Gm-ai- phd multi-target tracking method based on kernel density estimation

Abstract

The application provides a GM-AI-PHD multi-target tracking method based on kernel density estimation, the filter uses a kernel density estimation method to estimate an amplitude probability density function of a target and clutter in real time, solves the problem that a GM-AI-PHD multi-target tracking method based on parameter estimation can only be applied to specific scenes, and can realize real-time and accurate positioning and tracking of multi-targets in a complex environment (a large number of clutters, unknown statistical distribution of a real likelihood function).

Description

Technical Field

[0001] This invention belongs to the field of single-sensor multi-target tracking, and relates to a GM-AI-PHD multi-target tracking method based on kernel density estimation, which can realize the localization and tracking of multiple targets in real time and accurately in complex environments; Background Technology

[0002] Multi-target tracking refers to estimating the number, state, and other information of targets from complex data acquired by sensors. Single-sensor multi-target tracking methods are mainly divided into two categories: ① Data Association (DA) based methods; ② Random Finite Set (RFS) based methods. Among them, DA-based tracking methods often face the risk of combinatorial explosion due to their complex computational complexity when dealing with more complex target tracking problems such as sensor quality degradation and increased clutter intensity. In some complex environments, they are difficult to meet the needs of applications. In recent years, RFS-based tracking methods have attracted widespread attention, and some RFS-based filters have been proposed, such as Probability Hypothesis Density (PHD) filters, Potential PHD (CPHD) filters, and Amplitude Information (AI) assisted PHD (AI-PHD) filters.

[0003] The following are some representative works based on the RFS tracing method:

[0004] In 2003, R. Mahler proposed a PHD filter based on RFS, simplifying the probability space modeling of state variables to the probability hypothesis space modeling of state variables, but without obtaining a closed-form solution. Subsequently, Australian scholar BNVo proposed an implementable Gaussian mixture PHD (GM-PHD) filter and a sequential Monte Carlo PHD (SMC-PHD) filter. In 2007, R. Mahler proposed a CPHD filter. In 2008, Clark et al. first introduced amplitude information into the PHD filter, where the target and clutter amplitudes adopted a Rayleigh distribution. In 2009, Edmund F. Brekke et al. assumed that the amplitude information followed a K distribution and introduced it into the field of multi-target tracking. Subsequently, Li et al., for the case of heavy clutter tailing caused by high-resolution radar and low ground scratch angle, assumed that the amplitude followed a Weibull distribution and proposed an AI-assisted PHD filter.

[0005] The aforementioned AI-assisted target tracking methods all assume that the amplitudes of the target and clutter follow a known statistical distribution. Specifically, these methods introduce the probability density function corresponding to the statistical distribution into the tracking filter to achieve rapid and effective differentiation between target measurements and clutter measurements, thereby improving the tracking performance of the filter. However, when the actual statistical distribution is unknown, the above methods are not feasible. Therefore, this invention proposes to use the kernel density estimation method to estimate the amplitude probability density function of the target and clutter in real time, so that accurate tracking of multiple targets can be achieved even in scenarios where the statistical distribution is unknown. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of existing technologies by proposing a GM-AI-PHD multi-target tracking method based on kernel density estimation (KDE), abbreviated as GM-KDE-AI-PHD, the details of which are as follows:

[0007] Step (1): Construct a single-sensor multi-target tracking scenario and set relevant parameters, including the noise of the target motion process and the observation noise of the sensor;

[0008] Step (2): Model the state and observation of multiple targets;

[0009] Step (3): Construct the GM-KDE-AI-PHD filter;

[0010] Step (4): Use the built GM-KDE-AI-PHD filter to achieve multi-target tracking.

[0011] A second objective of this invention is to provide a GM-AI-PHD multi-target tracking device based on kernel density estimation, including a GM-KDE-AI-PHD filter.

[0012] A third object of the present invention is to provide a computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to perform the method described thereon.

[0013] A fourth object of the present invention is to provide a computing device, including a memory and a processor, wherein the memory stores executable code, and the processor executes the executable code to implement the method described herein.

[0014] The beneficial effects of this invention are:

[0015] This invention proposes a complete multi-target tracking scheme. It uses the kernel density estimation method to estimate the probability density function of the amplitude distribution of the target and clutter, and embeds the estimation result into the AI-PHD filter process. Finally, a linear Gaussian model is used to solve the filter. This invention can achieve real-time online tracking of multiple targets in complex scenarios with many clutter numbers and unknown amplitude information statistical distribution. It has a significant improvement in tracking performance compared to the original PHD filter and also a significant improvement in tracking performance compared to AI-PHD filters with known statistical distribution. It can effectively improve the efficiency, accuracy and robustness of multi-target tracking. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the specific implementation of the core part of the GM-KDE-AI-PHD method of this invention;

[0017] Figure 2 It is a multi-target motion trajectory diagram;

[0018] Figure 3 This is a comparison chart of the average number of targets estimated by the method of the present invention with those obtained by the real distribution GM-AI-PHD filter, the Rayleigh distribution GM-AI-PHD filter, and the GM-PHD filter without amplitude, under 200 Monte Carlo simulations.

[0019] Figure 4 This is a comparison chart of the OSPA average values ​​obtained by the method of this invention with those obtained by the real distribution GM-AI-PHD filter, the Rayleigh distribution GM-AI-PHD filter, and the GM-PHD filter without amplitude, under 200 Monte Carlo simulations. Detailed Implementation

[0020] The present invention will be further analyzed below with reference to specific embodiments;

[0021] The GM-AI-PHD multi-target tracking method based on kernel density estimation includes the following steps:

[0022] Step (1): Construct a single-sensor multi-target tracking scenario and set relevant parameters, including the noise during target motion and the observation noise of the sensor. Specifically:

[0023] The target moves in a two-dimensional plane, and its state is represented by x = [p x ,v x ,p y ,v y ] T , where p x ,p y These represent the target's positions in the x and y directions, respectively, and v x v y ...

[0024] The noise covariance of the target motion process is set as follows: σ x (k) 2 σ represents the noise variance of the environment at time k relative to the target's velocity x. y (k) 2 This represents the noise variance of the environment at time k related to the target's y-velocity;

[0025] Set the observation noise covariance of the sensor to be... Where δ x 2 δ y 2 These represent the noise variances of the sensor at the target's x and y positions, respectively.

[0026] Step (2) Modeling the state and observation of multiple targets, specifically:

[0027] 2-1 Target State Modeling

[0028] Let N be the number of targets at time k. k The target states are as follows: The target state at time k can be determined by a random finite set (RFS)X. k It means, that is

[0029]

[0030] Where χ represents the state space. It is the set of all finite subsets of χ;

[0031] The goal starts from a certain state x at time k-1. k-1 Transition to a certain state x at time k k This is called a state transition, assuming the probability density f for each target state transition. k|k-1 (x k |x k-1 It conforms to a linear Gaussian model, expressed as:

[0032] f k|k-1 (x k |x k-1 )=N(x k ;F k-1 x k-1 Q k-1 (2)

[0033] Where N(x) k ;F k-1 x k-1 Q k-1 ) represents the target state x k The spatial distribution of follows a state mean of F.k-1 x k-1 The covariance is Q k-1 Gaussian distribution, F k-1 Let Q be the state transition matrix. k-1 The process noise covariance matrix;

[0034] 2-2 Target Kinematic Observation Modeling

[0035] Let M be the number of target measurements received at time k. k The target measurements are as follows: The sensor measurement vector at time k is represented by z. k =[z x , z y ] T The target measurement at time k can be obtained from the finite set Z. k It means, that is

[0036]

[0037] Among them, z x ,z y These represent the target's positions measured by the sensors in the x and y directions, respectively, with T indicating transpose. For observation space, yes The set of all finite subsets;

[0038] Assume the sensor measurement model g at time k k|k-1 (z k |x k It conforms to a linear Gaussian model, expressed as:

[0039] g k|k-1 (z k |x k )=N(z k H k x k ,R k (4)

[0040] Where N(z) k H k x k ,R k ) represents a measurement z at time k. k The spatial distribution of follows a mean of H. k x k The covariance is R k Gaussian distribution, H k Let R be the observation matrix. k To measure the noise covariance matrix;

[0041] 2-3 Clutter Kinematic Observation Modeling

[0042] Suppose that the number of clutter received at time k follows a Poisson distribution with parameter λ, and the clutter positions in the measurement space follow a uniform distribution, i.e.

[0043]

[0044] Where, n c ρ(n) represents the expected clutter number at time k. c () represents the probability function of a Poisson distribution with parameter λ. The observed value of clutter j represents the value of the observed clutter. The probability density, where V represents the volume of the observation space;

[0045] Therefore, the intensity of the clutter at time k is expressed as:

[0046]

[0047] 2-4. Target Amplitude Observation Modeling:

[0048] To construct the target observation amplitude data, we assume that the target amplitude of this invention follows a Weibull distribution, and its probability density is expressed as:

[0049]

[0050] Where a represents amplitude, u is a proportional parameter, and v is a shape parameter. In this invention, u = 25 and v = 1.5 are taken.

[0051] Use g a (a) represents the target amplitude probability density function for a>0, i.e.:

[0052]

[0053] Let the amplitude threshold be τ. When the target measurement amplitude is greater than τ, it is considered that there is a probability p. D The probability that a target is detected by a sensor is called the detection probability. The probability density function of the target amplitude is then expressed as... express:

[0054]

[0055]

[0056] 2-5 Clutter Amplitude Observation Modeling

[0057] To construct clutter observation amplitude data, it is assumed that the clutter amplitude of this invention follows a Weibull distribution, with its probability density as shown in equation (7), where u = 3 and v = 1; using C a (a) represents the clutter amplitude probability density function for a>0, i.e.:

[0058]

[0059] When the clutter amplitude is greater than τ, it is assumed that there is a probability p. FA The probability that a clutter signal is detected as a target by a sensor is called the false alarm probability. The probability density function of the clutter amplitude is then expressed as... express:

[0060]

[0061]

[0062] Generally, p FA Since it is a constant value, the unique amplitude threshold τ can be determined by equation (12). and It is not difficult to determine;

[0063] Step (3) Construct the GM-KDE-AI-PHD filter, specifically:

[0064] 3-1PHD filter

[0065] In the Bayesian filter, using the random finite set (RFS) model, the multi-objective prediction probability density and update probability density are shown in equations (14)-(15):

[0066] P k|k-1 (X k |Z 1:k-1 )=∫f k|k-1 (X k |X k-1 )P k-1 (X k-1 |Z 1:k-1 )μ s (dX k-1 (14)

[0067]

[0068] Among them, Z 1:k Let P represent the set of all observations from time 1 to time k. k|k-1 (X k |Z 1:k-1 f represents the probability density function for multi-objective prediction at time k. k|k-1 (X k |X k-1 ) represents the state X from time k-1. k-1 State X at time k k The transition probability density function, P k-1 (X k-1 |Z 1:k-1 P represents the probability density function for the multi-target update at time k-1.k (X k |Z 1:k ) represents the multi-objective update probability density function at time k, g k (Z k |X k Let μ represent the likelihood function at time k. s Is Appropriate reference value, dX k-1 X represents k-1 The derivative;

[0069] The recursive equations (14)-(15) involve space The multiple integrals on the surface are computationally difficult to handle; the PHD filter is an approximation method developed to solve the computational intractability of multi-objective Bayesian filters. The PHD filter does not propagate the multi-objective update density in a timely manner, but rather propagates the update intensity; the predicted intensity and the update intensity are shown in equations (16)-(17), respectively:

[0070] v k|k-1 (x k )=∫P S,k f k|k-1 (x k |x k-1 )v k-1 (x k-1 )dx k-1 +γ k (x k (16)

[0071]

[0072] Where v k|k-1 (x k ) and v k (x k ) represent the multi-objective prediction density P in recursive equations (14) and (15), respectively. k|k-1 and multi-objective update density P k The intensity, γ k (x k Let P be the intensity of the newly appearing target RFS at time k. S,k Let f be the probability that the target retains its previous state at time k, i.e., the survival probability. k|k-1 (x k |x k-1 ) is from state x k-1 to state x k The transition probability density function, P D,k (x k Let x be the detection state at time k. k The probability of detection is c. k (z kLet g be the intensity of the clutter RFS at time k. k (z k |x k ) represents state x k To z k The likelihood function;

[0073] 3-2AI-PHD Filter

[0074] Amplitude information is introduced into the PHD filter to establish the recursive equation for AI-PHD;

[0075] ① Prediction Strength: The state vector of the AI-PHD filter is exactly the same as that of the PHD filter, therefore the prediction step formula is the same as that of the PHD filter, and the prediction strength is as follows:

[0076] D k|k-1 (x k )=∫P S,k f k|k-1 (x k |x k-1 )D k-1 (x k-1 )dx k-1 +γ k (x k (18)

[0077] ② Updated Intensity: After introducing the amplitude information of the target and clutter, the updated intensity changes as shown below:

[0078]

[0079]

[0080]

[0081] in, 'a' represents the magnitude of the measurement. For the finite set of amplitude measurements at time k, Indicates the intensity of amplitude-dependent noise (RFS). Represents the likelihood function with amplitude; This represents the detection probability after adding amplitude information, and g k (z k |x k ) and c k (z k ) represents the likelihood function of equation (17) and the clutter RFS intensity, g a (a) and C a (a) are the probability density functions of the target and clutter amplitudes, respectively;

[0082] Substituting equations (20) and (21) into equation (19), the expression for updating the intensity changes from equation (19) to equation (22):

[0083]

[0084] 3-3 KDE-AI-PHD (PHD based on kernel density estimation amplitude information assisted) filter

[0085] Using the KDE method combined with observed amplitude data to analyze the target amplitude probability density function g a (a) Clutter amplitude probability density function C a (a) An estimation is performed, and the formula for estimating the kernel density is shown in equation (23):

[0086]

[0087] Where α represents a random variable, f(α) is the probability density function of the kernel density estimate, N represents the number of known samples, h represents the bandwidth, and α i This represents the measured value of α. Represents the kernel function;

[0088] Before starting filtering, offline observation amplitude data of the scene to be filtered can be collected and compared with the target offline amplitude probability density function. Offline amplitude probability density function of clutter Estimation is performed, but if it is directly replaced by g in the filtering process (22) a (a) and C a (a) would lack accuracy and real-time performance. Therefore, this invention embeds KDE estimation into the filtering process and combines it with observed amplitude data for real-time estimation to ensure the accuracy and real-time performance of the filter. The specific implementation method is as follows:

[0089] Let the offline amplitude data collected before filtering be data A0 at time 0, and The amplitude data received at time k during the filtering process is Where k≥1, a represents amplitude, n0 represents the number of amplitude data points collected at time 0, and n k This represents the number of amplitude data points collected at time k, generally n0>n k The updated strength of the KDE-AI-PHD filter is calculated as follows:

[0090] Step 1: Data Processing

[0091] To ensure real-time performance, the amplitude data at time k is used for filtering. This represents the sum of the amplitude data from the first k time steps.

[0092] Step 2: Kernel density estimation

[0093] Step ①: Use an appropriate threshold τ (τ generally does not exceed 5) to process the offline data. To differentiate, if the amplitude 'a' is greater than 'τ', it is considered to be the target amplitude, thus forming the target amplitude dataset. Conversely, if the amplitude is not equal to the amplitude, it is considered to be clutter amplitude, thus forming a clutter amplitude dataset. The superscripts p and q represent set A respectively. t,k and A c,k Quantity;

[0094] Step 2: Select the kernel function and bandwidth h, The Gaussian function can be selected, and h can be 1.8, i.e.:

[0095]

[0096] Step 3: For offline sample A t and offline sample A c KDE estimation is performed using equation (23), and the corresponding results are obtained. and for:

[0097]

[0098]

[0099] Step 3: Calculate the values ​​estimated in Step 2. and Replace g in the filtering process equation (22) a (a) and C a (a) yields the real-time update intensity D. k (x k However, the predicted intensity remains unchanged;

[0100]

[0101] 3-4 GM-KDE-AI-PHD Filter

[0102] When the system's state equation and observation equation satisfy the linear Gaussian model of equations (2) and (4), the prediction and update of KDE-AI-PHD can be described by the closed form of Gaussian sum, and the Gaussian implementation of the prediction and update steps at time k is as follows:

[0103] Suppose that at time k-1, the multi-objective update intensity is expressed in the following Gaussian mixture form:

[0104]

[0105] Among them, Jk-1 Update the number of intensity Gaussian terms at time k-1. and These are the weights, mean, and covariance matrix of the i-th updated Gaussian term at time k-1, respectively.

[0106] The PHD of the newly emerging target RFS can be expressed as Equation (29):

[0107]

[0108] Among them, J γ,k Let k represent the number of newly generated objective Gaussian terms at time k. Let represent the weight, mean, and covariance matrix of the Gaussian term of the j-th newly generated target at time k, respectively;

[0109] ①Predicted intensity

[0110]

[0111] Where, γ k (x k J is given by equation (29). k-1 The number of Gaussian terms updating the intensity at time k-1 is expressed by the weights, mean, and covariance of the Gaussian terms in equation (30):

[0112]

[0113] Among them, P S,k F represents the survival probability of the target at time k. k-1 Let Q represent the state transition matrix. k-1 Represents the process noise covariance matrix;

[0114] The predicted intensity can be rewritten as equation (32):

[0115]

[0116] J k|k-1 =J k-1 +J γ,k (33)

[0117]

[0118] in, and Let the weights, mean, and covariance matrices of the Gaussian term for the l-th predicted target at time k be represented respectively.

[0119] ②Update strength

[0120]

[0121] in, and Let represent the weight, mean, and covariance matrix of the l-th updated Gaussian term at time k, respectively;

[0122]

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129] in, This represents the probability density function of the target amplitude at time k, as estimated in real time by KDE. H represents the probability density function of clutter amplitude at time k estimated in real time by KDE. k Let R be the observation matrix. k To measure the noise covariance matrix, T denotes transpose;

[0130] Step (4): Use the constructed GM-KDE-AI-PHD filter to achieve multi-target tracking;

[0131] The target tracking effect of this invention is as follows: Figure 2 , Figure 3 , Figure 4 As shown; Figure 2 To track the scene, the scene contains the real trajectories and filtered trajectories of three targets; Figure 3 , Figure 4 This is a comparison chart of the average number of target estimates and the average number of OSPA values ​​obtained after 200 Monte Carlo simulations. Figure 3 It can be seen that the target estimation method of this invention is more accurate than the Rayleigh distribution GM-AI-PHD filter (GM-AI-PHD based on parameter estimation) and the GM-PHD filter, and the difference from the true distribution GM-AI-PHD filter is small. Figure 4 It can be seen that the average OSPA of the method of the present invention is lower than that of the Rayleigh distribution GM-AI-PHD filter and the GM-PHD filter, and the difference from the real distribution GM-AI-PHD filter is small. Therefore, compared with the parameter estimation-based GM-AI-PHD and the amplitude-free GM-PHD, the algorithm of the present invention can accurately track multiple targets in real time.

Claims

1. A GM-AI-PHD multi-target tracking method based on kernel density estimation, characterized in that... Includes the following steps: Step (1): Construct a single-sensor multi-target tracking scenario and set relevant parameters, including the noise of the target motion process and the observation noise of the sensor; Step (2): Model the state and observation of multiple targets; Step (3) Construct the GM-KDE-AI-PHD filter, specifically: 3-1PHD filter In the Bayesian filter, using a random finite set model, the multi-objective prediction probability density and update probability density are shown in equations (14)-(15): P k|k-1 (X k |Z 1：k-1 )=∫f k|k-1 (X k |X k-1 )P k-1 (X k-1 |Z 1：k-1 )μ s (dX k-1 ) (14) Among them, Z 1：k Let P represent the set of all observations from time 1 to time k. k|k-1 (X k |Z 1：k-1 f represents the probability density function for multi-objective prediction at time k. k|k-1 (X k |X k-1 ) represents the state X from time k-1. k-1 State X at time k k The transition probability density function, P k-1 (X k-1 |Z 1：k-1 P represents the probability density function for the multi-target update at time k-1. k (X k |Z 1：k ) represents the multi-objective update probability density function at time k, g k (Z k |X k Let μ represent the likelihood function at time k. s Is Reference value on, dX k-1 X represents k-1 The derivative; The PHD filter does not propagate the multi-target update density in a timely manner, but instead propagates the update intensity; the predicted intensity and the update intensity are shown in equations (16)-(17), respectively: ν k|k-1 (x k )=∫P S，k f k|k-1 (x k |x k-1 )v k-1 (x k-1 )dx k-1 +γ k (x k ) (16) Where ν k|k-1 (x k ) and v k (x k ) represent the multi-objective prediction density P in recursive equations (14)-(15), respectively. k|k-1 and multi-objective update density P k The intensity, γ k (x k Let P be the intensity of the newly appearing target RFS at time k. S，k Let f be the probability that the target retains its previous state at time k, i.e., the survival probability. k|k-1 (x k |x k-1 ) is from state x k-1 to state x k The transition probability density function, P D，k (x k Let x be the detection state at time k. k The probability of detection is c. k (z k Let g be the intensity of the clutter RFS at time k. k (z k |x k ) represents state x k To z k The likelihood function; 3-2AI-PHD Filter Amplitude information is introduced into the PHD filter to establish the recursive equation for AI-PHD; ① Prediction Strength: The state vector of the AI-PHD filter is exactly the same as that of the PHD filter, therefore the prediction step formula is the same as that of the PHD filter, and the prediction strength is as follows: D k|k-1 (x k )=∫P S，k f k|k-1 (x k |x k-1 )D k-1 (x k-1 )dx k-1 +γ k (x k ) (18) ② Updated Intensity: After introducing the amplitude information of the target and clutter, the updated intensity changes as shown below: in, 'a' represents the magnitude of the measurement. For the finite set of amplitude measurements at time k, Indicates the intensity of amplitude-dependent noise (RFS). Represents the likelihood function with amplitude; This represents the detection probability after adding amplitude information, and and c k (z k ) represents the likelihood function of equation (17) and the clutter RFS intensity, g a (a) and C a (a) are the probability density functions of the target and clutter amplitudes, respectively; Substituting equations (20)-(21) into equation (19), the expression for updating the intensity changes from equation (19) to equation (22): 3-3KDE-AI-PHD filter Using the KDE method combined with observed amplitude data to analyze the target amplitude probability density function g a (a) Clutter amplitude probability density function C a (a) An estimation is performed, and the formula for estimating the kernel density is shown in equation (23): Where α represents a random variable, f(α) is the probability density function of the kernel density estimate, N represents the number of known samples, h represents the bandwidth, and α i This represents the measured value of α. Represents the kernel function; Before starting filtering, offline observation amplitude data of the scene to be filtered can be collected and compared with the target offline amplitude probability density function. Offline amplitude probability density function of clutter Estimation is performed, but if it is directly replaced by g in the filtering process (22) a (a) and C a (a) lacks accuracy and real-time performance, so KDE estimation is embedded in the filtering process and combined with the observed amplitude data for real-time estimation. Let the offline amplitude data collected before filtering be data A0 at time 0, and The amplitude data received at time k during the filtering process is Where k≥1, a represents amplitude, n0 represents the number of amplitude data points collected at time 0, and n k The number of amplitude data points collected at time k is represented by the value of k. The updated intensity of the KDE-AI-PHD filter is calculated as follows: Step 1: Data Processing To ensure real-time performance, the amplitude data at time k is used for filtering. This represents the sum of the amplitude data from the first k time steps. Step 2: Kernel density estimation Step ①: Apply a threshold τ to the offline data To differentiate, if the amplitude 'a' is greater than 'τ', it is considered to be the target amplitude, thus forming the target amplitude dataset. Conversely, if the amplitude is not equal to the amplitude, it is considered to be clutter amplitude, thus forming a clutter amplitude dataset. The superscripts p and q represent set A respectively. t，k and A c，k Quantity; Step 2: Select the kernel function and bandwidth h, that is: Step 3: For offline sample A t and offline sample A c KDE estimation is performed using equation (23), and the corresponding results are obtained. and for: Step 3: Calculate the values ​​estimated in Step 2. and Replace g in the filtering process equation (22) a (a) and C a (a) yields the real-time update intensity D. k (x k However, the predicted intensity remains unchanged; 3-4GM-KDE-AI-PHD filter When the system's state equation and observation equation satisfy a linear Gaussian model, the prediction and update of KDE-AI-PHD are described by a closed-form Gaussian sum. The Gaussian implementation of the prediction and update steps at time k is as follows: 3-4-1 Assume that at time k-1, the multi-objective update intensity is expressed in the following Gaussian mixture form: Among them, J k-1 Update the number of intensity Gaussian terms at time k-1. and These are the weights, mean, and covariance matrix of the i-th updated Gaussian term at time k-1, respectively. The PHD of the newly emerging target RFS is expressed as Equation (29): Among them, J γ，k Let k represent the number of newly generated objective Gaussian terms at time k. Let represent the weight, mean, and covariance matrix of the Gaussian term of the j-th newly generated target at time k, respectively; 3-4-2 Predicted Intensity Where, γ k (x k J is given by equation (29). k-1 The number of Gaussian terms updating the intensity at time k-1 is expressed by the weights, mean, and covariance of the Gaussian terms in equation (30): Among them, P S，k F represents the survival probability of the target at time k. k-1 Let Q represent the state transition matrix. k-1 Represents the process noise covariance matrix; The predicted intensity can be rewritten as equation (32): J k|k-1 *J k-1 +J γ，k (33) in, and Let represent the weight, mean, and covariance matrix of the Gaussian term of the l-th predicted target at time k, respectively; 3-4-3 Update Strength in, and Let represent the weight, mean, and covariance matrix of the l-th updated Gaussian term at time k, respectively; in, This represents the probability density function of the target amplitude at time k, as estimated in real time by KDE. H represents the probability density function of clutter amplitude at time k estimated in real time by KDE. k Let R be the observation matrix. k To measure the noise covariance matrix, T denotes transpose; Step (4): Use the built GM-KDE-AI-PHD filter to achieve multi-target tracking.

2. The method according to claim 1, characterized in that... Step (1) specifically involves: The target moves in a two-dimensional plane, and its state is represented by x = [p x v x p y v y ] T , where p x p y These represent the target's positions in the x and y directions, respectively, and v x v y ... The noise covariance of the target motion process is set as follows: σ x (k) 2 σ represents the noise variance of the environment at time k relative to the target's velocity x. y (k) 2 This represents the noise variance of the environment at time k related to the target's y-velocity; Set the observation noise covariance of the sensor to be... Where δ x 2 δ y 2 These represent the noise variance of the sensor at the target's x and y positions, respectively.

3. The method according to claim 1 or 2, characterized in that... Step (2) specifically involves: 2-1 Target State Modeling Let N be the number of targets at time k. k The target states are as follows: The target state at time k is determined by a random finite set (RFS)X. k It means, that is Where χ represents the state space. It is the set of all finite subsets of χ; The goal starts from a certain state x at time k-1. k-1 Transition to a certain state x at time k k This is called a state transition, assuming the probability density f for each target state transition. k|k-1 (x k |x k-1 It conforms to a linear Gaussian model, expressed as: f k|k-1 (x k |x k-1 )=N(x k ;F k-1 x k-1 ,Q k-1 ) (2) Where N(x) k ;F k-1 x k-1 Q k-1 ) represents the target state x k The spatial distribution of follows a state mean of F. k-1 x k-1 The covariance is Q k-1 Gaussian distribution, F k-1 Let Q be the state transition matrix. k-1 The process noise covariance matrix; 2-2 Target Kinematic Observation Modeling Let Mk be the number of target measurements received at time k, and the target measurements be as follows: The sensor measurement vector at time k is represented by z. k =[z x , z y ] T The target measurement at time k can be obtained from the finite set Z. k It means, that is Among them, z x , z y These represent the target's positions measured by the sensors in the x and y directions, respectively, with T indicating transpose. For observation space, yes The set of all finite subsets; Assume the sensor measurement model g at time k k|k-1 (z k |x k It conforms to a linear Gaussian model, expressed as: g k|k-1 (z k |x k )=N(z k H k x k R k (4) where N(z) k H k x k R k ) represents a measurement z at time k. k The spatial distribution of follows a mean of H. k x k The covariance is R k Gaussian distribution, H k Let R be the observation matrix. k To measure the noise covariance matrix; 2-3 Clutter Kinematic Observation Modeling Suppose that the number of clutter received at time k follows a Poisson distribution with parameter λ, and the clutter positions in the measurement space follow a uniform distribution, i.e. Where, n c ρ(n) represents the expected clutter number at time k. c () represents the probability function of a Poisson distribution with parameter λ. The observed value of clutter j represents the value of the observed clutter. The probability density, where V represents the volume of the observation space; Therefore, the intensity of the clutter at time k is expressed as: 2-4. Target Amplitude Observation Modeling: To construct the target observation amplitude data, we assume that the target amplitude of this invention follows a Weibull distribution, and its probability density is expressed as: Where a represents amplitude, u is a proportional parameter, and v is a shape parameter. In this invention, u = 25 and v = 1.5 are taken. Use g a (a) represents the target amplitude probability density function for a > 0, i.e.: Let the amplitude threshold be τ. When the target measurement amplitude is greater than τ, it is considered that there is a probability p. D The probability that a target is detected by a sensor is called the detection probability. The probability density function of the target amplitude is then expressed as... express: 2-5 Clutter Amplitude Observation Modeling To construct clutter observation amplitude data, it is assumed that the clutter amplitude of this invention follows a Weibull distribution, with its probability density as shown in equation (7), where u = 3 and v = 1; using C a (a) represents the clutter amplitude probability density function for a > 0, i.e.: When the clutter amplitude is greater than τ, it is assumed that there is a probability p. FA The probability that a clutter signal is detected as a target by a sensor is called the false alarm probability. The probability density function of the clutter amplitude is then expressed as... express:

4. A GM-AI-PHD multi-target tracking device based on kernel density estimation that implements the method of any one of claims 1-3, characterized in that... Including the GM-KDE-AI-PHD filter.

5. A computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to perform the method of any one of claims 1-3.

6. A computing device comprising a memory and a processor, wherein the memory stores executable code, and the processor, when executing the executable code, implements the method of any one of claims 1-3.

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