gaussian mixture probability hypothesis density filter method based on clutter density estimation

Abstract

The application relates to a Gaussian mixture probability hypothesis density filtering method based on clutter density estimation. First, potential target measurement and clutter measurement are estimated by combining multi-target Gaussian mixture intensity prediction value and measurement value, then the clutter density around each target is estimated and combined with a Gaussian mixture probability hypothesis density filter, the predicted Gaussian component is updated by the potential target measurement, and the multi-target state is estimated in combination. The method disclosed by the application does not depend on prior clutter distribution, can effectively estimate the distribution of the clutter, especially can effectively and continuously track multiple targets in a complex scene, improves the real-time performance of tracking, and improves the tracking precision of the target.

Description

Technical Field

[0001] This invention relates to the field of target tracking technology, and more specifically to a multi-target tracking method under conditions of unknown clutter distribution. Background Technology

[0002] The research object of this invention is multi-target under radar sensing. The research purpose is to estimate the motion state of the target in the observation area based on the measurement data obtained by radar and other sensors. Any target tracking algorithm is related to the surrounding environment. How to accurately estimate the surrounding clutter density is the key to affecting the final tracking result. The research content of this invention mainly involves the problem of estimating the clutter density around the target.

[0003] Target tracking refers to the process of using various active or passive sensors, such as radar, infrared, laser, and electronic support and intelligence measures, to detect moving targets. Through a series of optimized and integrated processing steps, it enables real-time target acquisition, estimation of the number, location, and speed of targets within the monitored area, and further identification of target attributes, analysis of intentions, and assessment of the situation's development, as well as threat estimation. Target tracking technology has wide applications in military fields such as airborne early warning, missile defense, battlefield monitoring, air attack, and maritime surveillance.

[0004] With the development of sensor networks and information technology, multi-target tracking technology has rapidly emerged. Multi-target tracking systems utilize measurements obtained from sensors to continuously track and predict the state of multiple targets. At each moment, the sensor receives measurements consisting of target data and clutter. In complex battlefield environments, uncertainties such as the changing number of targets over time during tracking increase the computational load and decrease the tracking accuracy of traditional multi-target tracking algorithms, posing a significant challenge.

[0005] Multi-target tracking algorithms can be broadly categorized into two types. The first type is based on data association, a tracking algorithm that starts with intuitive ideas but employs an indirect approach. Its basic idea is to match sensor measurements with targets, then update and estimate the states of each associated target. However, this traditional multi-target tracking algorithm requires very high accuracy in the association technique; otherwise, association errors will lead to inaccurate subsequent estimations, significantly increasing the algorithm's computational overhead. Therefore, implementing data association algorithms in complex environments presents a significant challenge. The second type is based on non-data association multi-target tracking algorithms, specifically those based on stochastic finite set theory. These algorithms model the multi-target tracking problem as a stochastic finite set, cleverly avoiding the data association problem in traditional algorithms. They can also naturally handle the start, end, and association of tracks, making them suitable for multi-target tracking in more complex environments. Mahler proposed stochastic finite set theory, which provides a rigorous mathematical description of phenomena such as sensor misses, false alarm clutter, and target appearance, emergence, and disappearance in multi-target tracking. Based on the theory of random finite sets, Mahler et al. proposed the PHD filter and presented its closed-form solutions under linear Gaussian and nonlinear non-Gaussian conditions, namely the Gaussian Mixture PHD (GM-PHD) filter and the Sequential Monte Carlo PHD (SMC-PHD) filter. Filters within the PHD filtering framework perfectly avoid data correlation between measurements and targets, have low computational cost, and can accurately estimate the joint number and motion state of multiple targets in cluttered and sensor-missed environments.

[0006] The multi-target tracking process in modern combat systems is influenced by many factors, such as the unknown location of newly emerging targets, the high maneuverability of targets, the difficulty in tracking multiple expanding targets, and clutter interference in the detection environment. In such a complex environment, achieving ideal combat results requires real-time and accurate positioning and tracking of each target within the monitored area. In multi-target tracking within a cluttered environment, measurement uncertainties exist; determining whether the uncertainty originates from clutter or from one of the targets is the primary problem to be solved in achieving target tracking.

[0007] Furthermore, in the original Gaussian mixture probability hypothesis density filter, it is assumed that the number of clutter follows a Poisson distribution and is uniformly distributed throughout the range. This setting does not pose a significant problem in scenarios where the number of clutter is small and does not change much. However, in reality, the distribution of clutter in the measurement space is unknown and time-varying. Therefore, this assumption can easily lead to losing the target and generating false alarms, resulting in a decrease in the tracking accuracy and robustness of the entire algorithm.

[0008] Therefore, the problem to be solved by the present invention is how to use the measurement data received by the sensor to find the unknown clutter distribution when the clutter distribution is unknown and time-varying, so as to accurately estimate the clutter density in the area around each target and input it into the multi-target tracking update equation to find the number of targets and the target state. Summary of the Invention

[0009] To address the shortcomings of existing technologies, this invention proposes a Gaussian mixture probability hypothesis density filter based on clutter density estimation. It estimates the clutter set using predicted and measured values ​​of multi-target Gaussian mixture intensity, and then combines the clutter density around each target with the Gaussian mixture probability hypothesis density filter to jointly estimate the multi-target state. To achieve the above objectives, the technical solution adopted by this invention is as follows:

[0010] A Gaussian mixture probability assumption density filtering method based on clutter density estimation includes the following steps:

[0011] S1. Initialization: Assume that the function of the target state set is a Gaussian mixture form;

[0012] S2, Multi-target intensity prediction: Based on the posterior intensity of multiple targets at time k-1, predict surviving targets and newly emerging targets;

[0013] S3. Clutter density estimation: Use the predicted Gaussian posterior intensity to find the clutter value in the measurement data, estimate the number of clutter around each target, and calculate the clutter density around each target.

[0014] S4. Multi-target intensity update: The estimated clutter density is brought in and the predicted Gaussian posterior intensity is updated by combining the measurement values.

[0015] S5, clipping and merging Gaussian components, for Gaussian components Prune the cropping process, retaining crops with weights greater than the pruning threshold T. p Gaussian components that satisfy the merging threshold T m Merge the Gaussian terms;

[0016] S6. Target state extraction and count estimation, target count estimation is as follows: The target state is estimated as the mean of the Gaussian component with the largest weight.

[0017] Furthermore, step S1 specifically involves: at time k = 0, assuming the intensity function of the multi-target is a Gaussian mixture form. Where: L 0|0 Let x be the number of Gaussian components at time 0, and let x be the value in the target state space. and These are the weights, mean, and variance of the i-th Gaussian component at time 0.

[0018] Furthermore, step S2 specifically includes the following operations:

[0019] At time k-1, assume the Gaussian mixture PHD of the posterior intensity of the multi-objectives is:

[0020]

[0021] Among them: J k-1 Let x be the number of Gaussian components at time k-1, and let x be the value in the target state space. and These are the weights, mean, and variance of the i-th Gaussian component at time k-1, respectively.

[0022] The PhD of the target who survives from time k-1 to time k is:

[0023]

[0024] Where: P S Let Gaussian components be the survival probability. and Let be the mean and covariance of the i-th Gaussian surviving component at time k, respectively.

[0025] The newly generated component at time k is

[0026] in, and J represents the weight, mean, and covariance of the i-th newly generated component at time k. B,k Let k be the number of newly generated Gaussian components at time k;

[0027] The Gaussian mixture of the predicted intensity at time k is the surviving Gaussian component v at time k. k|k-1,s (x) and the newly generated Gaussian component B at time k k The sum of (x), i.e., v k|k-1 (x)=v k|k-1,S (x)+B k (x).

[0028] Furthermore, step S3 specifically includes the following operations:

[0029] For the i-th Gaussian component at time k-1 Make predictions, the i-th predicted Gaussian component The tracking gate is calculated as follows:

[0030]

[0031] Where g is the tracking gate parameter, The new information covariance matrix, Let g be the prediction error measured at time k, and g be the tracking gate parameter.

[0032]

[0033] in, For the j-th measurement, h k For the measurement matrix, Let be the mean of the i-th Gaussian component at time k. The prediction error is the measurement taken at time k.

[0034] From the measurement set Z at time k k Nearest neighbor measurements that fall within the tracking gate are selected. remember Measurements are taken for potential targets; then, the measurement set Z at time k is used. k Remove from Obtain the current clutter measurement set

[0035] The position of the j-th clutter is

[0036] The mean of the predicted Gaussian component at time k for

[0037] Calculate the distance between the predicted mean of each clutter and each Gaussian component;

[0038] And sort the distances in ascending order;

[0039] If the average distance between the i-th target and each clutter is taken as the distance threshold β, then

[0040] Let η be the number of items in the distance set that are less than the distance threshold β, and let max(d) be the distance. ij ≤β);

[0041] The clutter density near the i-th predicted Gaussian component is then...

[0042] Furthermore, step S4 specifically includes the following operations:

[0043] Using the estimated clutter density, potential target measurement By updating the predicted Gaussian components using a Gaussian mixture probability hypothesis density filter, the posterior intensity of the multi-objective system is obtained:

[0044]

[0045] Where: P d For the detection probability, vk|k-1 (x) represents the predicted intensity, g k (·) is the likelihood function, c k (z) represents the clutter density.

[0046] Furthermore, step S5 specifically includes the following operations:

[0047] If J exists at time k-1 k-1|k-1 If there are n Gaussian mixture terms, then the number of Gaussian mixture terms at time k is:

[0048] J k|k =(J k-1|k-1 (1+J β,k )+J b,k )(1+|Z k |);

[0049] J β,k J b,k |Z k | represents the number of Gaussian mixture terms in the derived target state set, the number of new target state set, and the number of measurements, respectively;

[0050] Gaussian components in the posterior intensity function formula Prune the cropping process, retaining crops with weights greater than the pruning threshold T. p Gaussian components;

[0051]

[0052] Combining Gaussian components: Combining Gaussian components and satisfy The terms are merged to obtain the Gaussian mixture term at time k.

[0053] Furthermore, in step S6, the Gaussian mixture term of the posterior intensity at time k obtained in step S5 is used. Perform multi-target state extraction.

[0054] Beneficial Effects: This invention addresses the problem of multi-target tracking with unknown clutter intensity in changing clutter scenarios. It proposes a Gaussian mixture probability hypothesis density filter (PHD) based on clutter density estimation to improve PHD tracking performance in complex conditions. Since the clutter environment changes constantly, we do not need to consider the rationality of the initial value setting. We estimate the clutter set and potential target measurements by using the predicted and measured values ​​of the multi-target Gaussian mixture intensity at each time step. Then, we estimate the clutter density around each target at the current time and combine it with the Gaussian mixture probability hypothesis density filter to jointly estimate the multi-target state. This allows for real-time clutter density estimation, thereby improving target tracking accuracy. During the multi-target update stage, updates are made using potential target measurements, reducing clutter interference. Furthermore, during Gaussian component trimming and merging, redundant clutter Gaussian components do not need to be processed, eliminating the influence of clutter and improving real-time tracking performance. Attached Figure Description

[0055] Figure 1 This is a comparison chart of the optimal sub-mode distances of the target using two algorithms (the original GM-PHD algorithm and the improved CE-GM-PHD algorithm) throughout the simulation experiment.

[0056] Figure 2 This is a comparison chart of the trajectory errors of the target using the two methods throughout the simulation experiment;

[0057] Figure 3 This is a comparison chart showing the estimated number of clutter items for the target throughout the simulation experiment.

[0058] Note: Because the state error and cardinality error of the set need to be considered, the Optimal Subpattern Assignment (OSPA) evaluation metric is used to intuitively evaluate the tracking performance of a multi-target system. Detailed Implementation

[0059] In multi-target tracking systems, states and measurements are sets of the states and measurements of each individual target. The dimension of these sets changes over time. Multi-target tracking methods based on random finite sets define the states and measurements of multiple targets as separate random finite set variables:

[0060]

[0061]

[0062] In the formula: X k Z is a random set of multi-objective states at time k; k Let N be the random set of measurements at time k; k M is the number of targets at time k; k x is the number of measurements at time k;k,i (i = 1, 2, ..., N) k Let z be the state of the i-th target at time k; k,j (j = 1, 2, ..., M) k ) represents the j-th measurement at time k.

[0063] Let X be the multi-objective state set at time k-1. k-1 Let k be the multi-objective state set at time k, then it is as follows:

[0064] Among them B k|k-1 (x k-1 ), S k|k-1 (x k-1 () represent x at time k respectively k-1 The states of derived targets and surviving targets are random finite sets; Γ k This represents the random set of newly added target states at time k.

[0065] At time k, each state x k ∈X k Generate a random finite set Θ k (x), when the target is detected, Θ k (x) is {z k}, when the target is not detected, Θ k (x) is an empty set. Due to clutter interference in the real environment, the acquired measurement set may include not only measurements from the real target, but also sets K consisting of false alarms or clutter received by the sensor. k .

[0066] The observations of multiple targets can then be represented by a random finite set model as follows:

[0067] This invention provides a Gaussian mixture probability hypothesis density filtering method based on clutter density estimation, which specifically includes the following steps:

[0068] Step 1: Initialization

[0069] At time k = 0, assume that the function of the target state set is a Gaussian mixture form:

[0070]

[0071] Where: L 0|0 Let x be the number of Gaussian components at time 0, and let x be the value in the target state space. and These are the weights, mean, and variance of the i-th Gaussian component at time 0.

[0072] Step 2: Survival and Newborn Goals Prediction

[0073] At time k-1, assume the Gaussian mixture of the posterior intensities of the multiple targets (PHD) is:

[0074]

[0075] Among them: J k-1 Let x be the number of Gaussian components at time k-1, and let x be the value in the target state space. and These are the weights, mean, and variance of the i-th Gaussian component at time k-1, respectively.

[0076] Based on the posterior strength prediction of multiple targets at time k-1, the PHD of the surviving targets from time k-1 to time k is:

[0077]

[0078] Where: P S Let Gaussian components be the survival probability. and Let be the mean and covariance of the i-th Gaussian surviving component at time k, respectively.

[0079] Predicting the target of newborns, the newborn component at time k is:

[0080] in, and J represents the weight, mean, and covariance of the i-th newly generated component at time k. B,k Let k be the number of newly generated Gaussian components at time k;

[0081] The Gaussian mixture of the predicted intensity at time k is the surviving Gaussian component v at time k. k|k-1,s (x) and the newly generated Gaussian component B at time k k The sum of (x), i.e., v k|k-1 (x)=v k|k-1,S (x)+B k (x).

[0082] Step 3: Estimation of clutter density

[0083] By utilizing Gaussian mixture posterior intensity information feedback and thresholding techniques to eliminate potential target measurements, a clutter measurement set is obtained, reducing the impact of target measurements on clutter density estimation. Secondly, for each target, a nearby clutter subset is identified from the clutter measurement set, and an appropriate number is selected to estimate the clutter density around each target.

[0084] To achieve clutter density estimation, we need to distinguish between target measurements and clutter measurements from the measured values. An elliptical gate is used, centered on the predicted location of the tracked target, to determine the range within which the current observed values ​​of the target might appear. The size of this region is determined by the probability of correctly receiving the echo. When determining the gate size and shape, we aim to ensure that the true measurements fall within the gate with a high probability, while minimizing the entry of irrelevant values.

[0085] The specific steps for clutter density estimation are as follows:

[0086] For the i-th Gaussian component at time k-1 Make predictions, the i-th predicted Gaussian component The tracking gate is calculated as follows:

[0087]

[0088] in, The new information covariance matrix, Let g be the prediction error measured at time k, and g be the tracking gate parameter.

[0089]

[0090] in, For the j-th measurement, h k For the measurement matrix, Let be the mean of the i-th Gaussian component at time k. The prediction error is the measurement taken at time k.

[0091] Where g is the tracking gate parameter;

[0092] From the measurement set Z at time k k Nearest neighbor measurements that fall within the tracking gate are selected. remember Measurements are taken for potential targets; then, the measurement set Z at time k is used. k Remove from Obtain the current clutter measurement set

[0093]

[0094] The position of the j-th clutter is

[0095] The mean of the predicted Gaussian component at time k for

[0096] Calculate the distance between the predicted mean of each clutter and each Gaussian component;

[0097] The distances are sorted in ascending order.

[0098] Generally speaking, clutter points that are closer to the target have a greater impact on the density value around the target, while clutter points that are farther away have a smaller impact on the estimated density value around the target. Therefore, to calculate the clutter density around each target, it is only necessary to know the situation of the nearest clutter. By substituting the information of the nearest clutter into the density function, the clutter density value around the target can be obtained.

[0099] If the average distance between the i-th target and each clutter is taken as the distance threshold β, then

[0100] Let η be the number of items in the distance set that are less than the distance threshold β, and let max(d) be the distance. ij ≤β);

[0101] The clutter density near the i-th predicted Gaussian component is then...

[0102] Step 4: Target Status Update

[0103] Using the estimated clutter density, potential target measurement By combining the Gaussian mixture probability hypothesis density filter to update the predicted Gaussian components, clutter components can be reduced during the Gaussian component clipping step, thus obtaining the posterior intensity of multiple targets.

[0104] The estimated clutter density is then used to update the predicted Gaussian posterior intensity, incorporating the measured values:

[0105]

[0106] Where: P d For the detection probability, v k|k-1 (x) represents the predicted intensity, g k (·) is the likelihood function, c k (z) represents the clutter density.

[0107] Step 5: Clipping and merging Gaussian components

[0108] As time increases, the number of Gaussian terms in the posterior probability hypothesis density also increases, which increases the computational complexity.

[0109] If J exists at time k-1 k-1|k-1 If there are n Gaussian mixture terms, then the number of Gaussian mixture terms at time k is: J k|k =(J k-1|k-1 (1+J β,k )+J b,k )(1+|Z k |).

[0110] J β,k J b,k |Z k | represents the number of Gaussian mixture terms in the derived target state set, the number of new target state set, and the number of measurements, respectively.

[0111] To prevent the number of Gaussian terms from increasing excessively, Gaussian terms with too low a weight need to be discarded, which is called Gaussian component pruning. This involves pruning the Gaussian components in the posterior intensity function formula. Prune the cropping process, retaining crops with weights greater than the pruning threshold T. p Gaussian components;

[0112]

[0113] Meanwhile, many Gaussian terms with similar distributions satisfy the merging threshold T. m They can be merged into a single Gaussian term, reducing the total number of Gaussian terms, which is called merging Gaussian components;

[0114] Gaussian components and satisfy The terms are merged to obtain the Gaussian mixture term at time k.

[0115] Step 6: Target State Extraction and Count Estimation

[0116] The estimated number of targets is Since the mean of each Gaussian term corresponds to a local extremum of the posterior intensity, the estimation of the multi-objective state can be obtained from the weights of the Gaussian mixture terms. The target state is estimated as the mean of the Gaussian component with the largest weight. The Gaussian mixture terms of the posterior intensity at time k obtained in Step 5 are then used. Perform multi-target state extraction.

[0117] The effectiveness of the present invention is verified through simulation experiments, which are set up to track multiple targets in a complex scene.

[0118] To demonstrate the effectiveness of the proposed method, a relatively fair simulation environment was established. In this scenario, the number of clutter items at each moment is a number randomly generated by computer simulation within a certain range, and its distribution is unknown. The relevant parameters are set as follows:

[0119] Assume that the probability density function of clutter measurements in space is:

[0120]

[0121] In the formula, the weights are respectively U(·)=1 / S, where S represents the area of ​​the monitoring region in the two-dimensional measurement space; and These are the mean and covariance matrices of a Gaussian distribution, respectively. The simulation program executes 100 steps per run.

[0122] In the above scenario, the original GM-PHD and the improved CE-GM-PHD algorithm (i.e., the method described in this invention) are compared.

[0123] Appendix Figure 1-3 The estimation results of two algorithms (the original GM-PHD algorithm and the improved CE-GM-PHD algorithm) are presented. Figure 1 This is a comparison chart of the optimal sub-mode distances of the target using two algorithms (the original GM-PHD algorithm and the improved CE-GM-PHD algorithm) throughout the simulation experiment.

[0124] For single-target tracking, mean squared error (ME), minimum mean squared error (MMSE), and root mean square error are selected. These methods are no longer used for multi-target tracking because the state error and cardinality error of the set need to be considered. Optimal Subpattern Assignment (OSPA) is used as an evaluation metric to intuitively evaluate the tracking performance of a multi-target system. Therefore, this invention uses OPSA as the evaluation metric for the algorithm. Figure 1 Simulation results show that the tracking performance of the CE-GMPHD algorithm of this invention is significantly better than that of the original GM-PHD algorithm.

[0125] Figure 2 This is a comparison chart of the trajectory errors of the target using the two methods throughout the simulation experiment; GM-PHD with a fixed clutter density, due to the influence of clutter fluctuations, often exhibits deviations in target state estimation, such as... Figure 2 For example, the state of the third derived target may be unpredictable for a period of time, resulting in the loss of the target; while CE-GM-PHD will only deviate slightly at some times (such as when the target meets and when a derivative appears), proving that CE-GM-PHD also demonstrates its superiority in complex clutter conditions, continuously tracking the target with a small error and without losing the target, which greatly improves the tracking performance of the original algorithm.

[0126] Figure 3 This is a comparison chart of the estimated number of clutter items for the target throughout the simulation experiment. As can be seen from the chart, the clutter distribution estimated by the algorithm described in this invention is very close to the actual clutter distribution.

[0127] CE-GMPHD stably tracks the target with a smaller error than GMPHD with a fixed clutter density. This fully demonstrates that in complex environments, the CE-GMPHD algorithm can handle the relationship between clutter and the target well, estimate the clutter distribution more closely to the actual distribution, and has strong adaptability, while also ensuring the stability and robustness of the tracking.

[0128] In summary, this invention addresses the problem of fixed clutter density affecting the estimation performance of Gaussian Mixture Probability Hypothesis Density (CE-GMPHD) filters for multiple targets by proposing a CE-GMPHD based clutter density estimation. First, the potential target measurement and clutter measurement are estimated by jointly using the predicted and measured values ​​of the Gaussian mixture intensity of multiple targets. Then, the clutter density around each target is estimated and combined with the CE-GMPHD filter. The predicted Gaussian components are updated using the potential target measurement, and the states of multiple targets are jointly estimated. The CE-GMPHD algorithm does not rely on prior clutter distribution and can effectively estimate the clutter distribution. It is particularly effective in continuously tracking multiple targets in complex scenes, improving both real-time tracking performance and target tracking accuracy.

[0129] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A Gaussian mixture probability hypothesis density filtering method based on clutter density estimation, characterized in that, Includes the following steps: S1. Initialization: Assume that the function of the target state set is a Gaussian mixture form; S2, Multi-target intensity prediction: Based on the posterior intensity of multiple targets at time k-1, predict surviving targets and newly emerging targets; S3. Clutter density estimation: Using the predicted Gaussian posterior intensity, the clutter value in the measurement data is found, the number of clutter particles around each target is estimated, and the clutter density around each target is calculated. This includes the following operations: right The first moment Gaussian components To make a prediction, the first One predicted Gaussian component The tracking gate is calculated as follows: ； in, These are tracking gate parameters. The new information covariance matrix, for Prediction error of time measurement These are the tracking gate parameters; ； in, For the first Individual measurement, For the measurement matrix, for Time of the first The mean of the Gaussian components, for Prediction error of time measurement; from Time measurement set Nearest neighbor measurements that fall within the tracking gate are selected. ,remember Measurement for potential targets; then from Time measurement set Remove from Obtain the current clutter measurement set : ; No. The location of the clutter is ; The first moment The predicted mean of each Gaussian component for ; Calculate the distance between the predicted mean of each clutter and each Gaussian component; And sort the distances in ascending order; With the first The average distance from each target to each clutter is the distance threshold. ,but ; Let the distance set contain items smaller than the distance threshold. The number of The distance is ; Then the first The clutter density near the predicted Gaussian component is ; S4. Multi-target intensity update: The estimated clutter density is brought in and the predicted Gaussian posterior intensity is updated by combining the measurement values. S5. Trimming and merging Gaussian components. Prune the cropping process, retaining crops with weights greater than the pruning threshold. Gaussian components that satisfy the merging threshold Merge the Gaussian terms; S6. Target state extraction and count estimation, target count estimation is as follows: The target state is estimated as the mean of the Gaussian component with the largest weight.

2. The Gaussian mixture probability hypothesis density filtering method based on clutter density estimation as described in claim 1, characterized in that, Step S1 specifically involves: in At time t, assume the intensity function of the multi-objective system is a Gaussian mixture form. ,in: The number of Gaussian components at time 0. The value in the target state space. , and They are respectively at time 0. The weights, mean, and variance of each Gaussian component.

3. The Gaussian mixture probability hypothesis density filtering method based on clutter density estimation as described in claim 2, characterized in that, Step S2 specifically includes the following operations: exist At time t, suppose the Gaussian mixture of the posterior intensities of the multi-objectives (PHD) is: ； in: for The number of Gaussian components at time step (t) The value in the target state space. , and They are respectively Time of the first The weights, mean, and variance of each Gaussian component; Depend on Surviving until The target PhD at time t is: ； in: Let Gaussian components be the survival probability. and They are respectively Time of the first The mean and covariance of the Gaussian surviving components; The newborn component at time is in, , and They are respectively Time of the first The weights, mean, and covariance of each new component. for The number of newly generated Gaussian components at any given moment; The Gaussian mixture of the predicted intensity at time k is the surviving Gaussian component at time k. The newly generated Gaussian component at time k The sum of .

4. The Gaussian mixture probability hypothesis density filtering method based on clutter density estimation as described in claim 3, characterized in that, Step S4 specifically includes the following operations: Using the estimated clutter density, potential target measurement By updating the predicted Gaussian components using a Gaussian mixture probability hypothesis density filter, the posterior intensity of the multi-objective system is obtained: in: For detection probability, To predict intensity, Let be the likelihood function. This represents clutter density.

5. The Gaussian mixture probability hypothesis density filtering method based on clutter density estimation as described in claim 4, characterized in that, Step S5 specifically includes the following operations: if Always A Gaussian mixture term, then in The number of Gaussian mixture items at time t is: ； in , , These represent the number of Gaussian mixture terms in the derived target state set, the number of new target state set, and the number of measurements, respectively. Gaussian components in the posterior intensity function formula Prune the cropping process, retaining crops with weights greater than the pruning threshold. Gaussian components; ； Combining Gaussian components: Combining Gaussian components and satisfy The components are merged to obtain the final result. Gaussian mixture of time .

6. The Gaussian mixture probability hypothesis density filtering method based on clutter density estimation as described in claim 5, characterized in that, In step S6, the information obtained in step S5 is used. Gaussian mixture of posterior strengths at time step Perform multi-target state extraction.

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