion and uniform turning motion; introducing a hidden random variable representing the point track and target attribution relationship based on the unified vector motion state model, and establishing a mixed Gaussian track statistical model; iteratively solving the mixed Gaussian track statistical model by using an expectation maximization algorithm, jointly updating a target unknown parameter set and the posterior probability of each point track measurement data belonging to each target until a preset convergence condition is met, obtaining an optimal joint estimation result of the unknown parameter set, and completing multi-target track fitting; and determining the target category according to the maximum posterior probability of each point track measurement data, and completing multi-target track clustering. The application unifies multiple motion modeling, and realizes high-precision clustering and fitting of target tracks.

Description

Technical Field

[0001] This application relates to the field of target trajectory technology, and in particular to a target trajectory clustering fitting method and system applicable to multiple motion modes. Background Technology

[0002] In recent years, with the development of underwater detection equipment and underwater acoustic processing technology, the ability to monitor and track targets in complex marine environments has been significantly improved, and massive amounts of trajectory data have been successfully acquired. Underwater target trajectory monitoring systems are divided into centralized and distributed modes. Centralized systems involve multiple sensors directly transmitting raw observation data to a fusion center for final decision-making. While this preserves complete data information, it results in a large backend processing load and low fault tolerance. Distributed systems can alleviate transmission pressure and central computing load through local preprocessing, becoming the mainstream technology for multi-target trajectory information fusion. However, distributed systems still have certain performance limitations: the decision-making ability of the fusion center is constrained by local preprocessing capabilities. Research shows that preliminary data clustering can not only pre-identify target motion patterns and corresponding measurement information within the monitoring area, but also serve as input for tracking algorithms to support subsequent trajectory iteration updates, reducing additional data association calculations and significantly reducing the computational overhead of multi-target tracking.

[0003] Currently, existing track clustering methods are mainly based on the assumption of uniform linear motion and lack the ability to estimate motion state parameters and fit trajectories, making it difficult to meet the needs of track analysis in complex scenarios.

[0004] To address the problem of multi-target trajectory clustering and fitting based on an underwater distributed target trajectory monitoring system, Chinese patent application No. 202410233766.8 proposes a "multi-target trajectory clustering method and system based on expectation maximization". This method uses the latent variable model (LVM) and expectation maximization (EM) algorithm to design a clustering scheme. By linearly modeling each navigation trajectory, the latent variable model is used to establish the mapping relationship between each point and its corresponding navigation trajectory. The measurement values ​​of multiple target points are processed in batches through EM iteration, transforming the clustering problem into the probability estimation of the distribution of the sample's category.

[0005] However, existing technical solutions use linear motion models when modeling motion, without taking into account maneuvering motions such as target acceleration and turning. By linearly modeling each navigation trajectory, multiple linear motion tracks are clustered and fitted. However, the navigation assumptions of this method for linear motion have a large gap with the actual maneuvering model of maritime targets, and cannot be adapted to the target trajectory under the actual multi-motion model. Summary of the Invention

[0006] The purpose of this application is to overcome the above-mentioned deficiencies of the prior art and to provide a target trajectory clustering fitting method and system suitable for multiple motion modes, addressing the preprocessing requirements of multi-target trajectory clustering in distributed trajectory monitoring systems.

[0007] To address the aforementioned technical problems, the technical solution provided in this application offers a target trajectory clustering and fitting method applicable to multiple motion modes, comprising: Step 1: Obtain the point trace measurement data of multiple targets within the monitoring area and construct the point trace dataset; Step 2: Establish a unified vector motion state model applicable to uniform linear motion, uniformly accelerated linear motion, and uniform turning motion, wherein the state transition relationship of uniform turning motion is expanded using a second-order Taylor expansion. Step 3: Based on the unified vector motion state model, a hidden random variable representing the relationship between the point trace and the target is introduced to establish a mixture Gaussian trajectory statistical model; Step 4: The Gaussian mixture trajectory statistical model is iteratively solved using the expectation-maximization algorithm. The set of unknown parameters of the target and the posterior probability of each point trace measurement data belonging to each target are jointly updated until the preset convergence condition is met, and the optimal joint estimation result of the set of unknown parameters is obtained, thus completing the multi-target trajectory fitting. The set of unknown parameters includes the initial trajectory coordinates, motion parameter matrix, noise covariance matrix and target class probability. Step 5: Determine the target category based on the maximum posterior probability corresponding to each point trace measurement data, and complete the multi-target track clustering.

[0008] As an improvement to the above technical solution, step 2 includes: Step 2.1: Establish the recursive relationship of the target coordinates: ; in, For the first A coordinate vector, For the first A coordinate vector, Let it be the first unknown motion parameter vector containing the target velocity, target heading, target angular velocity, and target acceleration; Let it be a second unknown motion parameter vector containing the target velocity, target heading, target angular velocity, and target acceleration. For time intervals; Step 2.2: For uniform turning motion, when the sampling time interval is less than a preset time interval threshold and the target turning angular velocity is less than a preset target turning angular velocity threshold, perform a second-order Taylor expansion on the state transition relationship to obtain: ; in, For the first The x-axis coordinates of the point trace measurement data For the first The x-axis coordinates of the point trace measurement data For the target speed, For the course, For turning angular velocity, For the first The y-axis coordinates of the point trace measurement data For the first The y-axis coordinates of the point trace measurement data; Step 2.3: Further establish the unified vector state equation: ; in, Let be the target motion parameter matrix. , This represents finding the inverse of a matrix. These are the initial trajectory coordinates. , Indicates the first The motion time corresponding to each point trace measurement data , , This represents the total number of dot measurement data.

[0009] As an improvement to the above technical solution, step 3 includes: Step 3.1: Introduce hidden random variables , used to indicate the first The probability mass function of the target category to which each point trace measurement data belongs. Represented as: ; in, Indicates the first The number of dot measurement data belongs to the first The probability of each objective, satisfying the normalization constraint. , The target total number; Step 3.2: Establish a statistical model of the target trajectory: ; in, Indicates a Gaussian distribution. For the target index, Indicates the first The initial coordinates corresponding to each target Indicates the first The motion parameter matrix corresponding to each target Indicates the first The noise covariance matrix corresponding to each target; Step 3.3: Establish a Gaussian mixture trajectory statistical model : ; in, This represents a matrix of dot measurement data. Represents a set of unknown parameters. Let be the conditional probability density function; where, ; in, For the first Unknown parameters corresponding to each target Indicates the first The number of dot measurement data belongs to the first The probability of a target; ; in, To measure noise, , Represents matrix determinant operations. Represents finding the trace of a matrix. This indicates exponentiation.

[0010] As an improvement to the above technical solution, step 4 includes EM iteration; wherein, step 4 includes: Step 4.1: Obtain initial estimates of the set of unknown parameters; Step 4.2: In the E-step solution, the joint log-likelihood function of the point trace measurement data is solved using Jensen's inequality, and the posterior probability is updated; Step 4.3: In the M-step solution, maximize the lower boundary function, and based on the updated posterior probability, perform joint estimation of the set of unknown parameters to obtain the updated set of unknown parameters; Step 4.4: Update the lower boundary function in the E-step solution using the updated set of unknown parameters, and repeat steps 4.2 to 4.3 until the preset convergence condition is met, and obtain the optimal joint estimation result of the set of unknown parameters.

[0011] As an improvement to the above technical solution, step 4.2 includes: In the E-step solution, according to the first... The set of unknown parameters obtained in the next iteration is used to calculate the posterior probability that the measurement data of each point belongs to each target: ; in, For the first The estimation result of the posterior probability in the next iteration. For the first The estimation results of the unknown parameter set in the next iteration. For the first The second iteration The number of dot measurement data belongs to the first The probability estimation results of each target; Step 4.3 includes: in the M-step solution, based on The unknown parameter set is solved by maximizing the joint log-likelihood function. The optimal estimate, maximizing the joint log-likelihood function, is expressed as:

[0012] in, Indicates Logarithmic operations with base 0; Based on maximizing the joint log-likelihood function, the initial trajectory coordinates, motion parameter matrix, noise covariance matrix, and target class probability of the unknown parameter set are jointly updated.

[0013] As an improvement to the above technical solution, the joint update of the initial trajectory coordinates, motion parameter matrix, noise covariance matrix, and target category probability specifically includes: The target category probability is updated as follows: ; in, For the first The iteration of the ... The number of dot measurement data belongs to the first The probability estimation results of each target; The noise covariance matrix is ​​updated as follows:

[0014] in, For the first The iteration of the ... The estimation results of the noise covariance matrix corresponding to each target; The value is the result of a mathematical calculation. ; The motion parameter matrix is ​​updated as follows: ; in, For the first The iteration of the ... The estimation results of the motion parameter matrix corresponding to each target; Set the following process values: First process value : ; Second process value : ; Third process value : ; Fourth process value : ; Fifth process value : ; Sixth process value : ; Seventh process value : ; Eighth process value : ; The initial trajectory coordinates are updated as follows: ; Obtain the set of unknown parameters In the The joint estimation results of the next iteration: .

[0015] As an improvement to the above technical solution, step 5 includes: for each point measurement data, calculating its posterior probability of belonging to each target, selecting the target category corresponding to the maximum posterior probability as the target to which the point measurement data belongs, and clustering the point measurement data belonging to the same target category to obtain the trajectory fitting result corresponding to each target.

[0016] To achieve another objective of the present invention, the present invention also provides a target trajectory clustering and fitting system suitable for multiple motion modes, for implementing the above-mentioned target trajectory clustering and fitting method suitable for multiple motion modes, comprising: The dataset module is used to acquire point trace measurement data of multiple targets within the monitoring area and construct a point trace dataset; The motion modeling module is used to establish a unified vector motion state model applicable to uniform linear motion, uniformly accelerated linear motion, and uniform turning motion. Among them, the state transition relationship of uniform turning motion is performed by a second-order Taylor expansion. The statistical modeling module is used to establish a mixture Gaussian trajectory statistical model based on the unified vector motion state model by introducing hidden random variables that represent the relationship between point traces and target attribution. The parameter estimation module is used to iteratively solve the Gaussian mixture trajectory statistical model using the expectation-maximization algorithm, jointly updating the set of unknown parameters and the posterior probability of each point's trace measurement data belonging to each target, until a preset convergence condition is met, obtaining the optimal joint estimation result of the unknown parameter set, and completing multi-target trajectory fitting; wherein, the set of unknown parameters includes initial trajectory coordinates, motion parameter matrix, noise covariance matrix, and target class probability; and The track clustering module is used to determine the target category based on the maximum posterior probability corresponding to each track measurement data, thus completing multi-target track clustering.

[0017] The advantages of this application lie in its target trajectory clustering and fitting method and system applicable to multiple motion modes. Based on LVM and EM iterative algorithms, it constructs a vector state and statistical model that can uniformly describe uniform linear motion, uniformly accelerated linear motion, and uniform turning motion. It completes the analytical derivation of motion state parameters, measurement-target latent correlation variables, and posterior probabilities, breaking through the constraint that existing EM clustering methods are only applicable to linear motion, and further adapting to the real motion laws of maneuvering targets at sea. Simulation results show that compared with the two classic clustering algorithms, KNN and K-means, the proposed method has better clustering performance in scenarios with trajectory intersections and measurement noise interference, while also achieving good multi-target trajectory fitting. The algorithm output can serve as a pre-input for complex tracking frameworks, providing reliable prior information for multi-target trajectory prediction and motion behavior law analysis. Attached Figure Description

[0018] Figure 1(a) shows the actual dots from a single Monte Carlo test; Figure 1(b) shows the trajectory clustering results of the method in this application under a single Monte Carlo test; Figure 1(c) shows the trajectory clustering results of the KNN algorithm in a single Monte Carlo experiment; Figure 1(d) shows the trajectory clustering results of the K-means algorithm in a single Monte Carlo trial; Figure 2 A comparison chart showing the average classification errors of the proposed method, KNN algorithm, and K-means algorithm for each target point; Figure 3(a) shows the estimated values. Normalized root mean square error (NRMSE) plot relative to the true value; Figure 3(b) is Normalized root mean square error (NRMSE) plot relative to the true value; Figure 4 A flowchart of the target trajectory clustering fitting method applicable to multiple motion modes provided in this application. Detailed Implementation

[0019] The technical solutions provided in this application are further illustrated below with reference to the embodiments.

[0020] This application addresses the shortcomings of existing research by focusing on the clustering preprocessing problem in distributed trajectory monitoring systems, and proposes a trajectory clustering fitting method adapted to multiple motion modes. For example... Figure 4 As shown, this method is based on the theoretical framework of LVM and EM algorithms. It combines multiple target motion equations to complete model reconstruction, extending the existing trajectory representation paradigm based on straight-line equations to adapt to various maneuvering motion modes such as uniform linear motion, uniformly accelerated linear motion, and uniform turning motion. A unified vector state equation is constructed based on second-order Taylor expansion. Finally, the analytical derivation of trajectory motion parameters is completed by combining the EM iterative estimation process, realizing the joint optimization of target trajectory clustering and motion fitting. This method better reflects the actual motion characteristics of maritime targets and has strong application prospects.

[0021] 1. Scene statistical modeling An underwater distributed target trajectory monitoring system deploys K sensors within the same monitoring area to detect and track L moving targets. After initial detection, each sensor outputs target distance and orientation information, which is then converted into point measurement data in a Cartesian coordinate system. Within a preset time window, the system collects data from a total of L targets. Each point measurement data is indexed using a universal integer sequence number, denoted as . (1) in, For measuring datasets, This represents the x-axis coordinate of the first point measurement data in the Cartesian coordinate system. This represents the y-axis coordinate of the first point measurement data in the Cartesian coordinate system. This represents the x-axis coordinate of the second point measurement data in the Cartesian coordinate system. This represents the y-axis coordinate of the second point measurement data in the Cartesian coordinate system. Represents the first in the Cartesian coordinate system The x-axis coordinates of the point trace measurement data Represents the first in the Cartesian coordinate system The y-axis coordinates of the point trace measurement data This represents the total number of dot measurement data.

[0022] Consider three typical motion modes: uniform linear motion (CV), uniformly accelerated linear motion (CA), and uniform turning motion (CT). The coordinate recursion relationship for each motion model can be uniformly expressed as a function of time intervals. The second-order polynomial equations, and the recursive relationship of the basic coordinates of each motion model are as follows: (2) In the formula, Indicates the first A coordinate vector, , Indicates the first A coordinate vector, , Let the first unknown motion parameter vector contain the target velocity, target heading, target angular velocity, and target acceleration. ; Let it be a second unknown motion parameter vector containing the target velocity, target heading, target angular velocity, and target acceleration. ; This represents finding the inverse of a matrix. Represents the real number field.

[0023] In the uniform-speed turning CT model, the target heading has time-varying characteristics, and the target coordinates have a trigonometric function relationship with time. The state transition cannot be expressed as a vector product of state vectors, making it impossible to obtain a closed-form solution for the motion parameters by maximizing the expected log-likelihood. To address this problem, this application adopts a small-angle approximation strategy. That is, under the conditions of short sampling interval and small turning angular velocity, the trigonometric function state transition relationship is expanded by a second-order Taylor series according to the time variable, realizing the approximate transformation of the original nonlinear recursive relationship into a polynomial form. Therefore, the basic coordinate recursive relationship provided by equation (2) can be rewritten as: (3) in, For the first The x-axis coordinates of the point trace measurement data For the first The x-axis coordinates of the point trace measurement data For the target speed, For the course, For turning angular velocity, For the first The y-axis coordinates of the point trace measurement data For the first The y-axis coordinates of the point trace measurement data.

[0024] This is further transformed into a description of the target trajectory changing over time. The relationship between the target trajectory and time is as follows: (4) In the formula, Let be the target motion parameter matrix. ; These are the initial trajectory coordinates. , Indicates the first The motion time corresponding to each point trace measurement data .

[0025] 2. Algorithm Design The main design idea of ​​this application is as follows: to complete the model reconstruction by combining multiple target motion equations, to introduce latent random variables using LVM, to establish the correlation representation between trajectory measurement and moving target, and to complete the analytical derivation of trajectory motion parameters by combining the EM iterative estimation process, thereby realizing the joint optimization of target trajectory clustering and motion fitting.

[0026] 2.1 LVM Modeling set up The n independent and identically distributed latent random variables, the nth The latent random variable of the trace measurement data is , , The probability mass function is , , Characterizing the first The number of dot measurement data belongs to the first The probability of a target. Satisfy normalization constraints Considering error factors such as environmental noise, external signal interference, and sensor positioning deviation, it is assumed that the measurement noise follows a zero-mean Gaussian distribution, and its covariance matrix is ​​set as follows. , represented as: (5) In the formula, Indicates a Gaussian distribution. For the target index, Indicates the first The initial coordinates corresponding to each target Indicates the first The motion parameter matrix corresponding to each target Indicates the first The noise covariance matrix corresponding to each target.

[0027] The dot measurement data is modeled as a Gaussian mixture distribution based on a predefined category weighting to obtain the Gaussian mixture distribution. : (6) In the formula, This represents a matrix of dot measurement data. , This represents the first measured coordinate data / vector. Indicates the first N One measurement coordinate data / vector, Represents the set of all unknown parameters. , For the first Unknown parameters corresponding to each target , for The conditional probability density function is expressed as: (7) In the formula, To measure noise, , Represents matrix determinant operations. Represents finding the trace of a matrix. This indicates exponentiation.

[0028] 2.2 EM Estimation Process The E-step uses Jensen's inequality to solve for the latent variables. The posterior probability distribution is obtained to obtain the posterior probability. The iterative update expression is: (8) In the formula, For the first The estimation result of the posterior probability in the next iteration. For the first The estimation results of the unknown parameter set in the next iteration. For the first The second iteration The number of dot measurement data belongs to the first The estimated probability of each target.

[0029] Based on the E-step estimation results, the M-step solves for the unknown parameters by maximizing the joint log-likelihood function. The optimal estimation is expressed by the objective function as: (9) in, Indicates Logarithmic operations with base 0.

[0030] Known The objective function is expressed as: (10) Due to trajectory state parameters and probability parameters The maximization estimates are decoupled from each other and can be decomposed into independent parameter optimization problems. First, the Lagrange multiplier method is used to estimate... Obtain probability parameters No. Sub-iteration estimation : (11) Remove parameter-independent terms and solve. and The joint maximization estimate is obtained. (12) in, For the first The second iteration The noise covariance matrix of each target trajectory. This is an intermediate mathematical calculation process, without any special meaning. .

[0031] Will First substitute equation 7, then substitute equation (10) to find the answer regarding... The partial derivative of is obtained to get the first Motion parameter matrix corresponding to each target The The maximization estimation result of the second iteration : (13) To facilitate subsequent derivation, let First process value ; Second process value ; Third process value ; Get the first Initial coordinates of each target In the The maximization estimation expression for the next iteration is: (14) In the formula: (15) This completes the set of unknown parameters. In the The joint estimate in the next iteration is expressed as: .

[0032] Will In Substituting into equation (5), the target motion trajectory is obtained by fitting, and the corresponding coordinate of the nth coordinate is also calculated. Find {1,…, Find the maximum value among the nth elements to determine if the nth coordinate belongs to the nth element. The goal is to complete trajectory classification / clustering.

[0033] Algorithm Flow

[0034] 3. Simulation Analysis Consider a distributed target trajectory monitoring system that collects raw measurement data of all targets, integrates the measurement values ​​of each target point into the same Cartesian coordinate system, and has a sample size of [number missing]. obey The targets are uniformly distributed within the target area. They move randomly in one or more patterns, including CV, CA, or turning, and there are instances of multiple target tracks intersecting. To simulate measurement disturbances and sample mixing caused by environmental noise, signal interference, and positioning errors, Gaussian white noise with a mean of 0 and a standard deviation of 25 is superimposed on the original target coordinates. Monte Carlo simulation experiments are used to verify the iterative convergence, classification effectiveness, and parameter estimation performance of the proposed method. To visually demonstrate the clustering advantages of the proposed method, we introduce the classic supervised and unsupervised clustering methods KNN and K-means from the machine learning field as comparisons. Considering the number of targets... The motion parameters are shown in Table 1.

[0035] Table 1: Target motion parameter settings

[0036] The following section compares the clustering performance of the proposed method with that of the KNN and K-means methods in three aspects: the clustering results of the points in the Cartesian coordinate system, the average classification error of each target, and the overall average classification accuracy. Specifically, Figures 1(b)-1(d) show the trajectory clustering results of the proposed method and the comparison methods under a single Monte Carlo experiment (L=3). The results show that, compared with the original target points in Figure 1(a), the proposed method (Figure 1(b)) achieves the most accurate sample clustering. In addition, Figure 1(b) also shows the target motion fitting results of the proposed method, which perfectly matches the given measurement values, while the KNN and K-means methods themselves do not have the ability to estimate target motion parameters. Figure 2 The average classification error of the three methods for each target point was calculated in 300 independent trials. The results showed that the average classification error of the proposed method for each target point was significantly lower than that of the two comparative methods.

[0037] To evaluate the effect of the proposed method on various trajectory motion parameters and The estimation accuracy is shown in Figures 3(a) and 3(b), which respectively illustrate the estimated values. and The normalized root mean square error (NRMSE) relative to the true value. The results show that the proposed method can achieve accurate parameter estimation when the noise standard deviation is 0. As the noise standard deviation increases, the parameter NRMSE value shows an increasing trend. Target 2 and Target 3 correspond to the low-speed CA and CT approximation models, respectively. Compared with the conventional CV model of Target 1, the estimation error is higher than that of Target 1 due to the influence of path overlap and model complexity.

[0038] As can be seen from the above detailed description of this application, (1) This application addresses the multi-target trajectory clustering requirements of distributed trajectory monitoring systems and proposes a target trajectory clustering fitting method that adapts to multiple maneuvering modes. The proposed method breaks through the constraint that the existing EM clustering method is only applicable to linear motion and adds multiple motion modes such as acceleration and turning, further adapting to the real motion scenarios of maneuvering targets at sea.

[0039] (2) This application adopts a small-angle approximation strategy to appropriately simplify the CT model. Under the conditions of short sampling interval and small turning angular velocity, the trigonometric function state transition relationship is expanded by second-order Taylor according to the time variable, so as to realize the approximate representation of the original nonlinear recursive relationship in polynomial form.

[0040] (3) This application extends the trajectory representation paradigm based on the linear equation to adapt to various maneuvering motion modes such as uniform linear motion, uniformly accelerated linear motion and uniform turning motion, and constructs a unified vector state equation.

[0041] (4) Based on the EM algorithm and LVM model, this application completes the analytical derivation of motion state parameters, measurement-target latent correlation variables and posterior probabilities. It can jointly realize multi-target trajectory clustering, fitting and motion parameter estimation, and achieve a breakthrough in the applicable scenarios and capabilities of clustering.

[0042] (5 This application uses K-means clustering combined with least squares fitting to estimate the initial parameters for EM cyclic initialization. First, K-means clustering is used to initially separate the spatial trajectories, and then least squares fitting is performed on each cluster to obtain the trajectory initialization parameters, ensuring the robustness of subsequent EM clustering.

[0043] (6) In the M-step estimation of the EM iteration in this application, based on the determinant-trace inequality principle, the original determinant optimization problem can be transformed into a matrix trace form that is easy to solve, thereby realizing the joint optimization of motion parameters and deriving the analytical expression. Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application and are not intended to limit it. Although this application has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of this application do not depart from the spirit and scope of the technical solutions of this application, and should all be covered within the scope of the claims of this application.

Claims

1. A target trajectory clustering and fitting method applicable to multiple motion modes, comprising: Step 1: Obtain the point trace measurement data of multiple targets within the monitoring area and construct the point trace dataset; Step 2: Establish a unified vector motion state model applicable to uniform linear motion, uniformly accelerated linear motion, and uniform turning motion, wherein the state transition relationship of uniform turning motion is expanded using a second-order Taylor expansion. Step 3: Based on the unified vector motion state model, a hidden random variable representing the relationship between the point trace and the target is introduced to establish a mixture Gaussian trajectory statistical model; Step 4: The Gaussian mixture trajectory statistical model is iteratively solved using the expectation-maximization algorithm. The set of unknown parameters of the target and the posterior probability of each point trace measurement data belonging to each target are jointly updated until the preset convergence condition is met, and the optimal joint estimation result of the set of unknown parameters is obtained, thus completing the multi-target trajectory fitting. The set of unknown parameters includes the initial trajectory coordinates, motion parameter matrix, noise covariance matrix and target class probability. Step 5: Determine the target category based on the maximum posterior probability corresponding to each point trace measurement data, and complete the multi-target track clustering.

2. The target trajectory clustering and fitting method applicable to multiple motion modes according to claim 1, characterized in that, Step 2 includes: Step 2.1: Establish the recursive relationship of the target coordinates: ； in, For the first A coordinate vector, For the first A coordinate vector, Let it be the first unknown motion parameter vector containing the target velocity, target heading, target angular velocity, and target acceleration; Let it be a second unknown motion parameter vector containing the target velocity, target heading, target angular velocity, and target acceleration. For time intervals; Step 2.2: For uniform turning motion, when the sampling time interval is less than a preset time interval threshold and the target turning angular velocity is less than a preset target turning angular velocity threshold, perform a second-order Taylor expansion on the state transition relationship to obtain: ； in, For the first The x-axis coordinates of the point trace measurement data For the first The x-axis coordinates of the point trace measurement data For the target speed, For the course, For turning angular velocity, For the first The y-axis coordinates of the point trace measurement data For the first The y-axis coordinates of the point trace measurement data; Step 2.3: Further establish the unified vector state equation: ； in, Let be the target motion parameter matrix. , This represents finding the inverse of a matrix. These are the initial trajectory coordinates. , Indicates the first The motion time corresponding to each point trace measurement data , , This represents the total number of dot measurement data.

3. The target trajectory clustering and fitting method applicable to multiple motion modes according to claim 2, characterized in that, Step 3 includes: Step 3.1: Introduce hidden random variables , used to indicate the first The probability mass function of the target category to which each point trace measurement data belongs. Represented as: ； in, Indicates the first The number of dot measurement data belongs to the first The probability of each objective, satisfying the normalization constraint. , The target total number; Step 3.2: Establish a statistical model of the target trajectory: ； in, Indicates a Gaussian distribution. For the target index, Indicates the first The initial coordinates corresponding to each target Indicates the first The motion parameter matrix corresponding to each target Indicates the first The noise covariance matrix corresponding to each target; Step 3.3: Establish a Gaussian mixture trajectory statistical model : ； in, This represents a matrix of dot measurement data. Represents a set of unknown parameters. Let be the conditional probability density function; where, ； in, For the first Unknown parameters corresponding to each target Indicates the first The number of dot measurement data belongs to the first The probability of a target; ； in, To measure noise, , Represents matrix determinant operations. Represents finding the trace of a matrix. This indicates exponentiation.

4. The target trajectory clustering and fitting method applicable to multiple motion modes according to claim 3, characterized in that, In step 4, the iteration includes EM iteration; wherein, step 4 includes: Step 4.1: Obtain initial estimates of the set of unknown parameters; Step 4.2: In the E-step solution, the joint log-likelihood function of the point trace measurement data is solved using Jensen's inequality, and the posterior probability is updated; Step 4.3: In the M-step solution, maximize the lower boundary function, and based on the updated posterior probability, perform joint estimation of the set of unknown parameters to obtain the updated set of unknown parameters; Step 4.4: Update the lower boundary function in the E-step solution using the updated set of unknown parameters, and repeat steps 4.2 to 4.3 until the preset convergence condition is met, and obtain the optimal joint estimation result of the set of unknown parameters.

5. The target trajectory clustering and fitting method applicable to multiple motion modes according to claim 4, characterized in that, Step 4.2 includes: In the E-step solution, according to the first... The set of unknown parameters obtained in the next iteration is used to calculate the posterior probability that the measurement data of each point belongs to each target: ； in, For the first The estimation result of the posterior probability in the next iteration. For the first The estimation results of the unknown parameter set in the next iteration. For the first The second iteration The number of dot measurement data belongs to the first The probability estimation results of each target; Step 4.3 includes: in the M-step solution, based on The unknown parameter set is solved by maximizing the joint log-likelihood function. The optimal estimate, maximizing the joint log-likelihood function, is expressed as: in, Indicated by Logarithmic operations with base 0; Based on maximizing the joint log-likelihood function, the initial trajectory coordinates, motion parameter matrix, noise covariance matrix, and target class probability of the unknown parameter set are jointly updated.

6. The target trajectory clustering and fitting method applicable to multiple motion modes according to claim 5, characterized in that, The joint update of the initial trajectory coordinates, motion parameter matrix, noise covariance matrix, and target class probability specifically includes: The target category probability is updated as follows: ； in, For the first The iteration of the ... The number of dot measurement data belongs to the first The probability estimation results of each target; The noise covariance matrix is ​​updated as follows: in, For the first The iteration of the ... The estimation results of the noise covariance matrix corresponding to each target; The value is the result of a mathematical calculation. ; The motion parameter matrix is ​​updated as follows: ； in, For the first The iteration of the ... The estimation results of the motion parameter matrix corresponding to each target; Set the following process values: First process value : ; Second process value : ; Third process value : ; Fourth process value : ; Fifth process value : ; Sixth process value : ; Seventh process value : ; Eighth process value : ; The initial trajectory coordinates are updated as follows: ； Obtain the set of unknown parameters In the The joint estimation results of the next iteration: 。 7. The target trajectory clustering and fitting method applicable to multiple motion modes according to claim 1, characterized in that, Step 5 includes: for each point measurement data, calculating its posterior probability of belonging to each target, selecting the target category corresponding to the largest posterior probability as the target to which the point measurement data belongs, and clustering the point measurement data belonging to the same target category to obtain the trajectory fitting result corresponding to each target.

8. A target trajectory clustering and fitting system suitable for multiple motion modes, used to implement the target trajectory clustering and fitting method suitable for multiple motion modes according to any one of claims 1-7, comprising: The dataset module is used to acquire point trace measurement data of multiple targets within the monitoring area and construct a point trace dataset; The motion modeling module is used to establish a unified vector motion state model applicable to uniform linear motion, uniformly accelerated linear motion, and uniform turning motion. Among them, the state transition relationship of uniform turning motion is performed by a second-order Taylor expansion. The statistical modeling module is used to establish a mixture Gaussian trajectory statistical model based on the unified vector motion state model by introducing hidden random variables that represent the relationship between point traces and target attribution. The parameter estimation module is used to iteratively solve the Gaussian mixture trajectory statistical model using the expectation-maximization algorithm, jointly updating the set of unknown parameters and the posterior probability of each point's trace measurement data belonging to each target, until a preset convergence condition is met, obtaining the optimal joint estimation result of the unknown parameter set, and completing multi-target trajectory fitting; wherein, the set of unknown parameters includes initial trajectory coordinates, motion parameter matrix, noise covariance matrix, and target class probability; and The track clustering module is used to determine the target category based on the maximum posterior probability corresponding to each track measurement data, thus completing multi-target track clustering.

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