A method for underwater multi-target tracking based on sonar detection system

Abstract

The present invention discloses an underwater multi-target tracking method based on a sonar detection system, comprising the following steps: S1. setting an association gate based on the predicted state center of the target, eliminating clutter irrelevant to the target, and forming a confirmation matrix; S2. splitting the confirmation matrix according to the hypothesis to obtain a feasible matrix; S3. calculating the interconnection probability of the target and the measurement based on the feasible matrix; S4. combining the interconnection probability, using the maximum correlation entropy Kalman filter algorithm to update the state of the target. The present invention combines the maximum correlation entropy theory and the joint probability data association algorithm. Compared with other multi-target tracking algorithms, it can work in a complex underwater environment with non-Gaussian noise, and has the advantages of higher target tracking accuracy, smaller error, more stable algorithm structure, and higher robustness.

Description

Technical Field

[0001] The invention relates to underwater multi-target tracking, and in particular to a probability data association underwater multi-target tracking method based on maximum relevant entropy Kalman filtering. Background Art

[0002] As many countries pay more and more attention to marine development and security, underwater target detection and tracking have become increasingly important in various applications, such as ship navigation, seabed resource exploration and monitoring of underwater suspicious objects. Due to the particularity and complexity of the underwater environment, the acoustic detection method based on the sonar system is an effective way to achieve underwater target detection and tracking. This paper mainly studies the underwater multi-target tracking method based on the sonar system.

[0003] Sonar systems are divided into two categories: active sonar systems and passive sonar systems. Among them, passive sonar systems have attracted widespread attention due to their advantages such as long distance, strong concealment, and strong anti-noise ability, and have been widely used in underwater multi-target tracking. However, common passive sonar systems can only provide azimuth measurement of the target, but cannot provide distance information. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a probabilistic data association underwater multi-target tracking method based on maximum correlation entropy Kalman filtering, which has good target tracking performance when facing non-Gaussian noise and is not easy to diverge and has good robustness.

[0005] The object of the present invention is achieved through the following technical scheme: a method for underwater multi-target tracking based on a sonar detection system, characterized in that it comprises the following steps:

[0006] S1. Set the correlation gate based on the predicted state center of the target to remove clutter irrelevant to the target and form a confirmation matrix;

[0007] S2. Split the confirmation matrix according to the hypothesis to obtain a feasible matrix;

[0008] S3. Calculate the interconnection probability of the target and the measurement based on the feasible matrix;

[0009] S4. Combined with the interconnection probability, the target state is updated using the maximum correlation entropy Kalman filter algorithm to obtain the final state prediction result of multi-target tracking.

[0010] Furthermore, the step S1 comprises:

[0011] S101. Mathematically model the target tracking problem in a multi-sensor network. Assume that the state space model of the i-th target at time k is expressed as:

[0012]

[0013] In the formula, x i (k) represents the state vector of the target, and the state vector x at time k = 0 i (0) indicates the starting point of a given target; F i (k) represents the state transfer matrix, z i (k) represents the real measurement information of the target, H i (k) is the observation matrix, w i (k) and v i (k) represent the process noise and measurement noise of the system, which have a mean of 0 and are uncorrelated with each other. The covariance matrices are:

[0014] E[w i (k)(w i (k)) T ]=Q t (k)

[0015] E[v i (k)(v i (k)) T ]=Ri(k)

[0016] The state prior distribution of target i at time k is defined as:

[0017]

[0018] According to the state information of the target and the system state space model, the estimated value and covariance matrix of each target state are obtained as follows:

[0019]

[0020] P i (k|k-1)=F i (k-1)P i (k-1|k-1)F i (k-1)'+Q(k-1),

[0021] S102. Assume the confirmed measurement set at time k And the number of targets is n, the JPDA-MCCKF algorithm (probabilistic data association algorithm based on maximum correlation entropy Kalman filter) first obtains the association probability between the measurement and the target, and the relevant steps are as follows:

[0022] First, a measurement value verification region is set around the target prediction value to select the measurement values ​​of interest as candidate measurement values ​​for data association. This region is called the association gate.

[0023] According to the obtained prior estimates and prior covariance matrix, when the measurement information satisfy:

[0024]

[0025] Then the measurement is considered to fall within the verification region and is related to the target, where γ represents the threshold of the association gate;

[0026] If the target is detected and the measured value falls into the verification area, the echo is considered valid; otherwise, it will be rejected and considered as clutter and removed. After removing clutter from each target, the confirmation matrix of the target and the measured value is obtained:

[0027] Ω=[ω ji ],j=1,2,…,m k ; i=1,2,…,T

[0028] Among them, m k represents the number of valid echoes, T represents the number of targets; ω ji Indicates whether measurement j falls into the associated gate of target i, where j=0 means there is no target. Since all measurement values ​​may come from false alarms or clutter, the corresponding confirmation matrix columns are all 1 at this time.

[0029] Furthermore, in step S2, the confirmation matrix is ​​split according to the following assumptions to obtain a feasible matrix:

[0030] (1) Each measurement can only come from one target or clutter, that is:

[0031]

[0032] (2) Each target can only generate one echo at most, that is:

[0033]

[0034] Among them, feasible events It represents the event that measurement j in the a-th joint event at time k originates from the event of target i. The matrix corresponding to the feasible event is called the feasible matrix;

[0035] Furthermore, the step S3 comprises:

[0036] According to the feasible matrix obtained in step S2, the events that can be combined can be determined, and then the association probability β is calculated. ji for:

[0037]

[0038] in,

[0039] represents the cumulative confirmed measurement set up to time k; is the normalization constant; V represents the volume of clutter distribution; P D is the detection probability; φ(θ a (k)) represents the number of false measurements; Represents the event θ a (k) Whether target i is detected; Represents the event θ a (k) Whether there is a measurement associated with target i.

[0040] Furthermore, the step S4 comprises:

[0041] S401. Initialize time k = 0 and set the state at k = 0 Initialization: the initial value of the state vector given in advance;

[0042] S402. Initialize the number of iterations at time k t = 1;

[0043] S403. Based on the covariance matrix P obtained in step S1 i (k|k-1) and the noise covariance R i (k), and their Cholesky decomposition is obtained as:

[0044]

[0045]

[0046] The new error matrix is ​​calculated as follows:

[0047]

[0048] in,

[0049] Update through fixed-point iteration, the iterative update formula is:

[0050]

[0051] in,

[0052]

[0053] The rows in the new error matrix are decomposed into a diagonal matrix of the form

[0054]

[0055]

[0056] In order to complete the fixed-point iterative update,

[0057]

[0058]

[0059]

[0060] S404. Update the current k moment and the number of iterations t Recorded as The updated value at iteration t-1 is Recorded as When t = 1, Directly take the value obtained by iterative update at k-1 time

[0061] When satisfied When , stop the fixed-point iteration of the current time k, That is, the predicted tracking result at the current moment, and the process goes to step S405;

[0062] Otherwise, let t = t + 1, repeat steps S403 to S404, and continue to perform fixed-point iteration at the current time k, where ε is the preset threshold parameter

[0063] S405. After the iteration is completed, update the covariance matrix P i (k|k), the calculation formula is:

[0064]

[0065] in,

[0066]

[0067] S406. Let k=k+1, that is, update k, and the updated k is equal to the k before the update plus 1, and then return to step S402 to calculate the tracking result at the next moment, so as to achieve the tracking purpose.

[0068] The beneficial effects of the present invention are as follows: the present invention aims at the underwater multi-target tracking problem based on the sonar system, and the algorithm combines the maximum correlation entropy Kalman filter algorithm and the joint probability data association algorithm to design a new multi-target tracking algorithm. Since the algorithm has better performance than the traditional JPDAF algorithm in processing impulse noise, the algorithm has good target tracking performance in the face of non-Gaussian noise in a complex underwater environment, and is not easy to diverge and has good robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 is a flow chart of the method of the present invention;

[0070] Figure 2 The target trajectory tracking graph

[0071] Figure 3 This is a diagram of simulation experiment results. DETAILED DESCRIPTION

[0072] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings, but the protection scope of the present invention is not limited to the following.

[0073] One challenge of underwater multi-target tracking is the processing of non-Gaussian noise based on the measurement data of the sonar detection system. The existing underwater bearing-only multi-target tracking field uses Kalman and its extended algorithm based on the minimum mean square error criterion, which performs well in Gaussian noise environment. However, in the actual environment, the underwater environment is complex and diverse, and it is easy to have problems such as target bearing loss, trajectory interruption, trajectory intersection, outliers, false alarms, and many interfering targets; so its observation noise is usually Gaussian noise superimposed with other noises, such as impulse signals. At this time, the observation noise becomes heavy-tailed (or pulsed) non-Gaussian noise. The target tracking effect of the traditional Kalman filter will deteriorate under this condition. The main reason is that the minimum mean square error criterion is very sensitive to large outliers. Although particle filtering can be used for non-Gaussian noise, its convergence speed is slow and the calculation is complex. In recent years, optimization criteria in information theory learning have received more attention. Information theory learning links information theory, non-parametric estimation and reconstruction of Hilbert space in a simple and unconventional way. Researchers have proposed that the correlation entropy loss function has obvious advantages over the mean square error loss function in dealing with non-Gaussian noise problems. The reason is that the correlation entropy expansion is a weighted sum of the even-order moments of the error. Since the correlation entropy contains the high-order moment information of the error, and the mean square error loss function only contains the second-order moment information of the error, the maximum correlation entropy Kalman filter has a better performance in processing non-Gaussian noise.

[0074] Compared with single target tracking, multi-target tracking is more complicated. Multi-target tracking often faces problems such as the number of targets changing over time; mutual occlusion, similar appearance and track overlap between multiple targets; and mutual influence between multiple targets. As the scope of multi-target tracking applications becomes wider and wider, a large number of target tracking algorithms have been proposed, but the main multi-target tracking algorithms still follow the following steps: target detection, feature extraction, clutter removal, and data association, among which data association is an important stage in multi-target tracking. In many multi-target data association frameworks, Multiple Hypothesis Tracking and Joint Probabilistic Data Association Filter are two main methods. MHT usually achieves higher accuracy at the cost of higher computational effort, and JPDAF obtains reasonable results at a lower computational cost. Therefore, the underwater multi-target tracking framework based on the sonar detection system proposed in the present invention will adopt the JPDAF scheme.

[0075] Specifically, Figure 1 As shown, an underwater multi-target tracking method based on a sonar detection system comprises the following steps:

[0076] S1. Based on the predicted center of the target state, remove irrelevant echoes and obtain the confirmation matrix.

[0077] When the measurement information meets the following conditions:

[0078] Only when the echo signal is 0, we consider the measurement to be valid, otherwise it is an invalid echo.

[0079] S2. Split the confirmation matrix according to the assumptions to obtain a feasible matrix, and calculate the interconnection probability of the target and the measurement based on the feasible matrix.

[0080]

[0081] S3. Calculate the prior estimation value and prior covariance matrix of the target to be tracked, and update the posterior estimation value according to the maximum correlation entropy indefinite point iteration formula combined with the interconnection probability.

[0082] First, initialize the noise covariance and state transfer matrix, confirm the initial position and initial motion speed of the target, and select the appropriate Gaussian kernel width σ and convergence determination coefficient ε t . Kalman filtering based on maximum correlation entropy is used for each target, and the prior estimate and prior covariance matrix are calculated as follows:

[0083]

[0084] P i(k|k-1)=F i (k-1)P i (k-1|k-1)F i (k-1)'+Q(k-1),

[0085] Their Cholesky decomposition is obtained as:

[0086]

[0087]

[0088] Therefore, the new error matrix calculation is as follows:

[0089]

[0090] in, It can be updated through fixed-point iteration.

[0091]

[0092] The calculation steps are:

[0093]

[0094] S4. When the update of the posterior estimate satisfies the determination coefficient, stop updating, calculate the posterior covariance matrix, and start the next round of iteration, otherwise continue the fixed-point iteration at the current moment.

[0095] When satisfied When , stop the fixed-point iteration and update the posterior covariance matrix:

[0096]

[0097] in,

[0098]

[0099] This example aims at underwater multi-target tracking. Two targets moving at a constant speed are used in the simulation. Assume that the initial states of the two targets are x1 = [-300cm 10cm / s 200cm 10cm / s] and x2 = [500cm -10cm / s 150cm10cm / s]; the first two data represent the target position and target speed of the x coordinate, and the last two data represent the target position and target speed of the y coordinate. The state equation and observation equation of the target are defined as:

[0100]

[0101]

[0102] w i (k) is the covariance matrix Q t (k) = 10 -3 Zero-mean Gaussian noise of I, v i (k) is the covariance matrix R i (k) non-Gaussian noise, denoted as v i (k)~0.9N(0,2 2 )+0.1N(0,20 2 ). Set the sampling time T = 1s, the correlation gate threshold to 100, the Gaussian kernel width σ = 2., and the convergence determination coefficient ε = 10 -6 . Figure 2 The image shows the trajectory tracking effect of the JPDA-MCCKF algorithm. Figure 3 In order to compare this algorithm with other algorithms based on the root mean square error (RMSE) evaluation index, in the case of 300 Monte Carlo experiments, the distance error between the estimated value and the actual trajectory is defined as:

[0103]

[0104] The experimental results are as follows Figure 3 As shown, the representative curve of the present invention is JPDA-MCCKF, which shows that the algorithm of the present invention is better than the existing algorithm in the field of underwater multi-target tracking in a non-Gaussian noise environment in the above indicators.

[0105] The above description shows and describes a preferred embodiment of the present invention, but as mentioned above, it should be understood that the present invention is not limited to the form disclosed herein, and should not be regarded as excluding other embodiments, but can be used in various other combinations, modifications and environments, and can be modified within the scope of the invention concept described herein through the above teachings or the technology or knowledge of the relevant field. And the changes and modifications made by those skilled in the art do not depart from the spirit and scope of the present invention, and should be within the scope of protection of the claims attached to the present invention.

Claims

1. An underwater multi-target tracking method based on a sonar detection system, characterized in that: The following steps are involved: S1. Set the correlation gate based on the predicted state center of the target to remove clutter irrelevant to the target and form a confirmation matrix; The step S1 comprises: S101. Mathematically model the underwater multi-target tracking problem, assuming that the state space model of the i-th target at time k is expressed as: In the formula, x i (k) represents the state vector of the target, and the state vector x at time k = 0 i (0) indicates the starting point of the given target, F i (k) represents the state transfer matrix, z i (k) represents the real measurement information of the target, H i (k) is the observation matrix, w i (k) and v i (k) represent the process noise and measurement noise of the system, which have a mean of 0 and are uncorrelated with each other. The covariance matrices are: E[w i (k)(w i (k)) T ]=Q t (k) E[v i (k)(v i (k)) T ]=R i (k) The state prior distribution of target i at time k is defined as: According to the state information of the target and the system state space model, the estimated value and covariance matrix of each target state are obtained as follows: P i (k|k-1)=F i (k-1)P i (k-1|k-1)F i (k-1)'+Q(k-1), S102. Assume the confirmed measurement set at time k And the number of targets is n, to obtain the association probability between the measurement and the target, the relevant steps are as follows: First, a measurement value verification region is set around the target prediction value to select the measurement values ​​of interest as candidate measurement values ​​for data association. This region is called the association gate. According to the obtained prior estimates and prior covariance matrix, when the measurement information satisfy: Then the measurement is considered to fall within the verification region and is related to the target, where γ represents the threshold of the association gate; If the target is detected and the measured value falls into the verification area, the echo is considered valid; otherwise, it will be rejected and considered as clutter and removed. After removing clutter from each target, the confirmation matrix of the target and the measured value is obtained: Ω=[ω ji ],j=1,2,…,m k ;i=1,2,…,T Among them, m k represents the number of valid echoes, T represents the number of targets; ω ji Indicates whether measurement j falls into the associated gate of target i, where j = 0 means there is no target. Since all measurement values ​​may come from false alarms or clutter, the corresponding confirmation matrix columns are all 1 at this time; S2. Split the confirmation matrix according to the hypothesis to obtain a feasible matrix; In step S2, the confirmation matrix is ​​split according to the following assumptions to obtain a feasible matrix: (1) Each measurement can only come from one target or clutter, that is: (2) Each target can only generate one echo at most, that is: Among them, feasible events It represents the event that measurement j in the a-th joint event at time k originates from the event of target i. The matrix corresponding to the feasible event is called the feasible matrix; S3. Calculate the interconnection probability of the target and the measurement based on the feasible matrix; The step S3 comprises: According to the feasible matrix obtained in step S2, the events that can be combined are determined, and then the association probability β is calculated. ji for: in, represents the cumulative confirmed measurement set up to time k; is the normalization constant; V represents the volume of clutter distribution; P D is the detection probability; φ(θ a (k)) represents the number of false measurements; Represents the event θ a (k) Whether target i is detected; Represents the event θ a (k) whether there is a measurement associated with target i; S4. Combined with the interconnection probability, the target state is updated using the maximum correlation entropy Kalman filter algorithm to obtain the final state prediction result of multi-target tracking; The step S4 comprises: S401. Initialize time k = 0 and set the state at k = 0 Initialization: the initial value of the state vector given in advance; S402. Initialize the number of iterations at time k t = 1; S403. Based on the covariance matrix P obtained in step S1 i (k|k-1) and the noise covariance R i (k), and their Cholesky decomposition is obtained as: The new error matrix is ​​calculated as follows: in, Update through fixed-point iteration, the iterative update formula is: in, The rows in the new error matrix are decomposed into a diagonal matrix of the form To complete the fixed-point iterative update, calculate: S404. Update the current time k and the number of iterations t Recorded as The updated value at iteration t-1 is Recorded as When t = 1, Directly take the value obtained by iterative update at k-1 time When satisfied When , stop the fixed-point iteration of the current time k, That is, the predicted tracking result at the current moment, and the process goes to step S405; Otherwise, let t = t + 1, repeat steps S403 to S404, and continue to perform fixed-point iteration at the current time k, where ε is the preset threshold parameter S405. After the iteration is completed, update the covariance matrix P i (k|k), the calculation formula is: in, S406. Let k=k+1, that is, update k, and the updated k is equal to the k before the update plus 1, and then return to step S402 to calculate the tracking result at the next moment, so as to achieve the tracking purpose.

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