Underwater multi-target tracking method based on target state dimension expansion

Abstract

The invention provides an underwater multi-target tracking method based on target state dimension expansion, and aims to solve the problems of non-Gaussian measurement errors and detection probability time varying are not considered in a standard random finite set algorithm, so that model mismatching of the multi-target tracking method can be caused, the tracking performance is deteriorated, and even completely wrong target state estimation is given. A generalized label multi-Bernoulli filtering and Dirichlet process-hidden Markov chain hybrid model is utilized, the target state, the probability density distribution of observation noise and the detection probability are jointly estimated in real time in a self-adaptive mode through variational inference, the tracking error is remarkably reduced, and the track estimation precision and the track integrity are improved.

Description

Technical Field

[0001] The present invention relates to the field of target tracking technology, and in particular to an underwater multi-target tracking method based on target state dimension expansion. Background Art

[0002] Manned / unmanned collaborative clusters composed of submarines / UUVs and underwater unmanned clusters composed of UUVs are important means for the US military to maintain its underwater combat advantage. Therefore, it is urgent to seek faster and more effective underwater formation and clustered multi-target perception methods.

[0003] Affected by the inhomogeneity of the transmission medium and the reflection of objects and interfaces, the signal received by the receiver in the underwater acoustic channel has multipath interference, which leads to the multimodal statistical characteristics of the sensor node receiving measurement. At the same time, the random time-varying and space-varying characteristics of the underwater acoustic channel will seriously affect the communication link. The presence of clutter or false targets in the transmission medium often leads to missed detection and false alarm. In the underwater acoustic channel, as the distance of the target increases, the propagation loss causes the receiving signal-to-noise ratio to change all the time, causing the detection probability to change.

[0004] The standard random finite set algorithm assumes that the prior knowledge of the sensor noise statistics is known and follows a Gaussian distribution, and assumes that the detection probability is constant. In practice, it is usually difficult to build an accurate model for sensor noise, and the detection probability varies. If this error is not considered in the actual system, it will cause model mismatch in the multi-target tracking method, resulting in deterioration of tracking performance, or even giving completely wrong target state estimates.

[0005] Therefore, accurately tracking and locating multiple targets underwater has become a technical problem that needs to be solved urgently. Summary of the invention

[0006] In order to overcome the shortcomings of the prior art, the present invention provides an underwater multi-target tracking method based on target state expansion. In view of the problems of track jump, high track missed detection rate and low tracking accuracy in the traditional standard random finite set algorithm under non-Gaussian noise environment, and the fact that it is not suitable for the case where the underwater target detection probability varies with the distance between the target and the sensor, the present invention provides an underwater multi-target tracking method based on target state expansion to improve the accuracy and robustness of multi-target tracking.

[0007] The specific steps of the technical solution adopted by the present invention to solve the technical problem are as follows:

[0008] Step 1: Establish a spatial coordinate system to obtain the location coordinates and monitoring area of ​​the sensor;

[0009] Step 2: Based on the sonar equation, obtain the curve of detection probability changing with the distance between the target and the sensor and the blocking radius of the sensor;

[0010] Step 3: Based on the curve of detection probability changing with the distance between the target and the sensor, complete the construction of the multi-target measurement set;

[0011] Step 4: The sensor periodically acquires a measurement set, and obtains the number of targets and the associated measurement set of each target based on the generalized label multi-Bernoulli filter;

[0012] Step 5: Based on the expanded-dimensional state-measurement model, the associated measurement set is used to iteratively update the expanded-dimensional target state posterior probability density through the Dirichlet process-hidden Markov chain hybrid model;

[0013] Step 6: Update the estimated trajectory set according to each frame iteration, update the detection probability, and output each target track.

[0014] Furthermore, in step 2, the specific steps of obtaining the curve of detection probability changing with the distance between the target and the sensor and the blocking radius of the sensor are:

[0015] Using active detection, according to the Neyman-Pearson criterion, we have:

[0016]

[0017] P D is the detection probability, P F is the false alarm probability, N(·) represents Gaussian distribution, N -1 (·) represents the inverse cumulative distribution function of Gaussian distribution, SL is the emission source level, NL is the ambient noise level, TS is the target strength, DI is the directivity index, and r is the distance between the target and the sensor;

[0018] Define the blocking radius of the sensor as the distance r corresponding to a 90% probability of target detection 0 ,satisfy The target can be tracked better within the blockade radius, but the tracking performance is poor outside the blockade radius due to the low detection probability;

[0019] Furthermore, in step 3, the specific steps of constructing the multi-objective measurement set are:

[0020] For multi-target scenarios, at time 1:t, given the parameters SL, NL, TS, DI and P F , calculate the detection probability P of each target at time 1:t D , with the detection probability P of each target at time 1:t D Generate measurement, with 1-P D The probability does not generate a measurement. At the same time, the false target caused by clutter in time 1:t also generates a measurement.

[0021] Furthermore, in step 5, the specific steps of the extended-dimensional state-measurement model and the Dirichlet process-hidden Markov chain hybrid model are:

[0022] At time 1:t, the measurement information periodically acquired by the sensor The measurement information is the real target position information Position information of false targets caused by clutter Right now i is the time index; the number of targets N in the monitoring area and the expanded target state set are obtained through generalized label multi-Bernoulli filtering. and Associated Measurement Sets The target state X at the i-th moment is expanded. i for x j is the jth state, is the detection probability of the target, the measurement set Y at the i-th moment i for y j is the jth target x j The corresponding measurement, j is the target label index, x j,i is the state of the jth target at time i, y j,i is the measurement of the jth target at time i;

[0023] For the j-th dimension expansion target state and ) corresponding to the measurement The dimension expansion target state-measurement model is as follows:

[0024] x j,t =Fx j,t-1 +w j,t

[0025] y j,t =Hx j,t +ξ j,t

[0026] w j,t ~N(0,Q)

[0027]

[0028] F is the state transfer matrix, H is the measurement matrix; N(·) represents Gaussian distribution, w j,t is the state noise of the j-th target at time t that obeys a zero-mean Gaussian distribution, Q is the state noise variance; ξ j,t is the non-Gaussian distribution measurement noise of the jth target at time t, which is fitted by the mixed Gaussian model GMM; K is the number of Gaussian components in the mixed Gaussian model, e is the Gaussian component index, and w eis the amplitude of the e-th Gaussian component, satisfying (μ ξe ,Σ ξe ) are the distribution parameters of the e-th Gaussian component, which are the mean and variance respectively; x j,t-1 is the state of the jth target at time t-1, x j,t is the state of the jth target at time t, y j,t is the measurement corresponding to the jth target at time t. is the detection probability of the jth target at time t, r j,t is the distance between the jth target and the sensor at time t;

[0029] According to the extended dimension target state-measurement model, a Dirichlet process-hidden Markov chain hybrid model is established, and the broken stick model is used to construct a mathematical form of discrete distribution that obeys the Dirichlet process. The specific construction process is as follows:

[0030] V k ~Beta(1,α)

[0031]

[0032] α is the concentration parameter, which indicates the degree of discreteness of the generated distribution and is a scalar greater than 0. Beta(·) is the Beta distribution, k is the primary index of the number of cutoffs, and V k is the intermediate parameter of the kth truncation of the Beta distribution with parameters (1, α), r is the secondary index of the truncation times, V r is the intermediate parameter of the rth truncation of the Beta distribution with parameters (1,α), π k is the weight coefficient of the kth truncation, satisfying s j,t is the jth target state x at time t j,t The indicator factor; λ is the base distribution parameter, G(λ) is the base distribution; θ k is the basis obtained by the k-th sampling, represents the infinite number of bases obtained by sampling; Σ is the covariance matrix of the Gaussian distribution obeyed by the measurement.

[0033] Furthermore, in step 5, the specific steps of solving the variational inference of the Dirichlet process-hidden Markov chain hybrid model are as follows:

[0034] The posterior probability density of the jth target to be estimated at time t

[0035] V is the intermediate parameter V of infinite truncation k A collection of y j,1:tis the measurement set of the jth target in the 1:t time period, y j,1:t-1 is the measurement set of the jth target in the time period 1:t-1,

[0036] Through mean field theory, the variational distribution family is used to replace the true posteriori at time t and t-1:

[0037]

[0038] where q p (x j,t ) = ∫q(x j,t-1 )p(x j,t |x j,t-1 )dx j,t-1 ,s j,t-1 is the jth target state x at time t-1 j,t-1 The indicator factor is θ, which is obtained by infinite truncated sampling. k A collection of

[0039] By means of conjugate prior, (x j,t ,s j,t ,V,θ) sets the prior distribution at time t:

[0040]

[0041]

[0042] is the jth target x at time t j,t The mean and variance of the conjugate Gaussian prior, is the jth target x at time t-1 j,t The mean and variance of the conjugate Gaussian prior, m j,t for The one-step forecast mean, Σ j,t for The one-step prediction variance of Mult(·) is a multinomial distribution. is the parameter of the multinomial distribution at time t, is the parameter of the k-th truncated multinomial distribution at time t; (u k ,v k ) is the parameter of beta distribution; is the parameter of Gaussian distribution; since it needs to be updated iteratively over time, (u k ,v k )and Define as follows: is the parameter of the kth truncated beta distribution at time t-1, is the parameter of the kth truncated beta distribution at time t, is the parameter of the kth truncated Gaussian distribution at time t-1, is the parameter of the kth truncated Gaussian distribution at time t;

[0043] Based on the variational parameters and their prior distribution, variational inference is performed, and the recursive formula of each variational parameter at time t is obtained as follows:

[0044]

[0045] Furthermore, in step 6, the iterative update of the posterior probability density of each target state outputs the estimated track of each target, and the specific steps are:

[0046] For multi-target associated track sets: and Using the variational inference solution in step 5, at time 1:t, recursively update x through each variational parameter j,i The posterior probability of each target is finally obtained. And based on the estimated trajectory set obtained Calculate the distance r between the target and the sensor j,t , and complete the iterative update of the detection probability of each target at time 1:t Based on the obtained estimated track set, the estimated track of each target as it changes over time can be presented through visualization operations.

[0047] An electronic device comprises one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs are configured to execute the method as described above.

[0048] A computer-readable storage medium stores program codes, and the program codes can be called by a processor to execute the method as described above.

[0049] The beneficial effect of the present invention is that it provides an underwater multi-target tracking method based on target state expansion. Since the standard random finite set algorithm does not consider the non-Gaussian measurement error and the time-varying detection probability, it will cause model mismatch of the multi-target tracking method, thereby causing the tracking performance to deteriorate, and even giving a completely wrong target state estimation. By using the generalized label multi-Bernoulli filter and the Dirichlet process-hidden Markov chain hybrid model, the target state, the probability density distribution of the observation noise and the detection probability are jointly estimated in real time through variational inference adaptively, which significantly reduces the tracking error and improves the track estimation accuracy and track integrity. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 is a flow chart of an embodiment of the present invention;

[0051] Figure 2 is a flow chart of a specific embodiment of the present invention;

[0052] Figure 3 A schematic diagram of the actual tracks of multiple targets in the monitoring area in the simulation example of the present invention;

[0053] Figure 4 Detection probability curves under different false alarm probabilities in the simulation example of the present invention

[0054] Figure 5 It is a schematic diagram of the estimated track of the method in the simulation example of the present invention;

[0055] Figure 6 This is a schematic diagram of the estimated track OSPA distance of the method in the simulation example of the present invention;

[0056] Figure 7 It is a schematic diagram of the number of estimates of this method in the simulation example of the present invention.

[0057] Figure 8 Schematic diagram of target estimation number of JointGLMB algorithm in the simulation example of the present invention. DETAILED DESCRIPTION

[0058] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0059] The present invention relates to an underwater multi-target tracking method based on target state expansion, comprising the following steps: establishing a spatial coordinate system, obtaining the position coordinates and monitoring area of ​​the sensor; obtaining the detection probability curve with the distance between the target and the sensor and the blocking radius of the sensor based on the sonar equation; completing the construction of a multi-target measurement set based on the detection probability curve with the distance between the target and the sensor; the sensor periodically obtains the measurement set, and obtains the number of targets and the associated measurement set of each target based on the generalized label multi-Bernoulli filter; based on the expanded state-measurement model, the associated measurement set is subjected to iterative update of the expanded target state posterior probability density through the Dirichlet process-hidden Markov chain hybrid model; iteratively updates the estimated trajectory set according to each frame, updates the detection probability, and outputs each target track. The present invention combines the sonar equation, adopts the generalized label multi-Bernoulli filter and the Dirichlet process-hidden Markov chain hybrid model to iteratively update the expanded target state, significantly reduces the tracking error, and improves the track estimation accuracy and track integrity.

[0060] like Figure 1-Figure 8As shown, the present invention provides an underwater multi-target tracking method based on target state expansion, the method comprising the steps of:

[0061] S1: Scene setting: Establish a two-dimensional or three-dimensional space coordinate system. Take the two-dimensional space coordinate system xoy as an example to obtain the position coordinates of the sensor (x s ,y s ) and monitoring area x∈[r x1 ,r x2 ],y∈[r y1 ,r y2 ];

[0062] S2: Based on the sonar equation, the curve of detection probability changing with the distance between the target and the sensor and the blocking radius of the sensor are obtained;

[0063] Using active detection, according to the Neyman-Pearson criterion, we have:

[0064]

[0065] P D is the detection probability, P F is the false alarm probability, N(·) represents Gaussian distribution, N -1 (·) represents the inverse cumulative distribution function of Gaussian distribution, SL is the transmitting sound source level, NL is the ambient noise level, TS is the target strength, DI is the directivity index, and r is the distance between the target and the sensor.

[0066] Define the blocking radius of the sensor as the distance r corresponding to a 90% probability of target detection 0 ,satisfy

[0067] S3: Complete the construction of multi-target measurement set based on the curve of detection probability changing with the distance between the target and the sensor; at time 1:t, given parameters SL, NL, TS, DI and P F , calculate the detection probability P of each target at time 1:t D , each target has its own detection probability P D Generate measurement, with 1-P D The probability does not generate measurements. The sensor periodically obtains a set of measurements, and the set of measurement information in the i-th frame is recorded as Z i ; For the measurement information periodically acquired by the sensor within the 1:t time period The measurement information is the real target position information Position information of false targets caused by clutter Right now

[0068] S4: Based on the measurement set obtained by the sensor, obtain the associated measurement set of the number of targets N and each target through the generalized labeled multi-Bernoulli filter (BNVo, BTVo, and HGHoang, "An efficient implementation of the generalized labeled multi-Bernoulli filter," IEEE Transactions on Signal Processing, vol. 65, no. 8, pp. 1975–1987, Apr. 2017.): Expand the target state set and its associated measurements Where X is x j For a certain target state, is the detection probability of the target, Y is y j For the target x j The corresponding measurement.

[0069] Expand the target state set and Associated Measurement Sets The target state X at the i-th moment is expanded. i for x j is the jth state, is the detection probability of the target, the measurement set Y at the i-th moment i for y j is the jth target x j The corresponding measurement, j is the target label index, x j,i is the state of the jth target at time i, y j,i is the measurement of the jth target at time i;

[0070] S5: Based on the expanded dimension target state-measurement model, a Dirichlet process-hidden Markov chain hybrid model is established, and according to the associated measurement set, the posterior probability density of the target state is iteratively updated using the variational inference solution method;

[0071] S5.1: For the j-th dimension expansion target state The corresponding measurement The dimension expansion target state-measurement model is as follows:

[0072] x j,t =Fx j,t-1 +w j,t

[0073] y j,t =Hxj,t +ξ j,t

[0074] w j,t ~N(0,Q)

[0075]

[0076] F is the state transfer matrix, H is the measurement matrix; N(·) represents Gaussian distribution, w j,t is the state noise of the j-th target at time t that obeys a zero-mean Gaussian distribution, Q is the state noise variance; ξ j,t is the non-Gaussian distribution measurement noise of the jth target at time t, which is fitted by the mixed Gaussian model GMM; K is the number of Gaussian components in the mixed Gaussian model, e is the Gaussian component index, and w e is the amplitude of the e-th Gaussian component, satisfying (μ ξe ,Σ ξe ) are the distribution parameters of the e-th Gaussian component, which are the mean and variance respectively; x j,t-1 is the state of the jth target at time t-1, x j,t is the state of the jth target at time t, y j,t is the measurement corresponding to the jth target at time t. is the detection probability of the jth target at time t, r jt is the distance between the jth target and the sensor at time t.

[0077] According to the extended dimension target state-measurement model, a Dirichlet process-hidden Markov chain hybrid model is established, and the broken stick model is used to construct a mathematical form of discrete distribution that obeys the Dirichlet process. The specific construction process is as follows:

[0078] V k ~Beta(1,α)

[0079]

[0080] α is the concentration parameter, which indicates the degree of discreteness of the generated distribution and is a scalar greater than 0. Beta(·) is the Beta distribution, k is the primary index of the number of cutoffs, and V k is the intermediate parameter of the kth truncation that follows the Beta distribution with parameters (1,α), and r is the secondary index of the number of truncation. V r is the intermediate parameter of the rth truncation of the Beta distribution with parameters (1,α). π k is the weight coefficient of the kth truncation, satisfying s j,t is the jth target state x at time t j,t The indicator factor; λ is the base distribution parameter, G(λ) is the base distribution; θk is the basis obtained by the k-th sampling, represents the infinite number of bases obtained by sampling; Σ is the covariance matrix of the Gaussian distribution obeyed by the measurement.

[0081] S5.2: The solution to the variational inference of the Dirichlet process-hidden Markov chain mixed model is as follows:

[0082] The posterior probability density of the jth target to be estimated at time t

[0083] V is the intermediate parameter V of infinite truncation k A collection of y j,1:t is the measurement set of the jth target in the 1:t time period, y j,1:t-1 is the measurement set of the jth target in the time period 1:t-1,

[0084] Through mean field theory, the variational distribution family is used to replace the true posteriori at time t and t-1:

[0085]

[0086] where q p (x j,t ) = ∫q(x j,t-1 )p(x j,t |x j,t-1 )dx j,t-1 ,s j,t-1 is the jth target state x at time t-1 j,t-1 The indicator factor is θ, which is obtained by infinite truncated sampling. k A collection of

[0087] By means of conjugate prior, (x j,t ,s j,t ,V,θ) sets the prior distribution at time t:

[0088]

[0089] is the jth target x at time t j,t The mean and variance of the conjugate Gaussian prior, is the jth target x at time t-1 j,t The mean and variance of the conjugate Gaussian prior, m j,t for The one-step forecast mean, Σ j,t for The one-step prediction variance of Mult(·) is a multinomial distribution. is the parameter of the multinomial distribution at time t, is the parameter of the k-th truncated multinomial distribution at time t; (u k ,v k ) is the parameter of beta distribution; is the parameter of Gaussian distribution; since it needs to be updated iteratively over time, (u k ,v k )and Define as follows: is the parameter of the kth truncated beta distribution at time t-1, is the parameter of the kth truncated beta distribution at time t, is the parameter of the kth truncated Gaussian distribution at time t-1, is the parameter of the kth truncated Gaussian distribution at time t.

[0090] Based on the variational parameters and their prior distribution, variational inference is performed, and the recursive formula of each variational parameter at time t is obtained as follows:

[0091]

[0092]

[0093] S6: Iteratively update the estimated trajectory set based on the posterior probability density of each target state, update the detection probability, and output the estimated track of each target, specifically:

[0094] For multi-target associated track sets: and Using the variational inference solution in step 5, at time 1:t, recursively update x through each variational parameter j,i The posterior probability of each target is finally obtained. And based on the estimated trajectory set obtained Calculate the distance r between the target and the sensor j,t , and complete the iterative update of the detection probability of each target at time 1:t Based on the estimated track set obtained above, the estimated track of each target as it changes over time can be presented through visualization operations.

[0095] In order to better illustrate the technical solution of the present invention, the present invention is further described below in combination with simulation experiments:

[0096] The present invention proposes a multi-target tracking method for non-Gaussian measurement based on a Dirichlet process-hidden Markov chain hybrid model on the basis of a generalized labeled multi-Bernoulli (GLMB) filter.

[0097] 1. Simulation conditions

[0098] In the two-dimensional space coordinate system, consider the position coordinates of a single sensor node (x s ,y s ) is (0,0), and three targets are tracked in the monitoring area of ​​[-2000,2000]m×[-2000,2000]m. The sensor positioning error is The sampling period is T = 1s, and the total tracking time is 200s. The starting time of different targets is {1, 1, 20}, and the extinction time is {150, 200, 130}. The real track is as follows Figure 3 shown.

[0099] The parameters of the generalized label multi-Bernoulli filter are set as follows, including a single target state with position l and velocity v:

[0100] C=x=[l x ,v x ,l y ,v y ]; l x ,v x ,l y ,v y They are the x-coordinate and speed and the y-coordinate and speed of the target respectively.

[0101] Single target survival probability p s =0.99, the detection probability changes with movement, and the detection probability of the jth target at time t is Where P F =0.01, SL=145dB, NL=55dB, TS=10dB, DI=0, (l xj,t ,l yj,t ) is the position coordinate of the jth target; the detection probability curves under different false alarm probabilities are as follows Figure 4 As shown, the target state transfer matrix F and covariance matrix Q are

[0102]

[0103] In the above formula, q is the target process noise standard deviation. In this example, it is taken as 0.1;

[0104] The measurement function is:

[0105]

[0106] The target generation follows the GLMB distribution, and the parameter set is in

[0107] Mean and the covariance matrix P B for:

[0108]

[0109] P B =diag([5,5,5,5]);

[0110] The maximum number of tracks is 1000, the maximum number of assumptions in the update step is 100, and the track cutoff threshold is 10 -15 , single track Gaussian component cutoff threshold 10 -3 .

[0111] Through the above GLMB filter, we can get the target estimation number N and the expanded target state set and its associated measurements Where X is x j For a certain target state, is the detection probability of the target, Y is y j For the target x j The corresponding measurement.

[0112] For the jth target The corresponding measurement The following Dirichlet process-hidden Markov chain hybrid model is established:

[0113] V k ~Beta(1,α)

[0114]

[0115] In this example, α=2, λ=[5,20], and the base distribution G(·) is a Gaussian distribution.

[0116] Since k∈[1,+∞), k needs to be truncated so that k∈[1,K); by sampling: V k ~Beta(1,α), When k = K, if but Satisfied at this time

[0117] Solve the variational parameters based on the variational inference method:

[0118] Initialization parameters:

[0119] x j0 is the initial value of the jth target state,

[0120]

[0121] For multi-target associated track sets: and Using the variational inference solution in step 5, at time 1:t, recursively update x through each variational parameter j,i The posterior probability of each target is finally obtained. And based on the estimated trajectory set obtained Calculate the distance r between the target and the sensor j,t , and complete the iterative update of the detection probability of each target at time 1:t Based on the estimated track set obtained above, the estimated track of each target as it changes over time can be presented through visualization operations.

[0122] For different methods, the error between the actual track and the estimated track is measured based on the Optimal Sub-patten Assignment (OSPA), which measures the error between the two sets A = {a 1 ,a 2 ,…,a m} and B = {b 1 ,b 2 ,…,b n},m,n∈{0,1,2,…}, the distance D p,c (A,B):

[0123]

[0124] d (c) (a,b)=min(c,||ab||);

[0125] Π n represents all permutations on the set {1,2,3,…,n};

[0126] OSPA Distance It can be decomposed into positioning error distance and potential error distance:

[0127]

[0128] Take c = 100, p = 1 to obtain the OSPA distance between the actual track and the estimated track.

[0129] 2. Analysis of simulation results

[0130] Figure 5 The estimated track, sensor received measurement set and actual track of the proposed method in x and y directions are given;

[0131] Figure 6 The estimated track OSPA distance, positioning error distance and potential error distance of the proposed method are given

[0132] Figure 7 The target estimation number of the proposed method is given.

[0133] Figure 8 The target estimation number of the JointGLMB algorithm is given.

[0134] It can be seen that the method of the present invention can effectively track multiple underwater targets under the influence of time-varying underwater detection probability and multipath effect, and has better tracking performance than the JointGLMB algorithm.

[0135] It should be understood that the above-mentioned embodiments are merely illustrative and not restrictive. Without departing from the basic principles of the present invention, various obvious or equivalent modifications or substitutions that can be made by those skilled in the art to the above-mentioned details will all be included in the scope of the claims of the present invention.

Claims

1. An underwater multi-target tracking method based on target state expansion, characterized in that The steps include: Step 1: Establish a spatial coordinate system to obtain the location coordinates and monitoring area of ​​the sensor; Step 2: Based on the sonar equation, obtain the curve of detection probability changing with the distance between the target and the sensor and the blocking radius of the sensor; Step 3: Based on the curve of detection probability changing with the distance between the target and the sensor, complete the construction of the multi-target measurement set; Step 4: The sensor periodically acquires a measurement set, and obtains the number of targets and the associated measurement set of each target based on the generalized label multi-Bernoulli filter; Step 5: Based on the expanded-dimensional state-measurement model, the associated measurement set is used to iteratively update the expanded-dimensional target state posterior probability density through the Dirichlet process-hidden Markov chain hybrid model; Step 6: Update the estimated trajectory set according to each frame iteration, update the detection probability, and output each target track.

2. The underwater multi-target tracking method based on target state expansion according to claim 1 is characterized in that: In step 2, the specific steps of obtaining the curve of detection probability changing with the distance between the target and the sensor and the blocking radius of the sensor are: Using active detection, according to the Neyman-Pearson criterion, we have: P D is the detection probability, P F is the false alarm probability, N(·) represents Gaussian distribution, N -1 (·) represents the inverse cumulative distribution function of Gaussian distribution, SL is the emission source level, NL is the ambient noise level, TS is the target strength, DI is the directivity index, and r is the distance between the target and the sensor; The blocking radius of the sensor is defined as the distance r0 corresponding to a target detection probability of 90%, satisfying The target can be tracked better within the blockade radius, but the tracking performance is poor outside the blockade radius due to the low detection probability.

3. The underwater multi-target tracking method based on target state expansion according to claim 2 is characterized in that: In step 3, the specific steps of constructing the multi-objective measurement set are: For multi-target scenarios, at time 1:t, given the parameters SL, NL, TS, DI and P F , calculate the detection probability P of each target at time 1:t D , with the detection probability P of each target at time 1:t D Generate measurement, with 1-P D The probability does not generate a measurement. At the same time, the false target caused by clutter in time 1:t also generates a measurement.

4. The underwater multi-target tracking method based on target state expansion according to claim 3 is characterized in that: In step 5, the specific steps of the extended-dimensional state-measurement model and the Dirichlet process-hidden Markov chain hybrid model are: At time 1:t, the measurement information periodically acquired by the sensor The measurement information is the real target position information Position information of false targets caused by clutter Right now i is the time index; the number of targets N in the monitoring area and the expanded target state set are obtained through generalized label multi-Bernoulli filtering. and Associated Measurement Sets The target state X at the i-th moment is expanded. i for x j is the jth state, is the detection probability of the target, the measurement set Y at the i-th moment i for y j is the jth target x j The corresponding measurement, j is the target label index, x j,i is the state of the jth target at time i, y j,i is the measurement of the jth target at time i; For the j-th dimension expansion target state and ) corresponding to the measurement The dimension expansion target state-measurement model is as follows: x j,t =Fx j,t-1 +w j,t y j,t =Hx j,t +ξ j,t w j,t ~N(0,Q) F is the state transfer matrix, H is the measurement matrix; N(·) represents Gaussian distribution, w j,t is the state noise of the j-th target at time t that obeys a zero-mean Gaussian distribution, Q is the state noise variance; ξ j,t is the non-Gaussian distribution measurement noise of the jth target at time t, which is fitted by the mixed Gaussian model GMM; K is the number of Gaussian components in the mixed Gaussian model, e is the Gaussian component index, and w e is the amplitude of the e-th Gaussian component, satisfying (μ ξe ,Σ ξe ) are the distribution parameters of the e-th Gaussian component, which are the mean and variance respectively; x j,t-1 is the state of the jth target at time t-1, x j,t is the state of the jth target at time t, y j,t is the measurement corresponding to the jth target at time t; is the detection probability of the jth target at time t, r j,t is the distance between the jth target and the sensor at time t; According to the extended dimension target state-measurement model, a Dirichlet process-hidden Markov chain hybrid model is established, and the broken stick model is used to construct a mathematical form of discrete distribution that obeys the Dirichlet process. The specific construction process is as follows: In k ~Beta(1,α) α is the concentration parameter, which indicates the degree of discreteness of the generated distribution and is a scalar greater than 0. Beta(·) is the Beta distribution, k is the primary index of the number of cutoffs, and V k is the intermediate parameter of the kth truncation of the Beta distribution with parameters (1, α), r is the secondary index of the truncation times, V r is the intermediate parameter of the rth truncation of the Beta distribution with parameters (1,α), π k is the weight coefficient of the kth truncation, satisfying s j,t is the jth target state x at time t j,t The indicator factor; λ is the base distribution parameter, G(λ) is the base distribution; θ k is the basis obtained by the k-th sampling, represents the infinite number of bases obtained by sampling; Σ is the covariance matrix of the Gaussian distribution obeyed by the measurement.

5. The underwater multi-target tracking method based on target state expansion according to claim 4 is characterized in that: In step 5, the specific steps of solving the variational inference of the Dirichlet process-hidden Markov chain mixed model are as follows: The posterior probability density of the jth target to be estimated at time t V is the intermediate parameter V of infinite truncation k A collection of y j,1:t is the measurement set of the jth target in the 1:t time period, y j,1:t-1 is the measurement set of the jth target in the time period 1:t-1, Through mean field theory, the variational distribution family is used to replace the true posteriori at time t and t-1: where q p (x j,t ) = ∫q(x j,t-1 )p(x j,t |x j,t-1 )dx j,t-1 ,s j,t-1 is the indicator factor of the jth target state xj,t-1 at time t-1, and θ is the θ obtained by infinite truncated sampling k A collection of By means of conjugate prior, (x j,t ,s j,t ,V,θ) sets the prior distribution at time t: is the jth target x at time t j,t The mean and variance of the conjugate Gaussian prior, is the jth target x at time t-1 j,t The mean and variance of the conjugate Gaussian prior, m j,t for The one-step forecast mean, Σ j,t for The one-step prediction variance of Mult(·) is a multinomial distribution. is the parameter of the multinomial distribution at time t, is the parameter of the k-th truncated multinomial distribution at time t; (u k ,v k ) is the parameter of beta distribution; is the parameter of Gaussian distribution; since it needs to be updated iteratively over time, (u k ,v k )and Define as follows: is the parameter of the kth truncated beta distribution at time t-1, is the parameter of the kth truncated beta distribution at time t, is the parameter of the kth truncated Gaussian distribution at time t-1, is the parameter of the kth truncated Gaussian distribution at time t; Based on the variational parameters and their prior distribution, variational inference is performed, and the recursive formula of each variational parameter at time t is obtained as follows:

6. The underwater multi-target tracking method based on target state expansion according to claim 5 is characterized in that: In step 6, the iterative update of the posterior probability density of each target state outputs the estimated track of each target. The specific steps are: For multi-target associated track sets: and Using the variational inference solution in step 5, at time 1:t, recursively update x through each variational parameter j,i The posterior probability of each target is finally obtained. And based on the estimated trajectory set obtained Calculate the distance r between the target and the sensor j,t , and complete the iterative update of the detection probability of each target at time 1:t Based on the obtained estimated track set, the estimated track of each target as it changes over time can be presented through visualization operations.

7. An electronic device, characterized in that: include: one or more processors; Memory; One or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs are configured to execute the method according to any one of claims 1 to 6.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores program codes, and the program codes can be called by a processor to execute the method according to any one of claims 1 to 6.

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