A bearing potential function weighted dynamic programming method for underwater target detection and track-before-track

Abstract

The application relates to a bearing potential function weighting-based underwater acoustic target dynamic programming pre-detection tracking method and belongs to the field of passive sonar underwater acoustic multi-target tracking. The application aims to solve the problem that the traditional dynamic programming-based pre-detection tracking algorithm is prone to track trajectory merging or track trajectory mismatching. The application establishes an augmented target state model containing target bearing and bearing potential coefficient, establishes a sliding window during value function iteration, calculates the bearing potential coefficient of the track in the window, establishes a bearing potential function by considering the bearing potential coefficient which defines the bearing track change trend, adds the bearing potential function into the value function to reflect the bearing track change trend, and can reduce the probability of the tracking performance decline caused by the spatial spectrum response overlap when the adjacent tracks cross.

Description

Technical Field

[0001] This invention relates to a dynamic programming-based underwater acoustic target tracking method for detection based on azimuth potential function weighting, belonging to the field of passive sonar underwater multi-target tracking. Background Technology

[0002] A passive sonar system is an underwater acoustic device that detects, locates, and tracks targets by receiving their acoustic signals. One of the key research directions for passive sonar underwater multi-target tracking is the effective detection and accurate tracking of weak underwater acoustic targets with low signal-to-noise ratios.

[0003] In recent years, pre-detection tracking methods have gradually attracted attention. Pre-detection tracking methods have good performance in the field of underwater acoustic weak target detection and tracking. Unlike the traditional detection-then-tracking method, pre-detection tracking methods store the data received by the sonar array that exceeds or falls below a threshold. Without threshold processing, the sonar data is preprocessed directly, and the target is tracked by utilizing the correlation of target orientation estimation between adjacent frames and the non-correlation of noise.

[0004] Pre-detection tracking algorithms for underwater acoustic multi-target applications are mainly divided into particle filter-based pre-detection tracking and dynamic programming-based pre-detection tracking. Particle filter-based pre-detection tracking relies on the Monte Carlo integral approximation, using weighted particles to represent the posterior probability density of the target state, thereby establishing and maintaining the target trajectory. Dynamic programming-based pre-detection tracking essentially pre-calculates all possible target trajectories, stores these trajectories, accumulates observation data along these trajectories, and finally uses the trajectory corresponding to the accumulated data exceeding a threshold as the target's true trajectory. Compared to particle filter-based pre-detection tracking, dynamic programming-based pre-detection tracking has advantages such as lower computational complexity and higher determinism, making it more suitable for systems with high real-time requirements.

[0005] Traditional dynamic programming-based pre-detection tracking algorithms have good tracking performance when tracking targets with good separation and no measurement ambiguity. However, when targets cross each other in close proximity, strong targets may mask weak targets, causing aliasing of value functions and leading to problems such as merging or mismatching of tracking trajectories.

[0006] In summary, the tracking performance of existing passive sonar underwater target dynamic programming pre-detection tracking methods is still relatively limited in the case of nearby targets. Therefore, it is necessary to propose a new underwater acoustic nearby target dynamic programming pre-detection tracking method. Summary of the Invention

[0007] The purpose of this invention is to address the problem that traditional dynamic programming-based pre-detection tracking algorithms for underwater acoustic targets in passive tracking scenarios often result in tracking trajectory merging or mismatch when strong targets mask weak targets and value functions overlap during target proximity crossings. Therefore, this invention proposes a dynamic programming-based pre-detection tracking method for underwater acoustic targets with azimuth potential function weighting.

[0008] The specific process of a dynamic programming-based underwater acoustic target tracking method for pre-detection tracking based on azimuth potential function weighting is as follows:

[0009] Step 1: Beamforming is performed on the passive sonar detection signal to obtain spatial spectrum data;

[0010] Using spatial spectrum data as measurement data, the azimuth observation range of each frame in the measurement data is divided into B resolution units.

[0011] Step 2: Initialize the state transition number q;

[0012] When the number of state transitions is q, the measurement data transitions from the k-th frame to the (k+1)-th frame, obtaining the target state information x of the (k+1)-th frame. k+1 ;

[0013] Step 3: Initialize the frame number k in the measurement data to 1;

[0014] Step 4: Initialize the target count m = 1;

[0015] Step 5: Define the azimuth potential coefficient, and based on the azimuth potential coefficient, define augmented state information that includes the azimuth potential coefficient and target azimuth information.

[0016] Step 6: Based on the measurement data from Step 1 and the target state information x from Step 2 k+1 Step 5 includes augmented state information containing azimuth potential coefficients and target azimuth information. Initialize the augmented state information of the first n frames with a window length n equal to the azimuth potential coefficient. We obtain the value function and the track backtracking function;

[0017] Step 7: Determine if k > n. If yes, proceed to step 8; otherwise, set k = k + 1 and repeat steps 6 to 7.

[0018] Step 8: Add a weighted azimuth potential function to the value function obtained in Step 6 to obtain a new value function;

[0019] Based on the new value function and azimuth potential function, the trajectory backtracking function of the m-th target in the k-th frame is obtained;

[0020] Step 9: Determine if k = K. If yes, proceed to step 10. If no, set k = k + 1 and repeat steps 8 to 9.

[0021] K represents the total number of frames in the measurement data;

[0022] Step 10: Compare the obtained new value function with the decision threshold, remove the targets in the frames corresponding to the value functions that are less than the decision threshold, and keep the targets in the frames corresponding to the value functions that are greater than or equal to the decision threshold.

[0023] Step 11: Based on the target of the frame corresponding to the value function retained in Step 10 and the trajectory backtracking function in Step 8, perform trajectory backtracking to obtain the tracking trajectory of the m-th target;

[0024] Step 12: Determine if m = M. If so, obtain the tracking trajectories of M targets.

[0025] If not, let m = m + 1, and repeat steps 8 to 12 until m = M, to obtain M target tracking trajectories.

[0026] The beneficial effects of this invention are:

[0027] To address the target proximity tracking problem in passive sonar weak target scenarios, this invention proposes a dynamic programming detection-before-tracking method based on azimuth potential function weighting (APWDP-TBD). An augmented target state model is established, incorporating the target azimuth and azimuth potential coefficients. A sliding window is established during the value function iteration, and the azimuth potential coefficients of the trajectory within the window are calculated. The azimuth potential function is established by considering the azimuth potential coefficients that define the trend of azimuth tracking trajectory changes. Adding the azimuth potential function to the value function reflects the trend of azimuth trajectory changes, which can reduce the probability of tracking performance degradation caused by overlapping spatial spectrum responses when trajectories intersect.

[0028] In dynamic programming-based pre-detection tracking algorithms, value function broadening occurs due to mutual interference between different targets when targets intersect, easily leading to the accumulation of value function errors. This invention proposes a value function weighted by an azimuth potential function to replace the conventional value function. When constructing state variables, the influence of azimuth and azimuth potential coefficients is considered. By recording the azimuth potential coefficients, the probability of the predicted state belonging to the current target is determined, thus enabling correct separation of value functions for different targets in near-target scenarios. This solves the problem in existing underwater acoustic target passive tracking scenarios where traditional dynamic programming-based pre-detection tracking algorithms suffer from aliasing of value functions due to strong targets masking weak targets, easily leading to merging or mismatching of tracking trajectories when targets intersect. Simulation results show that the azimuth potential function-weighted dynamic programming pre-detection tracking method can achieve correct tracking even in low signal-to-noise ratio environments when targets intersect. Attached Figure Description

[0029] Figure 1 This is a flowchart of the method of the present invention;

[0030] Figure 2 This is a time-location history diagram after beamforming;

[0031] Figure 3(a) shows the tracking results of the DP-TBD algorithm in a nearby scene. DP-TBD is a tracking before detection based on dynamic programming.

[0032] Figure 3(b) shows the tracking results of the APWDP-TBD algorithm in a nearby scene. APWDP-TBD is a dynamic programming-based tracking before detection that is weighted by the azimuth potential function.

[0033] Figure 4(a) shows the optimal sub-pattern allocation error of the DP-TBD algorithm, where OSPA is the optimal sub-pattern allocation.

[0034] Figure 4(b) shows the optimal sub-pattern allocation error of the APWDP-TBD algorithm. Detailed Implementation

[0035] Specific Implementation Method 1: Combination Figure 1 This embodiment describes a dynamic programming-based underwater acoustic target tracking method for pre-detection tracking, weighted by azimuth potential function. The specific process is as follows:

[0036] Step 1: Beamforming is performed on the passive sonar detection signal to obtain spatial spectrum data;

[0037] Using spatial spectrum data as measurement data, the azimuth observation range of each frame in the measurement data is divided into B resolution units.

[0038] Step 2: Initialize the state transition number q;

[0039] When the number of state transitions is q, the measurement data transitions from the k-th frame to the (k+1)-th frame, obtaining the target state information x of the (k+1)-th frame. k+1 ;

[0040] Step 3: Initialize the frame number k in the measurement data to 1;

[0041] Step 4: Initialize the target count m = 1;

[0042] Step 5: Define the azimuth potential coefficient, and based on the azimuth potential coefficient, define augmented state information that includes the azimuth potential coefficient and target azimuth information.

[0043] Step 6: Based on the measurement data from Step 1 and the target state information x from Step 2 k+1 Step 5 includes augmented state information containing azimuth potential coefficients and target azimuth information. Initialize the augmented state information of the first n frames with a window length n equal to the azimuth potential coefficient. We obtain the value function and the track backtracking function;

[0044] Step 7: Determine if k > n. If yes, proceed to step 8; otherwise, set k = k + 1 and repeat steps 6 to 7.

[0045] Step 8: Add a weighted azimuth potential function to the value function obtained in Step 6 to obtain a new value function;

[0046] Based on the new value function and azimuth potential function, the trajectory backtracking function of the m-th target in the k-th frame is obtained;

[0047] Step 9: Determine if k = K. If yes, proceed to step 10. If no, set k = k + 1 and repeat steps 8 to 9.

[0048] K represents the total number of frames in the measurement data;

[0049] Step 10: Compare the obtained new value function with the decision threshold, remove the targets in the frames corresponding to the value functions that are less than the decision threshold, and keep the targets in the frames corresponding to the value functions that are greater than or equal to the decision threshold.

[0050] Step 11: Based on the target of the frame corresponding to the value function retained in Step 10 and the trajectory backtracking function in Step 8, perform trajectory backtracking to obtain the tracking trajectory of the m-th target;

[0051] Step 12: Determine if m = M. If so, obtain the tracking trajectories of M targets.

[0052] If not, let m = m + 1, and repeat steps 8 to 12 until m = M, to obtain M target tracking trajectories.

[0053] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that: in step 1, beamforming is performed on the passive sonar detection signal to obtain spatial spectrum data;

[0054] Using spatial spectrum data as measurement data, the azimuth observation range of each frame in the measurement data is divided into B resolution units.

[0055] The specific process is as follows:

[0056] Step 11: Initialize the number of linear array elements, element spacing, sampling frequency, sound velocity, and number of frames;

[0057] Step 12: Beamforming is performed on the passive sonar detection signal to obtain spatial spectrum data;

[0058] Step 13: Use the spatial spectrum data as measurement data, denoted as Z. 1:K ={z1,z2,...,z k ,...,z K};

[0059] Among them, Z1:K Let z1 be the first frame of the measurement data, z2 be the second frame of the measurement data, and z... k For the k-th frame of the measurement data, z K The Kth frame in the measurement data is K, where K is the total number of frames in the measurement data.

[0060] Step 14: Divide the azimuth observation range of each frame in the measurement data into B resolution units, each resolution unit being Δθ in size; the observation range of each frame must be divided into the same number of resolution units.

[0061] Use z k (b) represents the measurement data amplitude at the b-th resolution unit of the k-th frame. The measurement data amplitudes in all resolution units are independent and identically distributed, and b = 1, 2, ..., B.

[0062] z k (b) is represented as:

[0063]

[0064] Where, ω k (b) represents the noise amplitude of the b-th resolution unit in the k-th frame, A k (b) represents the target signal amplitude of the b-th resolution unit in the k-th frame.

[0065] The other steps and parameters are the same as in Specific Implementation Method 1.

[0066] Specific Implementation Method 3: This implementation method differs from Specific Implementation Method 1 or 2 in that: in step 2, the state transition number q is initialized (the value of the initial state transition number q ranges from 0 to 41);

[0067] When the number of state transitions is q, the measurement data transitions from the k-th frame to the (k+1)-th frame, obtaining the target state information x of the (k+1)-th frame. k+1 ;

[0068] The specific process is as follows:

[0069] Initialize the state transition number q, which represents the number of state transitions that the objective may undergo in the next observation stage in the dynamic programming algorithm;

[0070] When the state transition number is q, the measurement data transitions from the k-th frame to the (k+1)-th frame, and the target state information x in the (k+1)-th frame... k+1 for:

[0071]

[0072] Where, θ k Here is the orientation information for the k-th frame, Δθ is the size of the resolution cell, and δ... qx represents the state transition range when the number of state transitions is q; k+1 This represents the target state information in the (k+1)th frame.

[0073] Other steps and parameters are the same as in specific implementation method one or two.

[0074] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that: in step 5, an azimuth potential coefficient is defined, and based on the azimuth potential coefficient, augmented state information containing the azimuth potential coefficient and target azimuth information is defined. The specific process is as follows:

[0075] Step 51, Definition The azimuth potential coefficient of the m-th target in the k-th frame is represented as:

[0076]

[0077] Where n is the window length of the azimuth potential coefficient, m is the target count, and ω i Let θ be the weight of the i-th frame. i For the orientation information of the i-th frame, θ i-1 This refers to the orientation information of the (i-1)th frame;

[0078] Points closer to the current frame should have a larger weight to reflect changes in the potential coefficient;

[0079] Step 52: Based on the azimuth potential coefficient of the m-th target in the k-th frame. Define the augmented state information of the m-th target in the k-th frame, which includes the azimuth potential coefficient and the target's azimuth information; expressed as:

[0080]

[0081] in, This indicates the target location information of the m-th target in the k-th frame; This represents the augmented state information of the m-th target in the k-th frame.

[0082] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0083] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that: in step 6, the measurement data from step 1 and the target state information x from step 2 are used... k+1 Step 5 includes augmented state information containing azimuth potential coefficients and target azimuth information. Initialize the augmented state information of the first n frames with a window length n equal to the azimuth potential coefficient. We obtain the value function and the track backtracking function;

[0084] The specific process is as follows:

[0085] Step 61: Express the target's state transition equation and measurement equation as follows:

[0086]

[0087] Among them, f k-1 (·) represents the state transition function, h k (·) represents the measurement function, x k Represents the augmentation state information of the k-th frame, x k-1 w represents the augmentation state information of the (k-1)th frame. k Represents state transition noise, v k This represents measurement noise, all of which follow a Gaussian distribution, z. k This represents the measurement data for the k-th frame;

[0088] Step 62: The target sequence with the highest posterior probability Right now:

[0089]

[0090] in, This is the augmented state information of the target with the highest posterior probability in the first frame. This is the augmented state information of the target with the highest posterior probability density in the second frame. This represents the augmented state information of the target with the highest posterior probability in the k-th frame. Let be the set of target states with the highest posterior probability in the first k frames. Let p(X) be the maximum a posteriori probability density function. 1:k |Z 1:k ) is the posterior probability density function;

[0091] The posterior probability density function p(X) of the target 1:k |Z 1:k It is obtained from prior information about the target and the noise;

[0092] The posterior probability density function of the target represents the measurement data set Z. 1:k Given the target state set X 1:k The probability is determined;

[0093] Step 63: Perform a Bayesian transform on equation (6) from step 62, and obtain:

[0094]

[0095] Where p(X) 1:k |Z 1:k Let X be the posterior probability density function of the first k frames. 1:k Z represents the set of target states for the previous k frames. 1:k For the measurement data set, p(z)k |x k Let z be the likelihood function for the k-th frame. k Let x represent the measurement data of the k-th frame. k For the target state information of the k-th frame, p(x) k |x k-1 ) is the state transition density function, p(X) 1:k-1 |Z 1:k-1 Let p(z) be the posterior probability density function for the first k-1 frames. k |Z 1:k-1 Let be the state transition density function of the measurement data in the k-th frame;

[0096] Value function Value function I(X) 1:k The value function I(x) of the k-th frame in ) k The process of obtaining ) is as follows:

[0097]

[0098] Among them, X 1:K-1 Let I(x) be the set of target states for the first k-1 frames. k Let I(x) be the value function of the k-th frame. k-1 ) is the value function for the (k-1)th frame;

[0099] Take the logarithm of both sides of formula (8) and p(z) k |Z 1:k-1 By normalizing the coefficients, we obtain the value function of the dynamic programming algorithm; its expression is:

[0100]

[0101] Equation (9) describes the propagation of the value function from frame (k-1) to frame k. It is divided into two parts to realize the iterative update of the value function. One part is the log-likelihood function logp(z) k |x k One part is used to characterize the probability that the measurement area's orientation originates from a target; the other part is the transfer cost function logp(x). k |x k-1 ), used to characterize the probability of the target moving in each direction between frame k-1 and frame k;

[0102] Step 64: Based on the augmented state information x of the k-th frame k Initialize the target state, value function, and track backtracking function for the first n frames.

[0103] The other steps and parameters are the same as those in specific implementation methods one through four.

[0104] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that: in step 64, the augmented state information x based on the k-th frame... k Initialize the target state, value function, and track backtracking function for the first n frames; the expression is:

[0105]

[0106] Where k = 1, 2, ..., n, θ k Let p(z) be the azimuth angle of the k-th frame. k |x k ) is the likelihood function; This is the trajectory backtracking function.

[0107] The other steps and parameters are the same as those in specific implementation methods one through five.

[0108] Specific Implementation Method Seven: This implementation method differs from one of Specific Implementation Methods One to Six in that: in step 8, the value function obtained in step 6 is weighted by an azimuth potential function to obtain a new value function;

[0109] Based on the new value function and azimuth potential function, the trajectory backtracking function of the m-th target in the k-th frame is obtained;

[0110] The specific process is as follows:

[0111] Step 81: Based on the azimuth potential coefficients from Step 51, define the azimuth potential function μ(X). k-n:k-1 |X k-n+1:k );

[0112] Azimuth potential function μ(X) k-n:k-1 |X k-n+1:k Reflecting the set of states X k-n+1:k ={x k ,x k-1 ,x k-n+1} from the previous state set X k-n:k-1 ={x k-1 ,x k-2 ,x k-n} Probability level;

[0113] Azimuth potential function μ(X) k-n:k-1 |X k-n+1:k ) is represented as:

[0114]

[0115] Where, μ(X) k-n:k-1 |X k-n+1:k Let X be the azimuth potential function. k-n:k-1 Let X be the set of states from frame kn to k-1. k-n+1:kLet λ be the set of states from frame (k-n+1) to frame k. k Let λ be the azimuth potential coefficient of the k-th frame. k-1 The azimuth potential coefficient of the (k-1)th frame;

[0116] γ represents the variance of the Lorentz function. An appropriate γ can be selected to construct the azimuth potential function and perform value function weighting.

[0117] For value functions I(x) belonging to the same objective k+1 ) and I(x k For different targets, their state variables should have similar azimuth potential coefficients, which will result in a larger confidence value in the azimuth potential function; however, for different targets, their azimuth potential coefficients will differ greatly, resulting in a smaller confidence value in the azimuth potential function.

[0118] Step 82: For dynamic programming-based pre-detection tracking considering nearby targets, based on the likelihood function p(z) k |x k ), state transition density function p(x) k |x k-1 ) and azimuth potential function μ(X) k-n:k-1 |X k-n+1:k A new value function is obtained by adding a weighted azimuth potential function to the value function;

[0119] Based on the new value function and azimuth potential function μ(X) k-n:k-1 |X k-n+1:k ), to obtain the trajectory backtracking function of the m-th target in the k-th frame.

[0120] The other steps and parameters are the same as those in specific implementation methods one through six.

[0121] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One to Seven in that: in step 82, for dynamic programming pre-detection tracking considering nearby targets, based on the likelihood function p(z)... k |x k ), state transition density function p(x) k |x k-1 ) and azimuth potential function μ(X) k-n:k-1 |X k-n+1:k A new value function is obtained by adding a weighted azimuth potential function to the value function;

[0122] Based on the new value function and azimuth potential function μ(X) k-n:k-1 |X k-n+1:k ), obtain the trajectory backtracking function of the m-th target in the k-th frame;

[0123] The specific process is as follows:

[0124] The new value function is represented as:

[0125]

[0126] Wherein, τ(x) k p(x) represents the states that the target state can transition to within one frame. k |x k-1 Let I(x) be the state transition density function of the k-th frame. k-1 p(z) is the value function for frame k-1. k |x k ) is the likelihood function;

[0127] Based on the new value function and azimuth potential function μ(X) k-n:k-1 |X k-n+1:k ), obtain the trajectory backtracking function for the m-th target in the k-th frame, the trajectory backtracking function is expressed as:

[0128]

[0129] in, Let be the trajectory backtracking function for the m-th target in the k-th frame.

[0130] By weighting the value function and the track backtracking function using the azimuth potential function, the value function obtained for the same target will have a higher confidence level, thereby enhancing the accumulated value of the value function for that target at that location.

[0131] The other steps and parameters are the same as those in specific implementation methods one through seven.

[0132] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One through Eight in that: in step 10, the newly obtained value function is compared with the decision threshold, and targets in frames corresponding to value functions less than the decision threshold are eliminated, while targets in frames corresponding to value functions greater than or equal to the decision threshold are retained; the specific process is as follows:

[0133]

[0134] in, Λ represents the target state of the k-th frame corresponding to the value function that exceeds the threshold. T Indicates the threshold for judgment.

[0135] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0136] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One to Nine in that: in step 11, the target in the frame corresponding to the value function retained in step 10 and the trajectory backtracking function in step 8 are used for trajectory backtracking to obtain the tracking trajectory of the m-th target; the specific process is as follows:

[0137] If the value function I(x)K )≥Λ T Then for k = K-1,…,1, we have

[0138]

[0139] Where, ψ k (x k ) indicates the result of track backtracking;

[0140] If the value function I(x) K )<Λ T If so, no track retracing will be performed;

[0141] The results of track backtracking are used as target state estimation information for tracking, resulting in an estimated set of target trajectories.

[0142]

[0143] in This represents the tracking results of target state estimation information from frame 1 to frame K.

[0144] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.

[0145] Experimental Section

[0146] To verify the tracking performance of this invention in a scenario with weak underwater acoustic targets nearby, a passive 40-element uniform linear array was used as the receiving sonar. The element spacing was half a wavelength, the operating frequency band was f0 = 500Hz to 2500Hz, the signal-to-noise ratio was -25dB, and the data length was 120 frames. Three targets were set in the simulation scenario, where target 1 and target 2 were adjacent and their trajectories intersected at frame 40, while target 3 separated.

[0147] The simulated target was tracked using both APWDP-TBD (the present invention) and traditional DP-TBD algorithms. The state transition value q = 21, the resolution cell size was 0.1 degrees, and the window length of the DWDP-TBD azimuth potential coefficient was set to 2. The tracking results were compared, and the optimal submode allocation error (OSPA error) was selected as the evaluation index for the simulation.

[0148] The DP-TBD algorithm, due to its lack of consideration for target proximity, suffers from track mismatch when the tracks of target 1 and target 2 intersect, causing its OSPA error to increase after 40 frames and degrading the algorithm's tracking performance. The APWDP-TBD proposed in this invention can obtain correct tracking results even when target 1 and target 2 intersect in proximity, as well as when the trajectory of target 3 is encountered. It significantly improves the algorithm's tracking performance in target proximity scenarios and significantly reduces the OSPA error caused by track mismatch and other issues.

[0149] The examples provided in this invention are merely one instance of the calculation method and process of this invention, and are not intended to limit the implementation of the algorithm and process of this invention. For those skilled in the art, based on this invention, some embodiments that cannot be listed in this invention can be made, and these corresponding variations or modifications should still fall within the protection scope of the claims provided in this invention.

Claims

1. A dynamic programming-based underwater acoustic target tracking method for detection based on azimuth potential function weighting, characterized in that: The specific process of the method is as follows: Step 1: Beamforming is performed on the passive sonar detection signal to obtain spatial spectrum data; Using spatial spectrum data as measurement data, the azimuth observation range of each frame in the measurement data is divided into B resolution units. Step 2: Initialize the state transition number q; When the number of state transitions is q, the measurement data transitions from the k-th frame to the (k+1)-th frame, obtaining the target state information x of the (k+1)-th frame. k+1 ; Step 3: Initialize the frame number k in the measurement data to 1; Step 4: Initialize the target count m = 1; Step 5: Define the azimuth potential coefficient, and based on the azimuth potential coefficient, define augmented state information that includes the azimuth potential coefficient and target azimuth information. Step 6: Based on the measurement data from Step 1 and the target state information x from Step 2 k+1 Step 5 includes augmented state information containing azimuth potential coefficients and target azimuth information. Initialize the augmented state information of the first n frames with a window length n equal to the azimuth potential coefficient. We obtain the value function and the track backtracking function; Step 7: Determine if k > n. If yes, proceed to step 8; otherwise, set k = k + 1 and repeat steps 6 to 7. Step 8: Add a weighted azimuth potential function to the value function obtained in Step 6 to obtain a new value function; Based on the new value function and azimuth potential function, the trajectory backtracking function of the m-th target in the k-th frame is obtained; Step 9: Determine if k = K. If yes, proceed to step 10. If no, set k = k + 1 and repeat steps 8 to 9. K represents the total number of frames in the measurement data; Step 10: Compare the obtained new value function with the decision threshold, remove the targets in the frames corresponding to the value functions that are less than the decision threshold, and keep the targets in the frames corresponding to the value functions that are greater than or equal to the decision threshold. Step 11: Based on the target of the frame corresponding to the value function retained in Step 10 and the trajectory backtracking function in Step 8, perform trajectory backtracking to obtain the tracking trajectory of the m-th target; Step 12: Determine if m = M. If so, obtain the tracking trajectories of M targets. If not, let m = m + 1, and repeat steps 8 to 12 until m = M, to obtain M target tracking trajectories; In step 5, an azimuth potential coefficient is defined, and based on the azimuth potential coefficient, augmented state information containing the azimuth potential coefficient and target azimuth information is defined. The specific process is as follows: Step 51, Definition The azimuth potential coefficient of the m-th target in the k-th frame is represented as: Where n is the window length of the azimuth potential coefficient, m is the target count, and ω i Let θ be the weight of the i-th frame. i For the orientation information of the i-th frame, θ i-1 This refers to the orientation information of the (i-1)th frame; Step 52: Based on the azimuth potential coefficient of the m-th target in the k-th frame. Define the augmented state information of the m-th target in the k-th frame, which includes the azimuth potential coefficient and the target's azimuth information; expressed as: in, This indicates the target location information of the m-th target in the k-th frame; This represents the augmented state information of the m-th target in the k-th frame.

2. The underwater acoustic target dynamic programming pre-detection tracking method based on azimuth potential function weighting as described in claim 1, characterized in that: In step 1, beamforming is performed on the passive sonar detection signal to obtain spatial spectrum data; Using spatial spectrum data as measurement data, the azimuth observation range of each frame in the measurement data is divided into B resolution units. The specific process is as follows: Step 11: Initialize the number of linear array elements, element spacing, sampling frequency, sound velocity, and number of frames; Step 12: Beamforming is performed on the passive sonar detection signal to obtain spatial spectrum data; Step 13: Use the spatial spectrum data as measurement data, denoted as Z. 1:K ={z1,z2,...,z k ,...,z K }; Among them, Z 1:K Let z1 be the first frame of the measurement data, z2 be the second frame of the measurement data, and z... k For the k-th frame in the measurement data, z K The Kth frame in the measurement data is K, where K is the total number of frames in the measurement data. Step 14: Divide the azimuth observation range of each frame in the measurement data into B resolution units, and the size of each resolution unit is Δθ. Use z k (b) represents the measurement data amplitude at the b-th resolution unit of the k-th frame. The measurement data amplitudes in all resolution units are independent and identically distributed, and b = 1, 2, ..., B. z k (b) is represented as: Where, ω k (b) represents the noise amplitude of the b-th resolution unit in the k-th frame, A k (b) represents the target signal amplitude of the b-th resolution unit in the k-th frame.

3. The underwater acoustic target dynamic programming pre-detection tracking method based on azimuth potential function weighting as described in claim 2, characterized in that: In step 2, the state transition number q is initialized; When the number of state transitions is q, the measurement data transitions from the k-th frame to the (k+1)-th frame, obtaining the target state information x of the (k+1)-th frame. k+1 The specific process is as follows: Initialize the state transition number q; When the state transition number is q, the measurement data transitions from the k-th frame to the (k+1)-th frame, and the target state information x in the (k+1)-th frame... k+1 for: Where, θ k Here is the orientation information for the k-th frame, Δθ is the size of the resolution cell, and δ... q x represents the state transition range when the number of state transitions is q; k+1 This represents the target state information in the (k+1)th frame.

4. The underwater acoustic target dynamic programming pre-detection tracking method based on azimuth potential function weighting as described in claim 3, characterized in that: In step 6, the measurement data from step 1 and the target state information x from step 2 are used as the basis for the measurement data from step 1. k+1 Step 5 includes augmented state information containing azimuth potential coefficients and target azimuth information. Initialize the augmented state information of the first n frames with a window length n equal to the azimuth potential coefficient. We obtain the value function and the track backtracking function; The specific process is as follows: Step 61: Express the target's state transition equation and measurement equation as follows: Among them, f k-1 (·) represents the state transition function, h k (·) represents the measurement function, x k Represents the augmentation state information of the k-th frame, x k-1 w represents the augmentation state information of the (k-1)th frame. k Represents state transition noise, v k This represents measurement noise, all of which follow a Gaussian distribution, z. k This represents the measurement data for the k-th frame; Step 62: The target sequence with the highest posterior probability Right now: in, This is the augmented state information of the target with the highest posterior probability in the first frame. This is the augmented state information of the target with the highest posterior probability density in the second frame. This represents the augmented state information of the target with the highest posterior probability in the k-th frame. Let be the set of target states with the highest posterior probability in the first k frames. Let p(X) be the maximum a posteriori probability density function. 1:k |Z 1:k ) is the posterior probability density function; Step 63: Perform a Bayesian transform on equation (6) from step 62, and obtain: Where p(X) 1:k |Z 1:k Let X be the posterior probability density function of the first k frames. 1:k Z represents the set of target states for the previous k frames. 1:k For the measurement data set, p(z) k |x k Let z be the likelihood function for the k-th frame. k Let x represent the measurement data of the k-th frame. k For the target state information of the k-th frame, p(x) k |x k-1 ) is the state transition density function, p(X) 1:k-1 |Z 1:k-1 Let p(z) be the posterior probability density function for the first k-1 frames. k |Z 1:k-1 Let be the state transition density function of the measurement data in the k-th frame; Value function Value function I(X) 1:k The value function I(x) of the k-th frame in ) k The process of obtaining ) is as follows: Among them, X 1:K-1 Let I(x) be the set of target states for the first k-1 frames. k Let I(x) be the value function of the k-th frame. k-1 ) is the value function for the (k-1)th frame; Take the logarithm of both sides of formula (8) and p(z) k |Z 1:k-1 Normalizing the coefficients yields the value function; its expression is: Step 64: Based on the augmented state information x of the k-th frame k Initialize the target state, value function, and track backtracking function for the first n frames.

5. The underwater acoustic target dynamic programming pre-detection tracking method based on azimuth potential function weighting as described in claim 4, characterized in that: In step 64, the augmented state information x based on the k-th frame... k Initialize the target state, value function, and track backtracking function for the first n frames; the expression is: Where k = 1, 2, ..., n, θ k Let p(z) be the azimuth angle of the k-th frame. k |x k ) is the likelihood function; ψ xk This is the trajectory backtracking function.

6. The underwater acoustic target dynamic programming pre-detection tracking method based on azimuth potential function weighting as described in claim 5, characterized in that: In step 8, the value function obtained in step 6 is weighted by the azimuth potential function to obtain a new value function; Based on the new value function and azimuth potential function, the trajectory backtracking function of the m-th target in the k-th frame is obtained; The specific process is as follows: Step 81: Based on the azimuth potential coefficients from Step 51, define the azimuth potential function μ(X). k-n:k-1 |X k-n+1:k ); Azimuth potential function μ(X) k-n:k-1 |X k-n+1:k ) is represented as: Where, μ(X) k-n:k-1 |X k-n+1:k Let X be the azimuth potential function. k-n:k-1 Let X be the set of states from frame kn to k-1. k-n+1:k Let λ be the set of states from frame (k-n+1) to frame k. k Let λ be the azimuth potential coefficient of the k-th frame. k-1 The azimuth potential coefficient of the (k-1)th frame; γ represents the magnitude of the variance of the Lorentz function; Step 82: Based on the likelihood function p(z) k |x k ), state transition density function p(x) k |x k-1 ) and azimuth potential function μ(X) k-n:k-1 |X k-n+1:k A new value function is obtained by adding a weighted azimuth potential function to the value function; Based on the new value function and azimuth potential function μ(X) k-n:k-1 |X k-n+1:k ), to obtain the trajectory backtracking function of the m-th target in the k-th frame.

7. The underwater acoustic target dynamic programming pre-detection tracking method based on azimuth potential function weighting as described in claim 6, characterized in that: In step 82, the likelihood function p(z) is used as the basis. k |x k ), state transition density function p(x) k |x k-1 ) and azimuth potential function μ(X) k-n:k-1 |X k-n+1:k A new value function is obtained by adding a weighted azimuth potential function to the value function; Based on the new value function and azimuth potential function μ(X) k-n:k-1 |X k-n+1:k ), obtain the trajectory backtracking function of the m-th target in the k-th frame; The specific process is as follows: The new value function is represented as: Wherein, τ(x) k p(x) represents the states that the target state can transition to within one frame. k |x k-1 Let I(x) be the state transition density function of the k-th frame. k-1 p(z) is the value function for frame k-1. k |x k ) is the likelihood function; Based on the new value function and azimuth potential function μ(X) k-n:k-1 |X k-n+1:k ), obtain the trajectory backtracking function for the m-th target in the k-th frame, the trajectory backtracking function is expressed as: in, Let be the trajectory backtracking function for the m-th target in the k-th frame.

8. The underwater acoustic target dynamic programming pre-detection tracking method based on azimuth potential function weighting as described in claim 7, characterized in that: In step 10, the newly obtained value function is compared with the decision threshold. Targets in frames with value functions less than the decision threshold are removed, while targets in frames with value functions greater than or equal to the decision threshold are retained. The specific process is as follows: in, Λ represents the target state of the k-th frame corresponding to the value function that exceeds the threshold. T Indicates the threshold for judgment.

9. The underwater acoustic target dynamic programming pre-detection tracking method based on azimuth potential function weighting as described in claim 8, characterized in that: In step 11, the target in the frame corresponding to the value function retained in step 10 and the trajectory backtracking function in step 8 are used for trajectory backtracking to obtain the tracking trajectory of the m-th target; the specific process is as follows: If the value function I(x) K )≥Λ T Then for k = K-1,…,1, we have Where, ψ k (x k ) indicates the result of track backtracking; If the value function I(x) K )<Λ T If so, no track retracing will be performed; The results of track backtracking are used as target state estimation information for tracking, resulting in an estimated set of target trajectories. in This represents the tracking results of target state estimation information from frame 1 to frame K.

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