Fast UK-GMPHD multi-target tracking method in three-dimensional space

Abstract

The application discloses a fast UK-GMPHD multi-target tracking method in three-dimensional space. The application is to construct a single-sensor multi-target tracking scene, set relevant parameters, including process noise of target motion and observation noise of a sensor; model states and observation of the multi-target; perform F-UK-GMPHD filtering on the sensor to obtain a posteriori Gaussian component, and realize multi-target tracking. The updating step of the original UK-GMPHD is improved, and the merging operation is omitted to improve the operation efficiency, so that the proposed filter can significantly improve the calculation efficiency in a complex tracking environment. The application proposes a complete processing method and process, and the configuration structure is clear, which can effectively improve the multi-target tracking efficiency while ensuring the tracking accuracy, and can be widely applied in the field of single-sensor multi-target tracking.

Description

Technical Field

[0001] This invention belongs to the field of single-sensor multi-target tracking, and relates to a fast UK-GMPHD multi-target tracking method in three-dimensional space. In three-dimensional space, by improving the Gaussian mixture probability hypothesis density filter (GMPHD), a fast unscented Kalman Gaussian mixture probability hypothesis density filter (UK-GMPHD) multi-target tracking method is realized under nonlinear observation conditions. This method can maintain multi-target tracking accuracy in complex environments while significantly improving tracking efficiency. Background Technology

[0002] Multi-target tracking refers to jointly estimating information such as the number and status of targets from data acquired by sensors. Currently, the most popular multi-target tracking methods are divided into two types: one is based on data association (DA), and the other is based on random finite sets (RFS).

[0003] The theory of random finite sets (RFS) provides a new theoretical foundation for solving multi-target tracking problems and has attracted much attention from scholars both domestically and internationally. This theory models the target state and sensor observation information as separate finite sets, possessing strong mathematical foundations. One engineering implementation based on RFS is the Probability Hypothesis Density (PHD) filter. This filter approximates the probability density function of a multi-target RFS following a Gaussian distribution using first-order moments, thus avoiding the use of data association methods to solve the target dynamic state estimation problem. However, under nonlinear observation conditions, the original single-sensor Gaussian mixture probability hypothesis density filtering method (GNPHD) suffers from low tracking efficiency when tracking a large number of targets. Summary of the Invention

[0004] The first objective of this invention is to address the low tracking efficiency of the original single-sensor Gaussian mixture probability hypothesis density filtering (GNPHD) method when tracking a large number of targets under nonlinear observation conditions. To enhance practical engineering applications, a fast UK-GMPHD multi-target tracking method in three-dimensional space is proposed, abbreviated as F-UK-GMPHD, which effectively improves the multi-target tracking efficiency.

[0005] To achieve the above objectives, the technical solution adopted by the method of the present invention is as follows:

[0006] 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;

[0007] Step (2): Model the state and observation of multiple targets;

[0008] Step (3): Based on steps (1) and (2), perform F-UK-GMPHD filtering on the sensor to obtain the posterior Gaussian component;

[0009] Step (4) Repeat step (3) to obtain the multi-target estimation results for all time points under Monte Carlo simulation, realize multi-target tracking, and use the performance evaluation index - Optimal Submode Allocation (OSPA) to evaluate the performance of the method of the present invention.

[0010] Step (5): Repeat steps (3)-(4) to perform the next Monte Carlo filtering.

[0011] A second 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.

[0012] A third 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.

[0013] The beneficial effects of this invention are:

[0014] This invention proposes a fast UK-GMPHD multi-target tracking method (F-UK-GMPHD) under nonlinear observation conditions in three-dimensional space. By improving the update steps of the original UK-GMPHD and eliminating the merging operation, the operating efficiency is improved. Therefore, the filter proposed in this invention can significantly improve computational efficiency in complex tracking environments. This invention presents a complete processing method and workflow with a clear configuration structure, effectively improving multi-target tracking efficiency while ensuring tracking accuracy, and can be widely applied in the field of multi-target tracking. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating the specific implementation of the core part of the method of this invention;

[0016] Figure 2 This is a diagram of the actual movement trajectory of the targets (number of targets is 50);

[0017] Figure 3 This is a target tracking image using the F-UK-GMPHD filtering method;

[0018] Figure 4 This is a comparison graph showing the OSPA average of the method of this invention with that of the original single-sensor UK-GMPHD filter under 100 Monte Carlo simulations.

[0019] Figure 5 This is a comparison chart of the number of targets estimated by the method of this invention and the original single-sensor UK-GMPHD filter under 100 Monte Carlo simulations. Detailed Implementation

[0020] The specific embodiments of the present invention will be described in detail below with reference to the technical solutions and accompanying drawings.

[0021] A fast UK-GMPHD multi-target tracking method in three-dimensional space 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 is performing non-maneuvering motion in three-dimensional space, and its state is represented as x = [p x v x p y v y p z v z ] T , where p x p y p z These represent the target's positions in the x, y, and z directions, respectively, and v x v y v z These are the velocities of the target in the x, y, and z directions, respectively, with the superscript T indicating transpose;

[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 related to the target's velocity in the x-direction. y (k) 2 σ represents the noise variance of the environment at time k related to the target's velocity in the y-direction. z (k) 2 This represents the noise variance of the environment at time k in relation to the target's velocity in the z direction;

[0025] The spatial position of the sensor can be represented as obs = [p x，obs p y，obs p z，obs ] T p x，obs p y，obs p z，obs These represent the sensor positions in the x, y, and z directions, respectively, with the superscript T indicating transpose; the sensor's observation noise covariance is set to... Where δ d 2 δ θ 2 δ α 2 These represent the noise variances for sensor distance, azimuth, and elevation, respectively.

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

[0027] 2-1 Target State Modeling

[0028] For any existing target i, its state at time k is represented as x. i，k At time k-1, the states of the M(k-1) targets can be represented as X. k-1 ={x 1，k-1 x 2，k-1 , ..., x M(k-1)，k-1 At time k, these targets may die or continue to exist. Targets that continue to exist will evolve into their new states, and new targets may emerge. Therefore, the new states of M(k) targets can be represented as X. k ={x 1，k x 2，k , ..., x M(k)，k}

[0029] The state equations of motion for target i in a discrete system can be described as follows:

[0030] x i，k+1 =F·x i，k +G·Q i，k (1)

[0031] Where, x i，k+1 and x i，k Let F represent the state of target i at time k+1 and k, respectively; let G represent the noise driving matrix; let Q represent the state transition matrix; let Q ... i，k Let represent the process noise covariance of target i at time k.

[0032] 2-2 Sensor Observation Modeling

[0033] At time k, the target state x i The resulting observation equations are as follows:

[0034] z i，k =g(x i，k )+ε (2)

[0035] Among them, z i，k This indicates that the target state is x i，k The observation vector; g is the nonlinear observation function; ε represents the sensor's observation noise, which is generally assumed to follow a Gaussian random process with a mean of 0 and a known covariance of R.

[0036] At time k, in addition to acquiring measurements of the target, the sensor may also be affected by environmental clutter, resulting in spurious measurements. Assume that the number of clutter observations follows a Poisson process with intensity λ (also called the clutter expectation number), and its location is uniformly distributed within the observation area. Therefore, the clutter equation can be expressed as follows:

[0037]

[0038] Wherein, ρ(n) c，k () indicates that the clutter quantity at time k is n c，k The probability function of the Poisson distribution; This indicates that the i-th clutter was observed, and the observed value is... The probability density; V represents the volume of the observation space.

[0039] The measurement value received by the sensor at time k consists of the measurement generated by the target (Equation (2)) and clutter (Equation (3)), and the measurement generated by the target and the clutter are indistinguishable. Therefore, the measurement value received by the sensor at time k can be represented as Z. k ={z 1，k , z 2，k ,…,z N(k)，k}, where N(k) represents the number of measurements received by the sensor at time k.

[0040] Step (3): Based on steps (1) and (2), the sensor is subjected to F-UK-GMPHD filtering to obtain the posterior Gaussian component, specifically:

[0041] 3-1: F-UK-GMPHD Prediction

[0042] Suppose that at time k-1, the multi-objective PHD can be expressed as a Gaussian mixture as follows:

[0043]

[0044] Where D k-1 (x) represents the PHD with target state x at time k-1, J k-1 It is the number of Gaussian components at time k-1; and These are the weights, state mean, and state covariance of the i-th Gaussian component, respectively. Let x represent the spatial distribution of the target state, which follows a state mean of 1 / x. State covariance is The Gaussian distribution.

[0045] Then the predicted PhD at time k can be expressed as:

[0046] D k|k-1 (x)=Ds，k|k-1 (x)+γ k (x) (5)

[0047]

[0048]

[0049]

[0050]

[0051] Where D k|k-1 (x) represents the predicted PHD with target state x at time k; D S，k|k-1 (x) represents the predicted PHD with surviving target state x at time k; γ k (x) represents the predicted PHD with the newborn target state x at time k; p S，k G represents the survival probability; G represents the noise driving matrix; Q represents the survival probability. k-1 J represents the process noise covariance at time k-1; γ，k It is the number of Gaussian components of the new target; and These represent the weights, state mean, and state covariance of the Gaussian component of the i-th newly generated target at time k, respectively. Let x represent the spatial distribution of the target state, which follows a state mean of 1 / x. State covariance is The Gaussian distribution. denoted as the mean and covariance of the predicted state of the i-th surviving target at time k, respectively. Let x represent the spatial distribution of the target state, which follows a state mean of 1 / x. State covariance is The Gaussian distribution.

[0052] Because the prediction of PHD D at time k k|k-1 (x) is also a Gaussian mixture form, so equation (5) can be rewritten as follows:

[0053]

[0054] in,

[0055] J k|k-1 =J k-1 +J γ，k (11)

[0056]

[0057] Let x represent the spatial distribution of the target state, which follows a state mean of 1 / x. State covariance is Gaussian distribution; Let represent the weight, state mean, and state covariance of the i-th predicted Gaussian component at time k, respectively.

[0058] 3-2: Obtain the Sigma point set and corresponding weights

[0059] 3-2-1 Obtaining the Sigma point set

[0060] For J k|k-1 J is obtained by calculating the predicted Gaussian components. k|k-1 Sets of Sigma points, each set containing 2n points. x +1, then calculate the mean predicted state of each Sigma point within each Sigma point set.

[0061]

[0062] Where j represents the j-th Sigma point, j = 1, ..., 2n x +1; n x λ represents the state dimension. U =α U 2 (n x +k U )-n x α represents a scaling factor used to reduce the overall prediction error; U Indicates the distribution state of the sampling points; κ U This represents a preset parameter, which can take the value 0 and be adjusted by κ. U Make matrix (n) x +λ U P0 is a positive semi-definite matrix; P0 represents the initial covariance;

[0063] 3-2-2 Calculate the corresponding weights of the Sigma points

[0064]

[0065] in The weights are the state mean values ​​within the Sigma point set. β represents the weights corresponding to the state covariance within the Sigma point set, where the superscript j indicates the j-th Sigma point; U It is a non-negative number (i.e., β) U (≥0), generally 2 can be selected.

[0066] 3-3: F-UK-GM-PHD Update

[0067] Multi-objective prediction PHD D based on time k k|k-1(x), which will then be updated to obtain the posterior PHDD. k (x), the PhD update formula is as follows:

[0068]

[0069] Where φ represents a coefficient (0≤φ≤1, p) d D represents the detection probability. d，k (x; z) represents the measurement z to update the prediction PHD.

[0070] In formula (15), φ·(1-p) d )·D k|k-1 (x) represents the update of the missed component. Z is measured at time k. k Updated PhD forecasts.

[0071]

[0072]

[0073]

[0074]

[0075] in,

[0076]

[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084] In the above, This represents the weight, state mean, and state covariance of the l-th posterior Gaussian component at time k. J k This represents the updated number of Gaussian components; Let x represent the spatial distribution of the target state, which follows a state mean of 1 / x. State covariance is Gaussian distribution; p dFor detection probability; The spatial distribution of measurement z is represented by its mean being... covariance is Gaussian distribution; k k Z represents clutter intensity; g(·) is the nonlinear observation function; M，k Initially, it is an empty set used to record the measures used for updates. That is, after each prediction PHD is updated, the measure z corresponding to the PHD component with the largest weight is set. Ψ，k Join Z M，k gather; Let Ψ represent the likelihood of the i-th measurement z at time k, and let Ψ represent the measurement index. z represents the gain of the l-th posterior Gaussian component at time k; Ψ，k This represents the Ψth measurement at time k; Let R represent the mean of the Ψth predicted observation; R represents the measurement noise covariance. The weight is the state mean value of the j-th Sigma point within the Sigma point set. Let be the weight corresponding to the state covariance of the j-th Sigma point within the Sigma point set; Let represent the mean of the i-th predicted observation; This represents the mean of the j-th predicted state within the i-th Sigma point set; This represents the j-th predicted observation within the i-th Sigma point set; Let represent the covariance of the i-th predicted observation; Let represent the covariance of the i-th state measurement.

[0085] Notice, The posterior Gaussian component does not belong to D d，k (x; z), the number of Gaussian components J after the last update k ≤J k|k-1 .

[0086] To facilitate understanding, the update steps of the above PHD are explained. Unlike traditional PHD updates, for missed detection component updates, the original PHD retains the missed detection components, which increases computational cost. These are then multiplied by a weight φ to reduce the number of Gaussian components in subsequent pruning steps. For measurement updates, traditional PHD measurement updates generate a set of posterior PHD components for each measurement, each with a certain weight, and then normalize them. The update in this invention updates a specific PHD prediction component using each measurement, retains the PHD component with the highest weight, and simultaneously deletes the measurement z corresponding to the updated PHD component with the highest weight. Ψ，k(Since a target can generate at most one measurement). To speed up the update efficiency, when using measurements to update the predicted PHD, Mahalanobis distance can be introduced to segment the entire observation space into measurements, and some impossible measurements (measurements that are far from the target) can be deleted.

[0087] 3-4: Pruning

[0088] After updating at time k through steps 3-1 to 3-3, the number of posterior Gaussian components in the target posterior PHD faces the computational challenge of increasing over time. Traditional PHD methods employ pruning and merging operations to reduce the number of Gaussian components. However, merging involves traversal and performs Mahalanobis distance calculations each time, which involves matrix inversion calculations, resulting in low computational efficiency when there are many targets. Therefore, to improve computational efficiency, this invention only employs pruning operations, specifically by pruning components with weights less than a threshold τ. h Prune the Gaussian components, retaining those with higher weights:

[0089]

[0090] Where the trimming threshold 0 < τ h ≤1.

[0091] The pruned Gaussian components can be represented as follows:

[0092]

[0093] in, Let $\mathbf{i}$ represent the weight, state mean, and state covariance of the $i$-th Gaussian component after pruning at time $k$. This represents the number of Gaussian components after pruning at time k; Let x represent the spatial distribution of the target state, which follows a state mean of 1 / x. State covariance is Gaussian distribution;

[0094] 3-5: New target automatically starts

[0095] 3-5-1 Setting parameters: Maximum speed VMAX and minimum speed VMIN

[0096] Measurements of newborns at time 3-5-2k are represented as follows: ( Specifically by Z k -Z M，k (Calculated), the measurement of newborns at time k-1 is... N(k) represents the number of measurements taken at time k.

[0097] When the following formula holds true, the newborn target Beginning:

[0098]

[0099] Where h p (·) represents a mapping function, which maps the measurement to the Cartesian coordinate system.

[0100] 3-5-3 Repeat step 3-5-2 to iterate through all measurement sets. and Z k-1 The resulting Gaussian components of the new target are:

[0101]

[0102] 3-5-4 As the posterior multi-objective PHD at time k, while simultaneously incorporating the newborn γ k (x) is passed to time k+1 for the next time step PHD prediction and update.

[0103]

[0104] 3-6: Multi-objective state estimation

[0105] Pruning and merging yields posterior PhD D k The number of final targets can be estimated using the following formula: (x).

[0106]

[0107] The round(·) function represents the rounding operation.

[0108] Take before Each weight is greater than a certain threshold τ M The state mean is used as the multi-objective state at time k.

[0109] Step (4) repeats step (3) to obtain the multi-target estimation results for all time points under Monte Carlo simulation, thereby achieving multi-target tracking. The performance evaluation index—Optimal Submode Allocation (OSPA)—is then used to evaluate the performance of the method of this invention. This is a conventional technique and will not be described in detail here.

[0110] Step (5): Repeat steps (3)-(4) to perform the next Monte Carlo filtering. This is a standard technique and will not be described in detail.

[0111] The simulation experiment of this invention is as follows:

[0112] Simulation conditions: This invention was simulated on a computer with an Intel(R) Core(TM) i5-6300HQ CPU@2.30GHz and 8.00GB of memory, using MATLAB R2018b software.

[0113] Simulation scenario settings: The sensor's 3D spatial position is obs = [0, 0, 0] T The detection space is [0, 6km] × [0, 6km] × [0, 15km]. The process noise covariance is set to... The observation noise covariance is set to The detection probability pd = 0.9, and the survival probability p S，k =0.99, pruning threshold τ h =0.001, clutter expectation number λ = 100, tracking step size 100 times.

[0114] Simulation Result Analysis: Figure 2 The image shows the actual motion trajectory of the target (50 targets). The result after using the method of this invention is as follows. Figure 3 , Figure 4 , Figure 5 As shown in Table 1. Figure 3 To track the scene, the motion trajectories of multiple targets are simulated and the F-UK-GMPHD tracking results are presented; Figure 4 This is a comparison chart of the OSPA average value after 100 Monte Carlo simulations and the original single-sensor UK-GMPHD filter; Figure 5 This is a comparison chart of the number of target estimates after 100 Monte Carlo simulations and the original single-sensor UK-GMPHD filter; Table 1 shows the average time required to run one Monte Carlo simulation after 100 simulations. Figure 4 The comparison shows that the method of the present invention has a relatively large OSPA compared with the traditional UK-GMPHD. However, Table 1 shows that the method of the present invention has a significantly improved computational efficiency compared with the traditional UK-GMPHD. This demonstrates that the algorithm of the present invention can effectively and quickly improve the efficiency of multi-target tracking while ensuring tracking accuracy, and achieve a stable and fast tracking effect.

[0115] Table 1 compares the average time required for one Monte Carlo run of the method of this invention (F-UK-GMPHD) and the original PHD filter (UK-GMPHD) under 100 Monte Carlo runs.

[0116]

Claims

1. A fast UK-GMPHD multi-target tracking method in three-dimensional space, characterized in that, The method, abbreviated as F-UK-GMPHD, 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): Based on steps (1) and (2), the sensor is subjected to F-UK-GMPHD filtering to obtain the posterior Gaussian component, specifically: 3-1: F-UK-GMPHD Prediction Assuming in At time t, the multi-objective PHD is represented in the following Gaussian mixture form: in express The target state at any given time is PhD, yes The number of Gaussian components at time step; , and The first The weights, state mean, and state covariance of each Gaussian component; Indicates the target state is The spatial distribution of follows a state mean of . The state covariance is Gaussian distribution; So The prediction of the PhD at time point is expressed as: in express The target state at any given time is Predicted PhD; express The target state for survival at any time is Predicted PhD; ; Indicates the probability of survival; Represents the noise driving matrix; Indicates in Process noise covariance at any given time; It is the number of Gaussian components of the new target; , and Represent Time of the first The weights, state mean, and state covariance of the Gaussian components of the new target; Indicates the target state is The spatial distribution of follows a state mean of . The state covariance is Gaussian distribution; Represent Time of the first The mean and covariance of the predicted states of the Gaussian components of the surviving targets; Indicates the target state is The spatial distribution of follows a state mean of . The state covariance is Gaussian distribution; Represents the state transition matrix; because Predicting PhD in Time It is a Gaussian mixture form, therefore the equation is... Rewritten as follows: in, Indicates the target state is The spatial distribution of follows a state mean of . The state covariance is Gaussian distribution; They represent Time of the first The weights, state mean, and state covariance of each predicted Gaussian component; 3-2: Obtain the Sigma point set and corresponding weights 3-2-1 Obtaining the Sigma point set right The predicted Gaussian components are obtained through calculation. Group Sigma point sets, each group containing 1 / 2 Sigma points. Then calculate the mean predicted state of each Sigma point within each Sigma point set. ; in Indicates the first Sigma points, ; Indicates the dimension of the state; , Indicates the scaling factor. Indicates the distribution of sampling points. This represents the preset parameters, which can be adjusted... Make the matrix It is a positive semi-definite matrix; Indicates the initial covariance; 3-2-2 Calculate the corresponding weights of the Sigma points in The weights are the state mean values ​​within the Sigma point set. The superscript represents the weights corresponding to the state covariance within the Sigma point set. Indicates the first One Sigma point; It is a non-negative number; 3-3: F-UK-GMPHD Update Based on formula (15), multi-objective prediction PHD is performed. Update to obtain the posterior PhD : in To represent a coefficient, , For detection probability, Indicates measurement Updated predictions for PhD; In formula (15) This indicates an update of the missed detection components. express Time measurement Updated predictions for PhD; in, in express Time of the first The weights, state mean, and state covariance of each posterior Gaussian component; This represents the updated number of Gaussian components; Indicates the target state is The spatial distribution of follows a state mean of . The state covariance is Gaussian distribution; For detection probability; Indicates measurement The spatial distribution of follows a mean of . The covariance is Gaussian distribution; Indicates clutter intensity; It is a nonlinear observation function; This represents the measurement set corresponding to the PHD component with the largest weight. express Time of the first Individual measurement The likelihood, Indicates the measurement index; express Time of the first Gain of a posterior Gaussian component; express Time of the first Individual measurements; Indicates the first The mean of the predicted observations; Indicates the measurement noise covariance; For the Sigma point set, the first The weights corresponding to the state mean of each Sigma point; For the Sigma point set, the first The weights corresponding to the state covariance of each Sigma point; Indicates the first The mean of the predicted observations; Indicates the first Within the Sigma point set, the first The mean of each predicted state; Indicates the first Within the Sigma point set, the first One predictive observation; Indicates the first The covariance of each predicted observation; Indicates the first Covariance of state measurements; express The measurement value received by the time sensor; This indicates that the number of clutter observations generated follows the intensity. Represents the volume of the observation space; 3-4: Pruning Prune the posterior Gaussian components of the target posterior PHD, retaining the Gaussian components with larger weights: in Indicates the pruning threshold. ; The pruned Gaussian components are represented as follows: in, express The first time after pruning The weights, state mean, and state covariance of each Gaussian component; express The number of Gaussian components after pruning at any given time; Indicates the target state is The spatial distribution of follows a state mean of . The state covariance is Gaussian distribution; 3-5: New target automatically starts 3-5-1 Setting parameters: Maximum speed and minimum speed ; 3-5-2 The measurement time used for newborns is represented as follows: , The time used for measurement of newborns is... , express Number of measurements taken at any given time; When the following formula holds true, the newborn target Automatic start; in This represents a mapping function, which maps measurements to a Cartesian coordinate system. 3-5-3 Repeat step 3-5-2 to traverse all measurement sets. and The resulting Gaussian components of the new target are: 3-5-4 will As The posterior multi-objective PhD at time, while also including newborns Passed to The next time step of the PhD prediction and update is performed continuously. 3-6: Multi-objective state estimation Pruning and merging to obtain posterior PHD The estimated number of final targets can be obtained using the following formula: in Indicates the rounding operation; Take before Each weight is greater than the threshold State mean As Multi-objective state at all times ; Step (4) Repeat step (3) to obtain the multi-target estimation results for all time points under Monte Carlo simulation, thereby achieving multi-target tracking; Step (5): Repeat steps (3)-(4) to perform the next Monte Carlo filtering.

2. The method according to claim 1, characterized in that... Step (1) specifically involves: The target is performing non-maneuvering motion in three-dimensional space, and its state is represented as follows: ,in The target is in The position of direction, The target is in Speed ​​in direction, superscript Indicates transpose; The noise covariance of the target motion process is set as follows: , express The environment at any time affects the target. The noise variance of directional velocity, express The environment at any time affects the target. The noise variance of directional velocity, express The environment at any time affects the target. Noise variance of velocity; The sensor's spatial location is represented as ,in These represent the sensors at... The orientation of the position; setting the sensor's observation noise covariance to... ,in , , These represent the noise variances for sensor distance, azimuth, and elevation, respectively.

3. The method according to claim 2, characterized in that... Step (2) specifically involves: 2-1 Target State Modeling For any existing target ,That The state at time point is represented as ;exist time, The state of each objective is represented as: ;arrive At any given moment, these goals may die or continue to exist; those that continue to exist will develop into new states, and new goals may emerge. The new state of the objective is represented as follows: ; Objectives of Discrete Systems The equation of state for motion can be described as follows: in, and They represent and Momentary Goal The state; Represents the state transition matrix; Represents the noise driving matrix; express Momentary Goal Process noise covariance; 2-2 Sensor Observation Modeling At all times, the target state The resulting observation equations are as follows: in, Indicates that the target state is The observation vector; It is a nonlinear observation function; Indicates the observation noise of the sensor exist At any given time, in addition to acquiring measurements of the target, sensors may also be affected by environmental clutter, resulting in spurious measurements; assuming the number of clutter observations follows an intensity-dependent order. The Poisson process is uniformly distributed across the observation area; therefore, the clutter equation is expressed as follows: in, express The number of clutter at time is The probability function of the Poisson distribution; Indicates the observation of the first A clutter, observed value The probability density; Represents the volume of the observation space; exist The measurements received by the time sensor consist of both measurements generated by the target and clutter, and the measurements generated by the target and the clutter are indistinguishable; therefore, The measurement value received by the time sensor is represented as , express The number of measurements received by the time sensor.

4. 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.

5. 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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