An underwater multi-target tracking method based on target state dimension expansion

Abstract

The application provides an underwater multi-target tracking method based on target state extension, and since a standard random finite set algorithm does not consider non-Gaussian measurement error and detection probability time-varying problems, model mismatch of the multi-target tracking method is caused, thereby causing tracking performance deterioration, and even completely wrong target state estimation is given. By using a generalized labeled multi-Bernoulli filter and a Dirichlet process-hidden Markov chain hybrid model, a target state, a probability density distribution of observation noise and a detection probability are adaptively and real-timely estimated by using variational inference, tracking error is significantly reduced, and track estimation precision and track integrity are improved.

Description

Technical Field

[0001] This invention relates to the field of target tracking technology, and more specifically to an underwater multi-target tracking method based on target state dimensional expansion. Background Technology

[0002] Manned / unmanned coordinated swarms of submarines / UUVs and underwater unmanned swarms of UUVs are important means for the U.S. military to maintain its underwater combat advantage. Therefore, it is urgent to seek faster and more effective underwater formation and swarm multi-target perception methods.

[0003] Due to the inhomogeneity of the transmission medium and the influence of reflections from objects and interfaces, the signal received at the receiver in the underwater acoustic channel is subject to multipath interference. This results in multimodal statistical characteristics in the received measurements by the sensor node. Furthermore, the random, time-varying, and space-varying characteristics of the underwater acoustic channel severely affect the communication link's connectivity. The presence of clutter or false targets in the transmission medium often leads to missed detections and false alarms. In the underwater acoustic channel, as the target distance increases, propagation loss causes the received signal-to-noise ratio to change constantly, thus altering the detection probability.

[0004] Standard random finite set algorithms assume that prior knowledge of sensor noise statistics is known and follows a Gaussian distribution, and that the detection probability is constant. However, in practice, it is often difficult to construct an accurate model for sensor noise, and the detection probability varies. If this error is not considered in a real-world system, it will cause model mismatch in multi-target tracking methods, leading to degraded tracking performance and even completely incorrect target state estimates.

[0005] Therefore, accurate tracking and positioning of multiple targets underwater has become an urgent technical problem to be solved. Summary of the Invention

[0006] To overcome the shortcomings of existing technologies, this invention provides an underwater multi-target tracking method based on target state dimension expansion. Addressing the problems of traditional standard random finite set algorithms in non-Gaussian noise environments, such as track jumps, high track miss rates, and low tracking accuracy, and their unsuitability for situations where the underwater target detection probability varies with the distance between the target and the sensor, this invention provides an underwater multi-target tracking method based on target state dimension expansion to improve the accuracy and robustness of multi-target tracking.

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

[0008] Step 1: Establish a spatial coordinate system and obtain the sensor's position coordinates and monitoring area;

[0009] Step 2: Based on the sonar equation, obtain the curve of the detection probability as a function of 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 measurement sets, and obtains the number of targets and the associated measurement sets of each target based on generalized label multi-Bernoulli filtering;

[0012] Step 5: Based on the extended state-measurement model, the associated measurement set is iteratively updated to the posterior probability density of the extended target state through a Dirichlet process-Hidden Markov chain hybrid model.

[0013] Step 6: Iteratively update the estimated trajectory set based on each frame, update the detection probability, and output the trajectory of each target.

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

[0015] Using active detection, based on the Neyman-Pearson criterion, we have:

[0016]

[0017] P D For the detection probability, P F Let N(·) represent the false alarm probability, and let N(·) denote a Gaussian distribution. -1 (·) represents the inverse cumulative distribution function of the Gaussian distribution, SL is the emitted sound source level, NL is the ambient noise level, TS is the target intensity, DI is the directivity index, and r is the distance between the target and the sensor;

[0018] Define the blockade radius of the sensor as the distance r0 corresponding to a target detection probability of 90%, satisfying... Within the blockade radius, targets can be tracked better, but outside the blockade radius, due to the lower detection probability, the tracking performance is very poor.

[0019] Furthermore, in step 3, the specific steps for constructing the multi-target measurement set are as follows:

[0020] For multi-objective scenarios, at time 1:t, given parameters SL, NL, TS, DI, and P F Calculate the detection probability P of each target at time t. D The detection probability P of each target at time 1:t D Generate measurements, with 1-P D Probability does not generate measurements, but false targets caused by clutter at time 1:t also generate measurements.

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

[0022] At time 1:t, for the measurement information periodically acquired by the sensor The measurement information is the actual target location information. Location information of false targets caused by clutter Right now i represents the time index; the number of targets N and the expanded-dimensional target state set within the monitoring area are obtained through generalized label multi-Bernoulli filtering. and with Associated measurement set Where the expanded dimension target state X at time i is i for x j For the j-th state, Let Y be the detection probability of the target, and let Y be the measurement set at time i. i for y j For the j-th target x j The corresponding measurement, j is the target label index, x j,i Let y be the state of the j-th target at time i. j,i For the measurement of the j-th target at time i;

[0023] For the j-th dimension-expanded target state and Corresponding measurement The extended-dimensional 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 transition matrix, H is the measurement matrix; N(·) represents the Gaussian distribution, w j,t Let ξ be the state noise of the j-th target at time t, which follows a zero-mean Gaussian distribution, and let Q be the variance of the state noise. j,t The measurement noise of the j-th target at time t is non-Gaussian distributed and is fitted by a Gaussian mixture model (GMM); K is the number of Gaussian components in the GMM, e is the index of the Gaussian component, and w eLet the magnitude of the e-th Gaussian component satisfy... (μ ξe ,Σ ξe Let be the distribution parameters of the e-th Gaussian component, and let x be the mean and variance, respectively; j,t-1 Let x be the state of the j-th target at time t-1. j,t Let y be the state of the j-th target at time t. j,t Let t be the measurement corresponding to the j-th target at time t. Let r be the detection probability of the j-th target at time t. j,t Let be the distance between the j-th target and the sensor at time t;

[0029] Based on the extended-dimensional target state-measurement model, a Dirichlet process-Hidden Markov chain hybrid model is established. A broken-stick model is used to construct the mathematical form of the discrete distribution following the Dirichlet process. The specific construction process is as follows:

[0030] V k ~Beta(1,α)

[0031]

[0032] α is the concentration parameter, representing the degree of dispersion of the distribution; it is a scalar greater than 0. Beta(·) represents the Beta distribution, k is the first-level index of the cutoff number, and V k Let V be the intermediate parameter of the k-th truncation following a Beta distribution with parameters (1, α), and r be the second-level index of the truncation number. r Let π be the intermediate parameter of the r-th cutoff following a Beta distribution with parameter (1, α). k Let be the weight coefficient for the k-th truncation, satisfying s j,t Let x be the j-th target state at time t. j,t The indicator factor; λ is the basic distribution parameter, G(λ) is the basic distribution; θ k The basis obtained from the k-th sampling is... Σ represents the infinite number of bases obtained from sampling; Σ is the covariance matrix of the Gaussian distribution followed by the measurement.

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

[0034] The posterior probability density of the j-th target to be estimated at time t.

[0035] V is the intermediate parameter for infinitely many truncations. k The set, y j,1:tLet be the set of measurements for the j-th target within the time interval 1:t. y j,1:t-1 Let the set of measurements for the j-th target within the time interval 1:t-1 be the measurement set.

[0036] Using mean-field theory, a variational family of distributions is used to replace the true posterior at times 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 Let x be the j-th target state at time t-1. j,t-1 The indicator factor, θ is obtained by infinitely many truncation samplings. k The set,

[0039] By using conjugate priors, for (x j,t ,s j,t Let the prior distribution at time t be: (V,θ)

[0040]

[0041]

[0042] Let x be the j-th target at time t. j,t Mean and variance of conjugate Gaussian priors Let x be the j-th target at time t-1. j,t Mean and variance of conjugate Gaussian priors m j,t for The one-step prediction mean, Σ j,t for The one-step prediction variance; Mult(·) is a multinomial distribution. Let be the parameters of the multinomial distribution at time t. Let be the parameters of the multinomial distribution truncated to the kth time at time t; (u k ,v k ) represents the parameters of the beta distribution; The parameters are Gaussian distribution parameters; since iterative updates are needed over time, for (u) k ,v k )and Defined as follows: Let be the parameters of the k-th truncated beta distribution at time t-1. Let be the parameters of the k-th truncated beta distribution at time t. Let be the parameters of the k-th truncated Gaussian distribution at time t-1. Let be the parameters of the k-th truncated Gaussian distribution at time t;

[0043] Variational inference is performed based on the variational parameters and their prior distributions, yielding the recursive formulas for each variational parameter at time t as follows:

[0044]

[0045] Furthermore, in step 6, the iterative update of the posterior probability density of each target state, and the output of the estimated trajectory of each target, are as follows:

[0046] For multi-target associated track sets: and Using the variational inference method described in step five, x is iteratively updated at time 1:t through recursive formulas for each variational parameter. j,i The posterior probabilities are used to obtain the estimated trajectory set for each target. And based on the acquired estimated trajectory set Calculate the distance r between the target and the sensor. j,t And complete the iterative update of the detection probabilities of each target at time 1:t. Based on the acquired set of estimated tracks, the estimated tracks of each target can be displayed over time through visualization operations.

[0047] An electronic device includes 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 perform the methods described above.

[0048] A computer-readable storage medium storing program code that can be invoked by a processor to perform the method described above.

[0049] The beneficial effect of this invention lies in the provision of an underwater multi-target tracking method based on target state dimension expansion. Standard stochastic finite set algorithms do not consider non-Gaussian measurement errors and time-varying detection probabilities, leading to model mismatch in multi-target tracking methods, resulting in degraded tracking performance and even completely incorrect target state estimates. This invention utilizes a hybrid model of generalized labeled multi-Bernoulli filtering and Dirichlet process-Hidden Markov chain, adaptively and in real-time jointly estimating the target state, the probability density distribution of observation noise, and the detection probability through variational inference. This significantly reduces tracking errors and improves track estimation accuracy and track completeness. Attached Figure Description

[0050] Figure 1 This is a flowchart of an embodiment of the present invention;

[0051] Figure 2 This is a flowchart of a specific embodiment of the present invention;

[0052] Figure 3 This is a schematic diagram of the actual flight paths of multiple targets within the monitoring area in the simulation example of this invention;

[0053] Figure 4 The detection probability curves under different false alarm probabilities in the simulation examples of this invention are shown.

[0054] Figure 5 This is a schematic diagram of the trajectory estimation method in a simulation example of the present invention;

[0055] Figure 6 This is a schematic diagram illustrating the estimation of the OSPA distance of the track using the method in a simulation example of this invention;

[0056] Figure 7 This is a schematic diagram illustrating the estimation of the number using the method in a simulation example of this invention.

[0057] Figure 8 This is a schematic diagram illustrating the target estimation number in the JointGLMB algorithm of the simulation example of this invention. Detailed Implementation

[0058] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0059] This invention relates to an underwater multi-target tracking method based on target state-dimensional expansion, comprising the following steps: establishing a spatial coordinate system and acquiring the sensor's position coordinates and monitoring area; acquiring the detection probability variation curve with the distance between the target and the sensor and the sensor's blockade radius based on the sonar equation; constructing a multi-target measurement set based on the detection probability variation curve with the distance between the target and the sensor; periodically acquiring the measurement set by the sensor, and acquiring the number of targets and the associated measurement set of each target based on generalized label multi-Bernoulli filtering; iteratively updating the posterior probability density of the target state using a Dirichlet process-Hidden Markov chain hybrid model based on the expanded state-measurement model; iteratively updating the estimated trajectory set according to each frame, updating the detection probability, and outputting the trajectory of each target. This invention combines the sonar equation and uses a generalized label multi-Bernoulli filtering and a Dirichlet process-Hidden Markov chain hybrid model to iteratively update the expanded target state, significantly reducing tracking errors and improving trajectory estimation accuracy and trajectory completeness.

[0060] like Figures 1-8As shown, this invention provides an underwater multi-target tracking method based on target state dimension expansion, the method comprising the following steps:

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

[0062] S2: Obtain the detection probability as a function of the distance between the target and the sensor, and the blocking radius of the sensor, based on the sonar equation;

[0063] Using active detection, based on the Neyman-Pearson criterion, we have:

[0064]

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

[0066] Define the blockade radius of the sensor as the distance r0 corresponding to a target detection probability of 90%, satisfying...

[0067] S3: Construct a 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 t. D Each target has its own detection probability P. D Generate measurements, with 1-P D Probability does not generate measurements. The sensor periodically acquires a set of measurements, and the set of measurement information in the i-th frame is denoted as Z. i For the measurement information periodically acquired by the sensor within a time period of 1:t The measurement information is the actual target location information. Location information of false targets caused by clutter Right now

[0068] S4: Based on the measurement set acquired by the sensor, obtain the correlation measurement set between the number of targets N and each target through generalized labeled multi-Bernoulli filtering (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.). This is the expanded-dimensional target state set. and related measurements Where X is x j For a certain goal, Let Y be the detection probability of the target. y j For target x j The corresponding measurements.

[0069] Extended Dimension Target State Set and with Associated measurement set Where the expanded dimension target state X at time i is i for x j For the j-th state, Let Y be the detection probability of the target, and let Y be the measurement set at time i. i for y j For the j-th target x j The corresponding measurement, j is the target label index, x j,i Let y be the state of the j-th target at time i. j,i For the measurement of the j-th target at time i;

[0070] S5: Based on the extended-dimensional target state-measurement model, a Dirichlet process-hidden Markov chain hybrid model is established, and the posterior probability density of the target state is iteratively updated using variational inference based on the associated measurement set.

[0071] S5.1: For the j-th dimension-expanded target state Its corresponding measurement The extended-dimensional 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 transition matrix, H is the measurement matrix; N(·) represents the Gaussian distribution, w j,t Let ξ be the state noise of the j-th target at time t, which follows a zero-mean Gaussian distribution, and let Q be the variance of the state noise. j,t The measurement noise of the j-th target at time t is non-Gaussian distributed and is fitted by a Gaussian mixture model (GMM); K is the number of Gaussian components in the GMM, e is the index of the Gaussian component, and w e Let the magnitude of the e-th Gaussian component satisfy... (μ ξe ,Σ ξe Let be the distribution parameters of the e-th Gaussian component, and let x be the mean and variance, respectively; j,t-1 Let x be the state of the j-th target at time t-1. j,t Let y be the state of the j-th target at time t. j,t Let t be the measurement corresponding to the j-th target at time t. Let r be the detection probability of the j-th target at time t. jt Let be the distance between the j-th target and the sensor at time t.

[0077] Based on the extended-dimensional target state-measurement model, a Dirichlet process-Hidden Markov chain hybrid model is established. A broken-stick model is used to construct the mathematical form of the discrete distribution following the Dirichlet process. The specific construction process is as follows:

[0078] V k ~Beta(1,α)

[0079]

[0080] α is the concentration parameter, representing the degree of dispersion of the distribution; it is a scalar greater than 0. Beta(·) represents the Beta distribution, k is the first-level index of the cutoff number, and V k Let be the intermediate parameter for the k-th truncation of a Beta distribution with parameters (1, α), and r be the secondary index of the truncation number. r π represents the intermediate parameter of the r-th truncation of a Beta distribution with parameter (1, α). k Let be the weight coefficient for the k-th truncation, satisfying s j,t Let x be the j-th target state at time t. j,t The indicator factor; λ is the basic distribution parameter, G(λ) is the basic distribution; θk The basis obtained from the k-th sampling is... Σ represents the infinite number of bases obtained from sampling; Σ is the covariance matrix of the Gaussian distribution followed by the measurement.

[0081] S5.2: The solution method for variational inference of the Dirichlet process-Hidden Markov chain hybrid model is as follows:

[0082] The posterior probability density of the j-th target to be estimated at time t.

[0083] V is the intermediate parameter for infinitely many truncations. k The set, y j,1:t Let be the set of measurements for the j-th target within the time interval 1:t. y j,1:t-1 Let the set of measurements for the j-th target within the time interval 1:t-1 be the measurement set.

[0084] Using mean-field theory, a variational family of distributions is used to replace the true posterior at times 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 Let x be the j-th target state at time t-1. j,t-1 The indicator factor, θ is obtained by infinitely many truncation samplings. k The set,

[0087] By using conjugate priors, for (x j,t ,s j,t Let the prior distribution at time t be: (V,θ)

[0088]

[0089] Let x be the j-th target at time t. j,t Mean and variance of conjugate Gaussian priors Let x be the j-th target at time t-1. j,t Mean and variance of conjugate Gaussian priors m j,t for The one-step prediction mean, Σ j,t for The one-step prediction variance; Mult(·) is a multinomial distribution. Let be the parameters of the multinomial distribution at time t. Let be the parameters of the multinomial distribution truncated to the kth time at time t; (u k ,v k ) represents the parameters of the beta distribution; The parameters are Gaussian distribution parameters; since iterative updates are needed over time, for (u) k ,v k )and Defined as follows: Let be the parameters of the k-th truncated beta distribution at time t-1. Let be the parameters of the k-th truncated beta distribution at time t. Let be the parameters of the k-th truncated Gaussian distribution at time t-1. Let be the parameters of the k-th truncated Gaussian distribution at time t.

[0090] Variational inference is performed based on the variational parameters and their prior distributions, yielding the recursive formulas for each variational parameter at time t 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 trajectory of each target, specifically:

[0094] For multi-target associated track sets: and Using the variational inference method described in step five, x is iteratively updated at time 1:t through recursive formulas for each variational parameter. j,i The posterior probabilities are used to obtain the estimated trajectory set for each target. And based on the acquired estimated trajectory set Calculate the distance r between the target and the sensor. j,t And complete the iterative update of the detection probabilities 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.

[0095] To better illustrate the technical solution of the present invention, the following simulation experiments are used to further explain the present invention:

[0096] Based on the Generalized Labeled Multi-Bernoulli (GLMB) filtering, this invention proposes a multi-target tracking method for non-Gaussian measurements based on a Dirichlet process-Hidden Markov chain hybrid model.

[0097] 1. Simulation conditions

[0098] In a two-dimensional coordinate system, consider the position coordinates (x, y) of a single sensor node. s ,y s Given a coordinate (0,0), three targets are tracked within a 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 start times for different targets are {1, 1, 20}, and the disappearance times are {150, 200, 130}. The actual flight paths are as follows: Figure 3 As shown.

[0099] The parameters of the generalized labeled multi-Bernoulli filter are set as follows, including the 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 These represent the target's x-coordinate and velocity, and y-coordinate and velocity, respectively.

[0101] Single target survival probability p s =0.99, the detection probability changes with motion, and the detection probability of the j-th target at time t is Where P F =0.01, SL=145dB, NL=55dB, TS=10dB, DI=0, (l xj,t ,l yj,t Let be the location coordinates of the j-th target; the detection probability curves under different false alarm probabilities are as follows: Figure 4 As shown, the target state transition matrix F and covariance matrix Q are

[0102]

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

[0104] The measurement function is:

[0105]

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

[0107] mean 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 update steps is 100, and the track cutoff threshold is 10. -15 Single-track Gaussian component cutoff threshold 10 -3 .

[0111] The GLMB filter described above yields the target estimation number N and the expanded-dimensional target state set. and related measurements Where X is x j For a certain goal, Let Y be the detection probability of the target. y j For target x j The corresponding measurements.

[0112] For the j-th target Its corresponding measurement Establish the following Dirichlet process-Hidden Markov chain hybrid model:

[0113] V k ~Beta(1,α)

[0114]

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

[0116] Since k∈[1,+∞), We need to truncate k so that k∈[1,K); by sampling: V k ~Beta(1,α), When k = K, if the following conditions are met but This condition is satisfied at this time.

[0117] Solving for variational parameters using variational inference methods:

[0118] Initialization parameters:

[0119] x j0 Let be the initial value of the j-th target state.

[0120]

[0121] For multi-target associated track sets: and Using the variational inference method described in step five, x is iteratively updated at time 1:t through recursive formulas for each variational parameter. j,i The posterior probabilities are used to obtain the estimated trajectory set for each target. And based on the acquired estimated trajectory set Calculate the distance r between the target and the sensor. j,t And complete the iterative update of the detection probabilities 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.

[0122] For different methods, Optimal Sub-pattern Assignment (OSPA) measures the error between the actual and estimated tracks. It uses a distance sensitivity parameter p (1≤p≤∞) and an association sensitivity parameter c (c>0) to measure the error between two sets A={a1,a2,…,a…}. m} and B={b1,b2,…,b n The distance D between m,n∈{0,1,2,…} p,c (A,B):

[0123]

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

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

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

[0127]

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

[0129] 2. Simulation Result Analysis

[0130] Figure 5 The estimated trajectory, sensor-received measurement set, and actual trajectory in the x and y directions of the proposed method are presented.

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

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

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

[0134] This demonstrates 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 embodiments are merely exemplary and not restrictive. Various obvious or equivalent modifications or substitutions that can be made by those skilled in the art regarding the above details without departing from the basic principles of the present invention will be included within the scope of the claims of the present invention.

Claims

1. An underwater multi-target tracking method based on target state dimension expansion, characterized in that... Includes the following steps: Step 1: Establish a spatial coordinate system and obtain the sensor's position coordinates and monitoring area; Step 2: Based on the sonar equation, obtain the curve of the detection probability as a function of 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 measurement sets, and obtains the number of targets and the associated measurement sets of each target based on generalized label multi-Bernoulli filtering; Step 5: Based on the extended state-measurement model, the associated measurement set is iteratively updated to the posterior probability density of the extended target state through a Dirichlet process-Hidden Markov chain hybrid model. Step 6: Iteratively update the estimated trajectory set based on each frame, update the detection probability, and output the trajectory of each target.

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

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

4. The underwater multi-target tracking method based on target state dimension expansion according to claim 3, characterized in that: In step 5, the specific steps of the hybrid model of the extended-dimensional state-measurement model and the Dirichlet process-Hidden Markov chain model are as follows: At time 1:t, for the measurement information periodically acquired by the sensor The measurement information is the actual target location information. Location information of false targets caused by clutter Right now i represents the time index; the number of targets N and the expanded-dimensional target state set within the monitoring area are obtained through generalized label multi-Bernoulli filtering. and with Associated measurement set Where the expanded dimension target state X at time i is i for x j For the j-th state, Let Y be the detection probability of the target, and let Y be the measurement set at time i. i for y j For the j-th target x j The corresponding measurement, j is the target label index, x j,i Let y be the state of the j-th target at time i. j,i For the measurement of the j-th target at time i; For the j-th dimension-expanded target state and Corresponding measurement The extended-dimensional 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 transition matrix, H is the measurement matrix; N(·) represents the Gaussian distribution, w j,t Let ξ be the state noise of the j-th target at time t, which follows a zero-mean Gaussian distribution, and let Q be the variance of the state noise. j,t The measurement noise of the j-th target at time t is non-Gaussian distributed and is fitted by a Gaussian mixture model (GMM); K is the number of Gaussian components in the GMM, e is the index of the Gaussian component, and w e Let the magnitude of the e-th Gaussian component satisfy... (μ ξe ,Σ ξe Let be the distribution parameters of the e-th Gaussian component, and let x be the mean and variance, respectively; j,t-1 Let x be the state of the j-th target at time t-1. j,t Let y be the state of the j-th target at time t. j,t The measurement corresponding to the j-th target at time t; Let r be the detection probability of the j-th target at time t. j,t Let be the distance between the j-th target and the sensor at time t; Based on the extended-dimensional target state-measurement model, a Dirichlet process-Hidden Markov chain hybrid model is established. A broken-stick model is used to construct the mathematical form of the discrete distribution of the Dirichlet process. The specific construction process is as follows: In k ~Beta(1,α) α is the concentration parameter, representing the degree of dispersion of the distribution; it is a scalar greater than 0. Beta(·) represents the Beta distribution, k is the first-level index of the cutoff number, and V k Let V be the intermediate parameter of the k-th truncation following a Beta distribution with parameters (1, α), and r be the second-level index of the truncation number. r Let π be the intermediate parameter of the r-th cutoff following a Beta distribution with parameter (1, α). k Let be the weight coefficient for the k-th truncation, satisfying s j,t Let x be the j-th target state at time t. j,t The indicator factor; λ is the basic distribution parameter, G(λ) is the basic distribution; θ k The basis obtained from the k-th sampling is... Σ represents the infinite number of bases obtained from sampling; Σ is the covariance matrix of the Gaussian distribution followed by the measurement.

5. The underwater multi-target tracking method based on target state dimension expansion according to claim 4, characterized in that: In step 5, the specific steps for solving the variational inference of the Dirichlet process-Hidden Markov chain hybrid model are as follows: The posterior probability density of the j-th target to be estimated at time t. V is the intermediate parameter for infinitely many truncations. k The set, y j,1:t Let be the set of measurements for the j-th target within the time interval 1:t. y j,1:t-1 Let the set of measurements for the j-th target within the time interval 1:t-1 be the measurement set. Using mean-field theory, a variational family of distributions is used to replace the true posterior at times 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 Let x be the j-th target state at time t-1. j,t-1 The indicator factor, θ is obtained by infinitely many truncation samplings. k The set, By using conjugate priors, for (x j,t ,s j,t Let the prior distribution at time t be: (V,θ) Let x be the j-th target at time t. j,t Mean and variance of conjugate Gaussian priors Let x be the j-th target at time t-1. j,t Mean and variance of conjugate Gaussian priors m j,t for The one-step prediction mean, Σ j,t for The one-step prediction variance; Mult(·) is a multinomial distribution. Let be the parameters of the multinomial distribution at time t. Let be the parameters of the multinomial distribution truncated to the kth time at time t; (u k ,v k ) represents the parameters of the beta distribution; The parameters are Gaussian distribution parameters; since iterative updates are needed over time, for (u) k ,v k )and Defined as follows: Let be the parameters of the k-th truncated beta distribution at time t-1. Let be the parameters of the k-th truncated beta distribution at time t. Let be the parameters of the k-th truncated Gaussian distribution at time t-1. Let be the parameters of the k-th truncated Gaussian distribution at time t; Variational inference is performed based on the variational parameters and their prior distributions, yielding the recursive formulas for each variational parameter at time t as follows:

6. The underwater multi-target tracking method based on target state dimension expansion according to claim 5, characterized in that: In step 6, the iterative update of the posterior probability density of each target state and the output of the estimated trajectory of each target are carried out. The specific steps are as follows: For multi-target associated track sets: Using the variational inference method described in step five, x is iteratively updated at time 1:t through recursive formulas for each variational parameter. j,i The posterior probabilities are used to obtain the estimated trajectory set for each target. And based on the acquired estimated trajectory set Calculate the distance r between the target and the sensor. j,t And complete the iterative update of the detection probabilities of each target at time 1:t. Based on the acquired set of estimated tracks, the estimated tracks of each target can be displayed over time 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, the one or more programs being configured to perform the method as described in any one of claims 1-6.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores program code that can be invoked by a processor to execute the method as described in any one of claims 1-6.

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