An underwater multi-target tracking method based on kernel mean embedding belief propagation

Abstract

This invention discloses an underwater multi-target tracking method based on kernel mean embedding confidence propagation. It employs a kernel mean embedding method, approximating the probability density function of the target state with a small number of kernel particles. This overcomes the problem of incomplete observability of the system with lower computational complexity, transforming the strongly nonlinear problem of passive tracking in a low-dimensional measurement space into a linear problem in a high-dimensional feature space. This solves the problems of strong nonlinearity in underwater multi-target measurement functions and incomplete observability of target states, thus improving the tracking accuracy of underwater passive tracking. Furthermore, this invention overcomes the problem of excessively high computational complexity caused by the traditional BP algorithm using random particles or Gaussian mixture density to approximate the probability density distribution through a kernel mean confidence propagation method under the Gaussian assumption. It handles the matching problem between measurement results and targets with lower computational complexity, significantly improving the scalability of the system.

Description

Technical Field

[0001] This invention belongs to the field of underwater target tracking technology, specifically relating to an underwater multi-target tracking method based on kernel mean embedding belief propagation. Background Technology

[0002] Passive underwater target tracking is a crucial aspect of marine exploration. By passively receiving the azimuth information of the observed target, passive underwater target tracking achieves silent tracking while ensuring its own safety, offering superior stealth compared to active tracking. Furthermore, the detection platform does not require a high-power transmitting antenna, significantly reducing costs. With the rapid growth of military and civilian demands for marine resource exploration and territorial sea security monitoring, theoretical and applied research on passive underwater target tracking is of significant scientific and practical value for meeting public needs and safeguarding national security. Passive underwater target tracking technology in complex marine environments is an important means of marine exploration and has significant research implications. Due to the inherent incomplete observability and strong nonlinearity of the system, passive underwater target tracking faces challenges such as numerous false tracks and low tracking accuracy. Research on passive underwater multi-target tracking technology based on kernel mean embedding (KME) confidence propagation can improve the tracking accuracy and track quality of underwater passive detection systems, providing technical support for enhancing the performance of my country's near-shore defense systems and holding significant research importance for building a maritime power. Summary of the Invention

[0003] This invention proposes an underwater multi-target passive tracking method based on kernel mean embedding belief propagation, which reduces the false track rate of underwater target passive tracking, improves the quality of underwater detection and tracking, enhances the scalability of underwater target passive tracking system, and provides technical support for improving the performance of my country's near-shore underwater detection system.

[0004] This invention provides an underwater multi-target tracking method based on kernel mean embedding confidence propagation, which includes the following steps:

[0005] Step 1: Initialize nuclear particles M is the number of nuclear particles;

[0006] Step 2: Training the nuclear particles at the previous time step n-1 Make predictions and then predict the nuclear particles. Mapping to the regenerating nuclear Hilbert space, we obtain the set of characteristic mappings Φ of the nuclear particles. n,k ;

[0007] Step 3: Based on the feature mapping set Φ at the current time n n,k Based on the sensor measurements, kernel mean embedding is used to obtain the predicted state x of the target k at the current time n. n|n-1,k And the predicted covariance P n|n-1,k Based on the predicted state xn|n-1,k And the predicted covariance P n|n-1,k Obtain the posterior state x of the target k at the current time n. n|n,k and posterior covariance P n|n,k The expression is:

[0008]

[0009] in, Update information for covariance; This is for updating state information; s = 1, 2, ..., S; S is the number of sensors;

[0010] Step 4: Calculate the survival probability of the target k and determine whether to terminate the tracking of the target k.

[0011] Step 5: Construct and solve the correlation optimization objective function using track integral distance; correlate the tracks acquired by different sensors for the same target and assign global track labels; construct and solve the fusion optimization objective function using pseudo-measurement cross-validation until the error between the global track state and the pseudo-measurement mean is less than the error threshold h, and obtain the fused global track.

[0012] Step 6: Repeat steps 2 to 5 to obtain the global tracks of different targets at different times.

[0013] Preferably, in step three, the covariance update information is obtained. and status update information The method is as follows:

[0014] 3-1. Under the Gaussian assumption based on kernel mean embedding, obtain the predicted state x of the target k at the current time n. n|n-1,k And the predicted covariance P n|n-1,k as follows:

[0015]

[0016] P n|n-1,k =FP n-1|n-1,k F T +GQ n-1,k G T

[0017] Where F is the state transition matrix; Let G be the posterior state of the target k at the previous time n-1; G is the noise driving matrix; Q is the posterior state of the target k at the previous time n-1; n-1,k P is the process noise matrix; n-1|n-1,k Let be the posterior covariance of the target k at the previous time n-1;

[0018] 3-2. Based on the transfer rules of the factor graph, obtain the measurement evaluation message of sensor s.

[0019] 3-3. Iterate through all measurement results, based on the measurement evaluation message. and the correlation vector oriented towards the target being measured and correlation vectors oriented towards measurement results Obtain the result of the BP internal message iteration loop during each iteration. Until the preset number of iterations P is reached; where p = 1, 2, ..., P; according to Obtain data association information

[0020] 3-4. Based on data association information Get the state update information at the current time n Covariance update information for:

[0021]

[0022] in, This represents the particle kernel weight vector after training at the current time n. This is a Jacobian matrix; Let be the covariance matrix of the target k after updating the measurement result z.

[0023] Preferably, in step five, the expression for the constructed correlation optimization objective function F(B) is:

[0024]

[0025] in, The global track is represented by l; the local track by 'l'; and the number of sensors by 'S'. For the global set of tracks; The maximum number of tracks; ι rl B represents the association symbol for local tracks; B represents the association symbol for all local tracks. rl The correlation matrix; s c and s d The sensor sequences are unequal; c and l d For unequal local track sequences; D is the track integral distance; D' is the cost of lack of association. is the generalized Kronecker delta function; t is the number of local tracks of the sensor.

[0026] Preferably, in step five, the fusion optimization objective function is: in Global track status With pseudo-measured mean The error between them is expressed as:

[0027]

[0028] Where H is the azimuth measurement equation; This refers to the state of sensor s itself. The state of the target being measured; This is a pseudo-measurement mean; is the covariance matrix of the pseudo-measurement.

[0029] Preferably, in step three, the measurement evaluation message of sensor s The expression is:

[0030]

[0031] in, This represents the measurement result of sensor s at the current time n; Let be the measurement equation for sensor s at the current time n; R is a Jacobian matrix; (s) The measurement noise of sensor s; This is the association vector oriented towards the target being measured; Let be the number of measurement results of the s-th sensor at time n; It follows a Gaussian distribution.

[0032] Preferably, in step three, the result of the BP internal message iteration loop The expression is:

[0033]

[0034] Where K is the number of targets being tested; Ψ is the target exclusion indicator function; and k' is the target label that is different from k. For internal iteration information;

[0035] Data association information The expression is:

[0036]

[0037] Preferably, the initialization of nuclear particles The expression is:

[0038]

[0039] Where, x o and y o These are the initial horizontal and vertical coordinates of the sensor; r is a random distance number, r∈[R].min ,R max ]; v is a random number representing the velocity, v∈[v min ,v max ]; β is a random number representing the heading angle, β∈[0,2π]; θ is the azimuth angle of the target being measured; R min and R max These are the minimum and maximum distances between the target and the sensor, respectively; v min and v max These are the maximum and minimum values ​​of the velocity of the target being measured, respectively.

[0040] Preferably, in step two, the predicted nuclear particles The expression is:

[0041]

[0042] Among them, f k (·,·) represents the state transition equation; It is Gaussian noise.

[0043] Preferably, in step two, the feature mapping set Φ of the nuclear particles n,k Obtained through a polynomial kernel function.

[0044] Preferably, in step four, the criterion for determining whether to terminate the tracking of the target k is:

[0045] Establish the tracking maintenance hypothesis H1 and the tracking termination hypothesis H0, and calculate the likelihood function P for each hypothesis. 1k and P 0k Likelihood function P 1k and P 0k The expression is:

[0046]

[0047] Where, m a k is the number of tests. a P is the scan number; D and P F These are the detection probability and the false alarm probability, respectively.

[0048] Using the likelihood ratio function of the two hypotheses The survival probability U of the target k being tested k And set two corresponding thresholds, C1 and C2;

[0049] 1) When U k ≥C2, accept hypothesis H1, and maintain the position;

[0050] 2) When U k If ≤C1, accept hypothesis H0, and the tracking ends;

[0051] 3) When C1 < U k < C2, continue the inspection.

[0052] The beneficial effects of the present invention are as follows:

[0053] 1. The present invention adopts the kernel mean embedding method, approximates the probability density function of the target state through a small number of kernel particles, overcomes the problem of incomplete observability of the system with a low computational complexity, transforms the strong non - linear problem of passive tracking in a low - dimensional measurement space into a linear problem in a high - dimensional feature space, solves the problems of strong non - linearity of the underwater multi - target measurement function and incomplete observability of the target state, and improves the tracking accuracy of underwater passive tracking.

[0054] 2. The present invention uses the kernel mean belief propagation method under the Gaussian assumption, uses the mean and covariance of the Gaussian distribution to transmit messages between nodes in the factor graph, and obtains a more accurate state estimate by using the covariance of the Gaussian distribution, overcoming the problem of excessive computational complexity caused by the traditional BP algorithm using random particles or Gaussian mixture density to approximate the probability density distribution, and dealing with the matching problem between measurements and targets with a low computational complexity, greatly improving the scalability of the system.

[0055] 3. The present invention converts the track association problem into an optimal problem to solve and outputs the global track label; then converts the local track state estimated by the node into a pseudo - measurement relative to the sensor, estimates the target position by using cross - location, and performs optimal distributed fusion by minimizing the cost function, effectively alleviating the problem of ghost points and false track formation caused by traditional cross - location fusion, and improving the tracking accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is the overall flow chart of the present invention.

[0057] Figure 2 is the schematic diagram of kernel embedding of joint distribution and finite - sample estimation in the present invention.

[0058] Figure 3 is the schematic diagram of the factor graph model of kernel mean embedding belief propagation in the present invention.

[0059] Figure 4 is the flow chart of the multi - sensor multi - target passive tracking track fusion algorithm in the present invention.

[0060] Figure 5 is the schematic diagram of the mean square error of single - sensor single - target tracking and Gaussian particle filtering in the case of clutter.

[0061] Figure 6 is the schematic diagram of the OSPA index of multi - sensor tracking in the present invention and the PFBP and GaBP algorithms when the number of targets is different.

[0062] Figure 7 This is a schematic diagram of OSPA under different detection probabilities according to the present invention. Detailed Implementation

[0063] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0064] like Figure 1 As shown, an underwater multi-target tracking method based on kernel mean embedding confidence propagation includes the following steps:

[0065] Step 1: Use a sequence to represent the input of a time window containing num radar scans. If a measurement result is present within the relevant time window during the current time n scans, set the window value to 1; otherwise, set it to 0. When the number of detections in the window reaches a certain value, the track start is successful. After the track starts, the target status is initiated. Because the measurement information obtained from underwater pure azimuth is dimensionless, only the approximate azimuth angle of the target is known, points are scattered in the azimuth area of ​​the target. For the underwater target, its speed and passive detection range will be within a roughly defined range; points are scattered within this range.

[0066] For M nuclear particles (KME particles), the minimum value generated by each nuclear particle is R. min The maximum value is R. max Generate a uniformly distributed random number r that satisfies the condition that the minimum value is v. min The maximum value is v max The velocity random number v, and the heading angle random number β with a minimum value of 0 and a maximum value of 2π are generated. The initialization of the nuclear particle is expressed as:

[0067]

[0068] Where, x o and y o θ represents the initial horizontal and vertical coordinates of the sensor; θ is the azimuth angle of the target being measured; i = 1, 2, ..., M; M is the number of nuclear particles.

[0069] Step 2: Let X represent a random variable with a domain Ω and a distribution P(X), and let x represent an instance of X. RKHSF denotes a random variable with a kernel function k(x,x′) satisfying the function... The Hilbert space whose inner product is <·,·> FIts element k(x,·) satisfies the regeneration property:<f(·),k(x,·)> F =f(x) means that the function f is evaluated as an inner product at any point x∈Ω.

[0070] In the data space, based on the nuclear particles trained at the previous moment... To make a prediction, obtain the nuclear particles in the data space at the current time n. The expression is:

[0071]

[0072] Among them, f k (·,·) represents the state transition equation; It is Gaussian noise.

[0073] like Figure 2 As shown, the trained nuclear particles at the previous time step n-1 are mapped to the regenerated nuclear Hilbert space (RKHS). The set of feature maps is in, Characteristic mapping of nuclear particles; Characteristic mapping of nuclear particles Obtained through a polynomial kernel function.

[0074] Step 3, as follows Figure 4 As shown, in a multi-target tracking system, the expanded-dimensional state of each target is... Where, x n,k Let n be the hidden state of the target k at the current time n. and These are the x and y coordinates of the target k at the current time n, respectively. and These are the lateral and longitudinal velocities of the target k at the current time n, respectively.

[0075] 3-1. Target State Prediction

[0076] Under the Gaussian assumption based on kernel mean embedding, the state prediction α of the k-th target at time n is obtained. → (x n,k The expression for ,1) is:

[0077]

[0078] Where, f(x) n,k ,1|z n-1 (z) represents the posterior state obtained based on the measurement results from the previous time step; n-1 The measurement result at time n-1; N(x) n|n-1,k ,Pn|n-1,k P represents the predicted distribution of the target k at time n; n|n-1,k Let be the predicted covariance of the target k at time n; The kernel weight vector is predicted a priori for the target k at time n.

[0079] The predicted state x of the target k at the current time n n|n-1,k And the predicted covariance P n|n-1,k The expression is:

[0080]

[0081] P n|n-1,k =FP n-1|n-1,k F T +GQ n-1,k G T

[0082] Where F is the state transition matrix, F∈R 4×4 ; Let G be the posterior state of the target k at the previous time n-1; G is the noise driving matrix, G∈R 4×2 Q n-1,k P is the process noise matrix; n-1|n-1,k Let be the posterior covariance of the target k at time n-1.

[0083] In the context of kernel mean embedding, the mathematical form of the prediction from the previous time n-1 to the current time n in the data space is:

[0084]

[0085] in, These are the nuclear particles after training at the previous moment; The particle kernel weight vector after training at time n-1; The prior weight covariance matrix; Let be the particle weight covariance matrix after training at time n-1.

[0086] In the context of confidence propagation based on kernel mean embedding, the message transmitted in the factor graph is described by the mean and covariance, which reduces the computational complexity caused by random samples.

[0087] 3-2. Evaluate the sensor's measurement results

[0088] Based on the transmission rules of the factor graph, obtain the measurement evaluation message of the s-th sensor. The expression is:

[0089]

[0090] in, This is the association vector oriented towards the target being measured; The number of measurement results of sensor s at the current time n; represents the measurement result of sensor s at the current time n; g represents the factor node; This is the matching function.

[0091] Under Gauss's assumption, the above equation is rewritten as:

[0092]

[0093] in, Let be the measurement equation for sensor s at the current time n; R is a Jacobian matrix; (s) The measurement noise of sensor s; It follows a Gaussian distribution;

[0094] 3-3. Correlation and Iteration Data

[0095] For all Iterate through each measurement result until the iteration count p equals the preset iteration count P; initialize internal iteration information. The expression is:

[0096]

[0097] Where β represents the measurement and evaluation information; Ψ represents the target exclusion indicator function.

[0098] The result of the message iteration loop inside the BP (belief propagation algorithm) during each iteration. The expression is:

[0099]

[0100] in, This represents the result of the BP internal message iteration loop; K is the number of targets being measured. The correlation vector is oriented towards the measurement result; k' is the sequence of measured targets that is different from k; For internal iteration information, its expression is:

[0101]

[0102] Where m' is a sequence of measurement results that is different from m.

[0103] Related vector a n,k and b n,m The formula is:

[0104]

[0105] Based on the results of the BP internal message iteration loop Obtain data association information The expression is:

[0106]

[0107] 3-4. Update measurement results

[0108] The measurement update information γ of the s-th sensor for the k-th target at time n. (s) (x n,k The expression for ,1) is:

[0109]

[0110] Based on the above equation and Gauss's assumption, the above equation can be rewritten as:

[0111]

[0112] Under the condition of kernel mean embedding, the above equation is rewritten as:

[0113]

[0114] Therefore, the measurement update information γ (s) (x n,k ,1) is represented as:

[0115]

[0116] in, and These are the current state update information and covariance update information, respectively, and their expressions are:

[0117]

[0118] in, This represents the particle kernel weight vector after training at the current time n. Let be the covariance matrix of the target k after updating the measurement result z.

[0119] 3-5. Reliability Calculation

[0120] Under the Gaussian assumption, the distribution of the measured target at time n The expression is:

[0121]

[0122] Where, x n|n,k P represents the posterior state at time n; n|n,j Let n be the posterior covariance at the current time n; S is the number of sensors.

[0123] Step 4: Establish the tracking maintenance hypothesis H1 and the tracking termination hypothesis H0, and calculate the likelihood functions P 1k and P 0k respectively. The expressions of the likelihood functions P 1k and P 0k are as follows:

[0124]

[0125] where m a is the number of detections; k a is the number of scans; P D and P F are the detection probability and the false alarm probability respectively.

[0126] Take the likelihood ratio function of the two hypotheses as the survival probability U k of the measured target k, and set the corresponding two thresholds to C1 and C2 respectively.

[0127] 1) When U k ≥ C2, accept the hypothesis H1 and maintain the tracking;

[0128] 2) When U k ≤ C1, accept the hypothesis H0 and terminate the tracking;

[0129] 3) When C1 < U k < C2, continue the test.

[0130] Among them, the threshold values are given by experience and have great uncertainty in a dense clutter environment.

[0131] Step 5: Perform a distributed fusion algorithm based on maximum likelihood cross-fusion on the obtained target states to obtain the fused target states;

[0132] As shown in Figure 3 , use the global nearest neighbor method to find a track association combination, and the sum of the association costs between any two tracks in this combination reaches the minimum among all possible association combinations. Construct the association symbol ι re of the local track, and the expression is:

[0133]

[0134] where, is the global track,

[0135] Each row in the association matrix B corresponds to the association symbol ι sl of all local tracks under one sensor; Since the number of local tracks of each sensor is inconsistent, so when ιsl =0; where t is the number of local tracks of the sensor; This represents the maximum number of tracks. Therefore, ι sl =0 occurs in two cases: sensor s does not have a local track labeled l; or sensor s has a track labeled l but is not associated with any other track.

[0136] Since a local track *l* can only correspond to one real target track, its converse also holds: for a specific real target, each sensor has at most one corresponding local track. Therefore, it can be deduced that one local track from one sensor is associated with at most one local track from another sensor. Solving the track association problem is transformed into solving an optimization problem with the objective function F(B) and the inequality condition being the unique constraint on the association matrix B. The optimization problem is written as follows:

[0137]

[0138] Among them, s c and s d The sensor sequences are unequal; c and l d B represents unequal local track sequences; B is the correlation matrix of all local track association symbols. For the global set of tracks, D represents the track integral distance; D' represents the cost of missing correlation. It is the generalized Kronecker delta function.

[0139] The optimization problem above is essentially an NP-complete problem. To quickly obtain the minimum-cost incidence matrix B, an S-dimensional allocation algorithm is used. This algorithm transforms the S-dimensional allocation problem into a 2-dimensional allocation problem using the Lagrange relaxation algorithm. Although this method employs the relaxation concept and can only achieve a suboptimal solution for the S-dimensional allocation, satisfactory results can be achieved by setting a tolerance error.

[0140] The input to the S-dimensional allocation algorithm is an S-dimensional cost matrix, defined as follows: Its element value is:

[0141]

[0142] in, The expression is:

[0143]

[0144] After solving the trajectory correlation problem, we will get the following at each time step. Each global track label and its corresponding local track information, up to the number of global track labels. If the value exceeds a preset threshold, the solution to the S-dimensional allocation algorithm is stopped. A novel maximum likelihood cross-fusion algorithm is used to independently... The global flight paths are merged, but here we only focus on... The steps for merging a single tag are explained in detail. The other tags can be treated in the same way.

[0145] Convert the local track (s,l) into a pseudo-measurement, and then calculate the mean of the pseudo-measurement. With covariance The expression is:

[0146]

[0147] Where H is the azimuth measurement equation; This represents the state of the s-th sensor itself. The state of the target being measured; For azimuth pseudo-measurement; P sl Let be the covariance matrix.

[0148] Transfer all local tracks to the measurement space and obtain a set of pseudo-measurement means. By using pseudo-measurement and based on the idea of ​​maximum likelihood, the track fusion problem is transformed into a new fusion problem: given the states of each sensor and the corresponding pseudo-measured mean Estimate global track state And minimize the error between it and the target's true state. Since the true state of the measured target is unknown, the approach is to minimize the global track state. With pseudo-measured mean The error between them is estimated using a method. The global track state is defined as... and These are the horizontal and vertical coordinates of the target being measured; and These represent the lateral and longitudinal movement speeds of the target being measured; and the global trajectory status. With pseudo-measured mean error The expression is:

[0149]

[0150] Based on the aforementioned pseudo-measurement transformation and error definition, the new fusion problem is solved through optimization. Due to the continuity and infinity of the target state space, randomly selecting initial values ​​may lead to slow solution speed or low accuracy. Therefore, a geometric crossover method is used to constrain the solution space; the pseudo-measurement mean is then used. Obtained pseudo-measurement of angle and sensor position Perform the calculation of the intersection points and constrain the solution space. The constrained solution space is as follows:

[0151]

[0152] in, K sl Pseudo-measurement The corresponding slope. The above optimization problem is solved using a sequential quadratic programming algorithm until the global trajectory state is reached. With pseudo-measured mean error Obtain the fused global trajectory. Here, h is the error threshold.

[0153] Figure 5 To compare the RMSE (mean square error) of the proposed algorithm with that of Gaussian particle filtering in the case of single sensor and single target, it can be seen from the figure that the proposed algorithm has a much better ability to deal with nonlinearity in underwater passive target tracking than Gaussian particle filtering. Figure 6 This invention (KME-GaBP) and the PFBP and GaBP algorithms achieve an OSPA (Optimal Submode Allocation) metric for multi-sensor tracking when the number of targets is limited. Figure 6 As can be seen, the curve exhibits four peaks. The first peak corresponds to the emergence of the target, followed by gradual convergence. The latter three peaks correspond to the disappearance of the target, indicating that the error increases when the target leaves the scene. The estimation error of this invention is the smallest, and its algorithm performance is superior to the other two algorithms. This is because this invention reduces the nonlinearity of the system and alleviates the strong nonlinearity problem of passive tracking in a low-dimensional measurement space. Figure 7 This describes the OSPA of the algorithm of this invention under different detection probabilities (Pd). Figure 7 This demonstrates that the tracking accuracy of the present invention remains relatively stable under different detection probabilities, and combines... Figure 6 This is superior to the other two comparison algorithms; the number of particles is 50 in all the above cases.

[0154] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and these variations still fall within the protection scope of the present invention.

Claims

1. An underwater multi-target tracking method based on kernel mean embedding belief propagation, characterized in that: Includes the following steps: Step 1: Initialize nuclear particles ; M represents the number of nuclear particles; Step 2: Training the nuclear particles at the previous time step n-1 Make predictions and then predict the nuclear particles. Mapping to the regenerating nuclear Hilbert space, we obtain the set of feature maps for predicting nuclear particles. ; Step 3: Use the state transition matrix to obtain the predicted state of the target k at the current time n. and predicted covariance Based on the predicted state Predicting covariance Feature Mapping Set Based on the sensor measurements, the posterior state of the target k at the current time n is obtained using the kernel mean embedding Gaussian belief propagation algorithm. and posterior covariance The expression is: ； ； in, Update information for covariance; Update status information; S represents the number of sensors; Let n be the predicted covariance of the target k at the current time n; Step 4: Calculate the survival probability of the target k and determine whether to terminate the tracking of the target k. Step 5: Construct and solve the correlation optimization objective function using track integral distance; correlate the tracks acquired by different sensors for the same target and assign global track labels; construct and solve the fusion optimization objective function using pseudo-measurement cross-validation until the error between the global track state and the pseudo-measurement mean is less than the error threshold h, and obtain the fused global track. Step 6: Repeat steps 2 to 5 to obtain the global tracks of different targets at different times.

2. The underwater multi-target tracking method based on kernel mean embedding confidence propagation according to claim 1, characterized in that: In step three, covariance update information is obtained. and status update information The method is as follows: 3-1. Under the Gaussian assumption based on kernel mean embedding, obtain the predicted state of the target k at the current time n. and predicted covariance as follows: ； ； in, This is the state transition matrix; Let n be the posterior state of the target k at the previous time n-1. This is the noise driving matrix; This is the process noise matrix; Let be the posterior covariance of the target k at the previous time n-1; 3-2. Based on the transfer rules of the factor graph, obtain the measurement evaluation message of sensor s. ; 3-3. Iterate through all measurement results, based on the measurement evaluation message. and the correlation vector oriented towards the target being measured and correlation vectors oriented towards measurement results Obtain the result of the BP internal message iteration loop during each iteration. This continues until the preset number of iterations P is reached; where, ;according to Obtain data association information ; 3-4. Based on data association information Get the state update information at the current time n Covariance update information for: ； ； in, This represents the particle kernel weight vector after training at the current time n. This is a Jacobian matrix; Let z be the covariance matrix of the target k after being updated with respect to the measurement result z. The quantity of measurement results.

3. The underwater multi-target tracking method based on kernel mean embedding belief propagation according to claim 1, characterized in that: In step five, the constructed correlation optimization objective function The expression is: ； in, For the global trajectory; The local flight path; S represents the number of sensors; For the global set of tracks; The maximum number of tracks; B represents the association symbol for local tracks; B represents the association symbol for all local tracks. The correlation matrix; and These are unequal sensor sequences; and These are unequal local track sequences; D is the track integral distance. The cost of lack of association; For the generalized Kronecker delta function; t is the number of local tracks of the sensor; This is an association symbol for the local track.

4. The underwater multi-target tracking method based on kernel mean embedding belief propagation according to claim 1, characterized in that: In step five, the fusion optimization objective function is min{ };in, This is a set of pseudo-measurement means; Global track status With pseudo-measured mean The error between them is expressed as: ； in, The equation for azimuth measurement; This refers to the state of sensor s itself. The state of the target being measured; This is a pseudo-measurement mean; is the covariance matrix of the pseudo-measurement.

5. The underwater multi-target tracking method based on kernel mean embedding belief propagation according to claim 2, characterized in that: In step three, the measurement evaluation message of sensor s The expression is: ； in, This represents the measurement result of sensor s at the current time n; Let be the measurement equation for sensor s at the current time n; ; This is a Jacobian matrix; The measurement noise of sensor s; This is the association vector oriented towards the target being measured; ; Let be the number of measurement results of the s-th sensor at time n; It follows a Gaussian distribution.

6. The underwater multi-target tracking method based on kernel mean embedding belief propagation according to claim 2, characterized in that: In step three, the result of the BP internal message iteration loop The expression is: ； Where K is the number of targets being measured; Exclude indicator functions for the target; The labels of the tested targets are different from k; For internal iteration information; Data association information The expression is: 。 7. The underwater multi-target tracking method based on kernel mean embedding confidence propagation according to claim 1, characterized in that: The initialization of nuclear particles The expression is: ； in, and These are the initial horizontal and vertical coordinates of the sensor; The distance is a random number. ; For speed, random numbers ; The heading angle is a random number. ; The azimuth of the target being measured; and These are the minimum and maximum distances between the target and the sensor, respectively. and These are the maximum and minimum values ​​of the velocity of the target being measured, respectively.

8. The underwater multi-target tracking method based on kernel mean embedding confidence propagation according to claim 1, characterized in that: In step two, the predicted nuclear particles The expression is: ； Among them, f k (·,·) represents the state transition equation; It is Gaussian noise.

9. The underwater multi-target tracking method based on kernel mean embedding belief propagation according to claim 1, characterized in that: In step two, the feature mapping set of nuclear particles Obtained through a polynomial kernel function.

10. The underwater multi-target tracking method based on kernel mean embedding belief propagation according to claim 1, characterized in that: In step four, the criterion for determining whether to terminate the tracking of the target k is as follows: Establish the tracking and maintenance hypothesis and tracking the termination hypothesis Calculate the likelihood functions for the two hypotheses respectively. and Likelihood function and The expression is: ； in, a k is the number of tests. a Number of scans; and These are the detection probability and the false alarm probability, respectively. Using the likelihood ratio function of the two hypotheses The survival probability of the target k being tested And set two corresponding thresholds respectively and ; 1) When Accept the hypothesis Track and maintain; 2) When Accept the hypothesis The tracking has ended; 3) When Continue testing.

Images