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

Abstract

The invention discloses an underwater multi-target tracking method based on kernel mean value embedding belief propagation, which adopts a kernel mean value embedding method, and overcomes the problem of incomplete observability of a system with lower calculation complexity by approaching a probability density function of a target state through a small number of kernel particles. A strong nonlinear problem of a passive tracking low-dimensional measurement space is converted into a linear problem of a high-dimensional feature space, the problems of strong nonlinearity of an underwater multi-target measurement function and incomplete observability of a target state are solved, and the tracking precision of underwater passive tracking is improved. Meanwhile, by means of the kernel mean belief propagation method under Gaussian hypothesis, the problem that the calculation complexity is too high when random particles or Gaussian mixed density is used for approximating probability density distribution in a traditional BP algorithm is solved, the problem of matching of a measurement result and a target is solved with low calculation complexity, and the accuracy of the measurement result is improved. And the expandability of the system is greatly improved.

Description

Technical Field

[0001] The invention belongs to the technical field of underwater target tracking, and in particular relates to an underwater multi-target tracking method based on kernel mean embedding belief propagation. Background Art

[0002] Passive tracking of underwater targets is an important part of ocean detection. Passive tracking of underwater targets passively receives the azimuth information of the observed target and realizes silent tracking under the condition of ensuring its own safety. Compared with active tracking, it has good concealment. At the same time, the detection platform does not need to be equipped with a high-power transmitting antenna, which greatly reduces the cost. With the rapid growth of military and civilian needs such as marine resource exploration and territorial waters security monitoring, the theoretical and applied research on passive tracking of underwater targets has important scientific significance and application value for meeting people's needs and ensuring national security. Underwater target passive tracking technology in complex marine environment is an important means of marine detection and has important research significance. Due to the inherent incomplete observability and strong nonlinearity of the system, passive tracking of underwater targets faces the problems of many false tracks and low tracking accuracy. The research on underwater multi-target passive tracking technology based on kernel mean embedding (KME) belief propagation can improve the tracking accuracy and track quality of underwater passive detection system, provide technical support for the performance improvement of my country's offshore defense system, and has important research significance for building a strong maritime country. Summary of the invention

[0003] The present invention proposes a method for passively tracking underwater multiple targets based on kernel mean embedded belief propagation, which reduces the false track rate of passive tracking of underwater targets, improves the quality of underwater detection and tracking, enhances the scalability of the passive tracking system of underwater targets, and provides technical support for the performance improvement of my country's offshore underwater detection system.

[0004] The present invention provides an underwater multi-target tracking method based on kernel mean embedding belief propagation, which comprises the following steps:

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

[0006] Step 2: After training, the kernel particles of the previous moment n-1 Make predictions and assign the predicted nuclear particles Map to the reproducing kernel Hilbert space and obtain the characteristic mapping set Φ of the nuclear particles n,k ;

[0007] Step 3: According to the feature mapping set Φ at the current time n n,k and the sensor’s measurement results, and use kernel mean embedding to obtain the predicted state x of the measured target k at the current time n n|n-1,k and the predicted covariance P n|n-1,k ; According to the predicted state xn|n-1,k and the predicted covariance P n|n-1,k Get the posterior state x of the target k at the current time n n|n,k and the posterior covariance P n|n,k The expression is:

[0008]

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

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

[0011] Step 5: Use the track integral distance to construct and solve the association optimization objective function; associate the tracks obtained by different sensors for the same target and assign a global track label; use pseudo-measurement cross-construction to construct and solve the fusion optimization objective function 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 3, covariance update information is obtained. and status updates 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 transfer matrix; is the posterior state of the target k at the last moment n-1; G is the noise driving matrix; Q n-1,k is the process noise matrix; P n-1|n-1,k is the posterior covariance of the measured target k at the previous moment n-1;

[0018] 3-2.According to the transmission rules of the factor graph, obtain the measurement evaluation message of sensor s

[0019] 3-3. Iterate all measurement results and evaluate the message based on the measurement and the correlation vector for the target being measured and the correlation vector for the measurement results Get the results 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 Get data association information

[0020] 3-4. According to the data association information Get the status update information of the current time n and covariance update information for:

[0021]

[0022] in, is the particle nuclear weight vector after training at the current moment n; is the Jacobian matrix; is the updated covariance matrix of the measured target k for the measurement result z.

[0023] Preferably, in the step 5, the expression of the association optimization objective function F(B) constructed is:

[0024]

[0025] in, is the global track; l is the local track; S is the number of sensors; is the global track set; is the maximum number of tracks; rl is the associated symbol of the local track; B is the associated symbol of all local tracks ι rl The correlation matrix of c and d is an unequal sensor sequence; l c and l d is an unequal sequence of local tracks; D is the track integration distance; D' is the missing association cost; is the generalized Kronecker delta function; t is the number of local tracks of the sensor.

[0026] Preferably, in step 5, the fusion optimization objective function is: in Global track status and pseudo-measurement mean The error between them is expressed as:

[0027]

[0028] Among them, H is the azimuth measurement equation; is the state of sensor s itself; is the state of the target being measured; is the pseudo-measurement mean; is the covariance matrix of the pseudo measurements.

[0029] Preferably, in step 3, the measurement evaluation message of sensor s The expression is:

[0030]

[0031] in, is the measurement result of sensor s at the current time n; is the measurement equation of sensor s at the current time n; is the Jacobian matrix; R (s) is the measurement noise of sensor s; is the correlation vector facing the target; is the number of measurement results of the sth sensor at time n; is a Gaussian distribution.

[0032] As a preferred embodiment, in the step 3, the result of the BP internal message iteration cycle The expression is:

[0033]

[0034] Where K is the number of targets to be measured; Ψ is the target exclusion indicator function; k' is the target label that is different from k; It is the internal iteration information;

[0035] Data association information The expression is:

[0036]

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

[0038]

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

[0040] As a preference, in step 2, the predicted nuclear particles The expression is:

[0041]

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

[0043] Preferably, in step 2, the feature mapping set Φ of the core particles n,k Obtained through a polynomial kernel function.

[0044] Preferably, in step 4, the basis for determining whether to terminate the tracking of the measured target k is:

[0045] Establish the tracking maintenance hypothesis H1 and the tracking termination hypothesis H0, and calculate the likelihood function P of the two hypotheses respectively. 1k and P 0k , the likelihood function P 1k and P 0k The expression is:

[0046]

[0047] Among them, m a is the number of detections; k a is the scan number; P D and P F are the detection probability and false alarm probability respectively;

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

[0049] 1) When U k ≥C2, accept hypothesis H1 and follow up;

[0050] 2) When U k ≤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 to approximate 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 nonlinear problem of passive tracking in a low-dimensional measurement space into a linear problem in a high-dimensional feature space, solves the strong nonlinearity of the underwater multi-target measurement function and the problem of 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, overcomes the problem of excessive computational complexity caused by the traditional BP algorithm using random particles or Gaussian mixture densities to approximate the probability density distribution, processes the matching problem between measurements and targets with a low computational complexity, and greatly improves 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 alleviates the problem of false points generated by traditional cross-location fusion and forming false tracks, and improves the tracking accuracy. Description of the Drawings

[0056] Figure 1 is the overall flowchart 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 flowchart 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 not the case.

[0062] Figure 7 Schematic diagram of OSPA under different detection probabilities of the present invention. DETAILED DESCRIPTION

[0063] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work 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 belief propagation includes the following steps:

[0065] Step 1: Use a sequence to represent the input of a time window containing num radar scans; if the relevant time window contains a measurement result when scanning n times at the current moment, set the window value to 1, otherwise set it to 0; when the number of detections in the window reaches a certain value, it means that the track is successfully started. After the track is started, the state of the target being measured is started. Because the measurement information obtained by underwater pure bearing is dimensionless, only the approximate azimuth of the target being measured can be known, so points are scattered in the azimuth area where the target being measured is located. For underwater targets, their movement speed and passive detection range will be in a roughly determined range, and points are scattered within this range.

[0066] For M core particles (KME particles), each core particle generates a minimum value of R min , the maximum value is R max The uniformly distributed random number r of the distance is generated to meet the minimum value v min , the maximum value is v max The speed random number v is generated, and the heading angle random number β is generated with a minimum value of 0 and a maximum value of 2π. The initialization of the nuclear particle is expressed as:

[0067]

[0068] Among them, x o and o are the initial horizontal and vertical coordinates of the sensor respectively; θ is the azimuth 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 domain Ω and distribution P(X), and let x represent an instance of X. RKHSF represents a kernel function k(x,x′) on Ω that satisfies the function The Hilbert space of , whose inner product is <·,·> F, whose elements k(x,·) satisfy the regeneration property:<f(·),k(x,·)> F =f(x), which means that the function f evaluated at any point x∈Ω is the inner product.

[0070] In the data space, according to the core particles trained at the last moment Make a prediction and obtain the nuclear particles in the current n data space The expression is:

[0071]

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

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

[0074] Step 3: Figure 4 As shown in the multi-target tracking system, the expanded dimension state of each detected target is Among them, x n,k is the hidden state of the target k at the current time n, and are the horizontal and vertical coordinates of the measured target k at the current time n respectively; and are the lateral and longitudinal velocities of the measured 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 kth measured target at the current time n is → (x n,k ,1) is:

[0077]

[0078] Among them, f(x n,k ,1|z n-1 ) is the a posteriori state obtained based on the measurement result at the previous moment; z n-1 is the measurement result at time n-1; N(x n|n-1,k ,Pn|n-1,k ) is the predicted distribution of the measured target k at time n; P n|n-1,k is the predicted covariance of the measured target k at time n; A priori prediction of the kernel weight vector 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 transfer matrix, F∈R 4×4 ; is the posterior state of the target k at the last moment n-1; G is the noise driving matrix, G∈R 4×2 ;Q n-1,k is the process noise matrix; P n-1|n-1,k is the posterior covariance of the measured target k at time n-1.

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

[0084]

[0085] in, is the core particle after training at the last moment; is the particle nuclear weight vector after training at time n-1; is the prior weight covariance matrix; is the particle weight covariance matrix after training at time n-1.

[0086] In the context of kernel mean embedding belief propagation, the mean and covariance are used to describe the messages transmitted in the factor graph, which reduces the computational complexity problem caused by random samples.

[0087] 3-2. Evaluating sensor measurement results

[0088] According to the transmission rules of the factor graph, obtain the measurement evaluation message of the sth sensor The expression is:

[0089]

[0090] in, is the correlation vector facing the target; is the number of measurement results of sensor s at the current time n; is the measurement result of sensor s at the current time n; g is the factor node; is the matching function.

[0091] Under the Gaussian assumption, the above formula can be rewritten as:

[0092]

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

[0094] 3-3. Associated Iteration Data

[0095] For all Iterate the measurement results until the number of iterations p equals the preset number of iterations P; initialize the internal iteration information The expression is:

[0096]

[0097] Among them, β is the measurement evaluation information; Ψ is the target exclusion indicator function.

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

[0099]

[0100] in, is the result of the iterative loop of messages within BP; K is the number of targets to be measured; The correlation vector for the measurement results; k' is a measured target sequence different from k; is the internal iteration information, and its expression is:

[0101]

[0102] Wherein, m' is a measurement result sequence different from m.

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

[0104]

[0105] The result of iterative loop based on BP internal message Get data association information The expression is:

[0106]

[0107] 3-4. Update measurement results

[0108] The measurement update information γ of the kth target measured by the sth sensor at time n (s) (x n,k ,1) is:

[0109]

[0110] According to the above formula and Gaussian hypothesis, the above formula can be rewritten as:

[0111]

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

[0113]

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

[0115]

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

[0117]

[0118] in, is the particle nuclear weight vector after training at the current moment n; is the updated covariance matrix of the measured target k for the measurement result z.

[0119] 3-5. Reliability calculation

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

[0121]

[0122] Among them, x n|n,k is the posterior state at the current moment n; P n|n,j is the posterior covariance at the current moment 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 target k to be measured, 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 the 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 Figure 3 shown, 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 its 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 a 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; is the maximum number of tracks. sl = 0 occurs in two cases: sensor s does not have a local track with label l; or sensor s has a track with label l but is not associated with any other track.

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

[0137]

[0138] Among them, s c and d is an unequal sensor sequence; l c and l d is a sequence of unequal local tracks; B is the correlation matrix of all local track correlation symbols; is the global track set, D is the track integration distance; D' is the missing association cost; is the generalized Kronecker delta function.

[0139] The above optimization problem is essentially an NP problem. In order to quickly obtain the minimum cost association matrix B in a short time, the S-dimensional allocation algorithm is used to solve it; this algorithm transforms the S-dimensional allocation problem into a 2-dimensional allocation problem through the Lagrangian relaxation algorithm and solves it. Although this method uses the idea of ​​relaxation and can only achieve a suboptimal solution for the S-dimensional allocation, it can achieve satisfactory results by setting the tolerance error.

[0140] The input of the S-dimensional allocation algorithm is an S-dimensional cost matrix, defined as Its element values ​​are:

[0141]

[0142] in, The expression is:

[0143]

[0144] After solving the track association problem, we will get global track tags and corresponding local track information, up to the number of global track tags If the value is greater than the preset threshold, the S-dimensional allocation algorithm is stopped. The global tracks are fused. The fusion step of a label in is elaborated in detail. The rest of the tags can be processed in the same way.

[0145] Convert the local track (s, l) into pseudo-measurement and convert it into the mean value of pseudo-measurement With covariance The expression is:

[0146]

[0147] Among them, H is the azimuth measurement equation; is the state of the sth sensor itself; is the state of the target being measured; is the azimuth pseudo measurement; P sl is the covariance matrix.

[0148] Transfer all local tracks to the measurement space and obtain the pseudo-measurement mean set With the help of pseudo-measurement and based on the maximum likelihood idea, the track fusion problem is transformed into a new fusion problem: given the state of each sensor and the corresponding pseudo-measurement mean Estimating global track state And minimize the error between it and the target’s true state. Since the true state of the target is unknown, the global track state is minimized. and pseudo-measurement mean The error between is estimated by the method. The global track state is defined as and are the horizontal and vertical coordinates of the measured target respectively; and are the lateral and longitudinal moving speeds of the target under test respectively; global track status and pseudo-measurement mean Error The expression is:

[0149]

[0150] Based on the above pseudo-measurement transformation and error definition, the new fusion problem is solved by optimization. Due to the continuity and infinity of the target state space, randomly selecting initial values ​​may lead to slow or low-precision optimization problem solving. Next, the geometric crossover method is used to limit the solution space; using the pseudo-measurement mean The resulting angle pseudo-measurement and sensor location Calculate the position intersection and limit the solution space. The solution space after restriction is:

[0151]

[0152] in, K sl Pseudo-measurement The corresponding slope. The above optimization problem is solved using the sequential quadratic programming algorithm until the global track state and pseudo-measurement mean Error Get the fused global track, where h is the error threshold.

[0153] Figure 5 The RMSE (mean square error) comparison between the proposed algorithm and the Gaussian particle filter in the case of a single sensor and a single target. It can be seen from the figure that the proposed algorithm is much better than the Gaussian particle filter in dealing with nonlinearity in underwater passive target tracking; Figure 6 The OSPA index (optimal sub-mode allocation index) of the present invention (KME-GaBP) and PFBP and GaBP algorithms for multi-sensor tracking when the number of targets is unknown is obtained from Figure 6 It can be seen that the curve has four peaks, the first one corresponds to the birth of the target, and the subsequent ones gradually converge. The last three times correspond to the disappearance of the target, indicating that when the target leaves the scene, the error will increase. The estimation error of the present invention is the smallest, and the algorithm performance is better than the other two algorithms. The reason is that the present invention weakens the nonlinearity of the system and alleviates the strong nonlinearity problem of passive tracking low-dimensional measurement space. Figure 7 is the OSPA of the algorithm of the present invention under different detection probabilities (Pd), Figure 7 It shows that the tracking accuracy of the present invention is relatively stable under different detection probabilities, and combined with Figure 6 It is better than the other two compared algorithms; the number of particles in the above cases is 50.

[0154] The embodiments of the present invention are 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 of these embodiments are made without departing from the principles and spirit of the present invention, and still fall within the scope of protection of the present invention.

Claims

1. An underwater multi-target tracking method based on kernel mean embedding belief propagation, characterized by: The following steps are involved: Step 1: Initialize the core particles M is the number of nuclear particles; Step 2: After training, the kernel particles of the previous moment n-1 Make predictions and assign the predicted nuclear particles Map to the reproducing kernel Hilbert space and obtain the feature mapping set Φ of the predicted nuclear particles n,k ; Step 3: Use the state transfer matrix 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 ; According to the predicted state x n|n-1,k , prediction covariance P n|k-1,k , feature map set φ n,k The kernel mean embedding Gaussian belief propagation algorithm is used to obtain the posterior state x of the measured target k at the current time n. n|n,k and the posterior covariance P n|m,k The expression is: in, Update information for covariance; is the status update information; s=1,2,...,S; S is the number of sensors; Step 4: Calculate the survival probability of the detected target k, and determine whether to terminate the tracking of the detected target k; Step 5: Use the track integral distance to construct and solve the association optimization objective function; associate the tracks obtained by different sensors for the same target and assign a global track label; use pseudo-measurement cross-construction to construct and solve the fusion optimization objective function 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 measured targets at different times.

2. The underwater multi-target tracking method based on kernel mean embedded belief propagation according to claim 1 is characterized by: In step 3, the covariance update information is obtained and status updates The method is as follows: 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: P n|n-1,k =FP n-1|n-1,k F T +GQ n-1,k G T Where, F is the state transfer matrix; is the posterior state of the target k at the last moment n-1; G is the noise driving matrix; Q n-1,k is the process noise matrix; P n-1|n-1,k is the posterior covariance of the measured target k at the previous moment n-1; 3-2.According to the transmission rules of the factor graph, obtain the measurement evaluation message of sensor s 3-3. Iterate all measurement results and evaluate the message based on the measurement and the correlation vector for the target being measured and the correlation vector for the measurement results Get the results 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 Get data association information 3-4. According to the data association information Get the status update information of the current time n and covariance update information for: in, is the particle nuclear weight vector after training at the current moment n; is the Jacobian matrix; is the updated covariance matrix of the measured target k for the measurement result z.

3. The underwater multi-target tracking method based on kernel mean embedded belief propagation according to claim 1 is characterized by: In the step 5, the expression of the constructed association optimization objective function F(B) is: in, is the global track; e is the local track; S is the number of sensors; is the global track set; is the maximum number of tracks; rl is the associated symbol of the local track; B is the associated symbol of all local tracks ι rl The correlation matrix of c and d is an unequal sensor sequence; l c and l d is an unequal sequence of local tracks; D is the track integration distance; D' is the missing association cost; is the generalized Kronecker delta function; t is the number of local tracks of the sensor.

4. The underwater multi-target tracking method based on kernel mean embedded belief propagation according to claim 1 is characterized in that: In the step 5, the fusion optimization objective function is: in Global track status and pseudo-measurement mean The error between them is expressed as: Among them, H is the azimuth measurement equation; is the state of sensor s itself; is the state of the target being measured; is the pseudo-measurement mean; is the covariance matrix of the pseudo measurements.

5. The underwater multi-target tracking method based on kernel mean embedded belief propagation according to claim 2 is characterized by: In step 3, the measurement evaluation message of sensor s The expression is: in, is the measurement result of sensor s at the current time n; is the measurement equation of sensor s at the current time n; is the Jacobian matrix; R (s) is the measurement noise of sensor s; is the correlation vector facing the target; is the number of measurement results of the sth sensor at time n; is a Gaussian distribution.

6. The underwater multi-target tracking method based on kernel mean embedded belief propagation according to claim 2 is characterized by: In step 3, the result of the BP internal message iteration cycle The expression is: Where K is the number of targets to be measured; Ψ is the target exclusion indicator function; k' is the target label that is different from k; It is the internal iteration information; Data association information The expression is:

7. The underwater multi-target tracking method based on kernel mean embedded belief propagation according to claim 1 is characterized by: The initialization core particles The expression is: Among them, x o and o are the initial horizontal and vertical coordinates of the sensor respectively; r is a random distance number, r∈[R min ,R max ]; v is a random speed number, v∈[v min ,v max ]; β is a random number of heading angle, β∈[0,2π]; θ is the azimuth of the target being measured; R min and R max are the minimum and maximum distances between the target and the sensor respectively; v min and v max are the maximum and minimum values ​​of the measured target speed respectively.

8. The underwater multi-target tracking method based on kernel mean embedded belief propagation according to claim 1 is characterized by: In the step 2, the predicted nuclear particles The expression is: Among them, f k (·,·) is the state transfer equation; is Gaussian noise.

9. The underwater multi-target tracking method based on kernel mean embedding belief propagation according to claim 1 is characterized by: In the step 2, the feature mapping set Φ of the core particle n,k 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 the step 4, the basis for determining whether to terminate the tracking of the measured target k is: Establish the tracking maintenance hypothesis H1 and the tracking termination hypothesis H0, and calculate the likelihood function P of the two hypotheses respectively. 1k and P 0k , the likelihood function P 1k and P 0k The expression is: Among them, m a is the number of detections; k a is the scan number; P D and P F are the detection probability and false alarm probability respectively; The likelihood ratio function of the two hypotheses As the survival probability U of the measured target k k , and set the corresponding two thresholds C1 and C2; 1) When U k ≥C2, accept hypothesis H1 and follow up; 2) When U k ≤C1, accept hypothesis H0 and the tracking ends; 3) When C1 < U k < C2, continue the inspection.

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