A robust parameterized spatiotemporal adaptive pre-detection tracking method

Abstract

This invention discloses a robust parameterized spatiotemporal adaptive pre-detection tracking method, comprising: receiving echo data acquired by a uniform sonar linear array; representing the reverberation signals in the data of the target unit and the auxiliary unit using a MAR model based on a binary hypothesis test and a parameterized method; obtaining the joint probability density function under the two hypotheses according to the MAR model representation; obtaining the detection statistic of parameterized RAO according to the RAO criterion; using the detection statistic as a value function for dynamic programming iteration and optimization to obtain the cumulative maximum value function of parameterized RAO-DP-TBD; comparing the final cumulative maximum value function of parameterized RAO-DP-TBD with a detection threshold; if it does not meet the requirements, the target to be detected does not exist; otherwise, the target exists, and the maximum value function of the last frame is used to achieve trajectory backtracking and estimate the trajectory of the target.

Description

Technical Field

[0001] This invention belongs to the field of active sonar detection technology, and particularly relates to a robust parameterized spatiotemporal adaptive pre-detection tracking method. Background Technology

[0002] In complex shallow-sea hydrological environments, reverberation severely impacts the detection performance of active sonar. Especially when the sonar carrier moves at a certain speed, reverberation occurs from different cone angles, causing a significant expansion of its power spectrum in the two-dimensional space-time plane, exhibiting space-time coupling characteristics. Currently, underwater targets, represented by underwater vehicles, are characterized by low target strength, low speed, and high stealth, making them easily submerged in reverberation, posing new challenges to active sonar target detection. To address this problem, an effective solution is to employ an underwater monopulse space-time adaptive detection-before-tracking algorithm based on dynamic programming (STAD-DP-TBD). This algorithm improves the signal-to-mixing ratio of the received active sonar signal by effectively suppressing reverberation in the space-time domain and accumulating the target signal across multiple frames in the time domain, thereby achieving reliable detection of low-speed, weak targets.

[0003] Due to the complex and variable underwater environment, especially in shallow waters, it is difficult to obtain sufficient independent and identically distributed auxiliary data. This leads to a significant decrease in the estimation performance of the reverberation covariance matrix by the STAD-DP-TBD algorithm, thus greatly affecting its detection performance. According to the RMB criterion, to ensure that the algorithm's detection loss does not exceed 3dB, the number of auxiliary data points must be at least twice the system's spatiotemporal dimension. Insufficient auxiliary data will cause inaccurate covariance matrix estimation, thereby affecting the algorithm's accuracy.

[0004] Existing spatiotemporal adaptive pre-detection tracking methods based on dual knowledge bases exhibit good detection and tracking performance when the amount of auxiliary data is greater than or equal to 1 / 2 of the spatiotemporal dimension. They can function normally when the amount of auxiliary data is between 1 / 4 and 1 / 2 of the system's spatiotemporal dimension. However, their detection and tracking performance deteriorates significantly as the amount of auxiliary data decreases, and they fail to function normally when the amount of auxiliary data is less than 1 / 4 of the spatiotemporal dimension. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and to propose a robust parameterized spatiotemporal adaptive pre-detection tracking method.

[0006] To achieve the above objectives, this invention proposes a robust parameterized spatiotemporal adaptive pre-detection tracking method, the method comprising:

[0007] Step 1) Receive the echo data collected by the uniform sonar line array, and use the parameterization method to represent the reverberation signal in the data of the unit to be detected and the auxiliary unit data using the MAR model based on the binary hypothesis test.

[0008] Step 2) Based on the MAR model representation, obtain the joint probability density function under the two assumptions respectively;

[0009] Step 3) Based on the RAO criterion, obtain the detection statistics of parameterized RAO;

[0010] Step 4) Use the detection statistic as the value function to perform dynamic programming iteration and optimization to obtain the cumulative maximum value function of parameterized RAO-DP-TBD.

[0011] Step 5) Compare the maximum value function of the parameterized RAO-DP-TBD accumulated in Step 4) with the detection threshold. If it does not meet the requirements, the target to be detected does not exist; otherwise, the target exists. Then, use the maximum value function of the last frame to backtrack the trajectory and estimate the trajectory of the target.

[0012] Preferably, the uniform sonar linear array in step 1) has N sonar array elements, M sampling points in each range unit, and L range units. Each time the uniform sonar linear array emits a single pulse signal, it obtains MN×L dimensional spacetime data as one frame of echo data. Emitting K single pulse signals yields K frames of echo data.

[0013] Preferably, step 1) is based on binary hypothesis testing, using a parametric method to represent the reverberation signals in the data of the unit to be detected and the auxiliary unit data using a MAR model; including:

[0014] For the k-th frame of echo data, based on the binary hypothesis test, H0 and H1 represent the no-target-signal hypothesis and the target-signal hypothesis, respectively, satisfying the following equation:

[0015]

[0016] Where z represents the data of the unit to be detected; z l For auxiliary unit data; α is the unknown signal amplitude, v is the signal space-time steering vector; K s Indicates the number of auxiliary distance units; n and n l , are independent and identically distributed complex Gaussian vectors with mean 0 and covariance matrix R, respectively, and are the reverberation signals in the data of the unit to be detected and the reverberation signals in the auxiliary data unit;

[0017] The reverberation signal n is obtained by using a parameterization method. l (m) is represented using the MAR model:

[0018]

[0019] in, Denotes the -P order MAR coefficient matrix. Let A represent an N-dimensional complex number, P represent the total order, and A represent the total number of orders.H (p) represents the p-th order MAR coefficient matrix, where p = 1, ..., P. k l (m) represents a multi-channel Gaussian process that is whitened in the time domain and colored in the spatial domain. It is described as a complex Gaussian random vector with a mean of 0 and a covariance matrix of Q, where m = 1, ..., M; m represents the m-th sampling point.

[0020] The data of the unit to be detected z and the auxiliary unit data z l The reverberation signal n in the data of the unit to be detected, and the reverberation signal n in the auxiliary data unit. l The space-time steering vector v of the signal can be written in the following form:

[0021] z = [z T (1),z T (2),...,z T (M)] T

[0022]

[0023] n = [n T (1),n T (2),...,n T (M)] T

[0024]

[0025] v = [v T (1),v T (2),...,v T (M)] T

[0026] The binary hypothesis testing problem can then be rewritten in the following form:

[0027]

[0028] Preferably, step 2) includes:

[0029] The data of the unit to be detected z and the data of the auxiliary unit z l The reverberation signal in the image is modeled as a P-order MAR process, and z and z are obtained respectively. l The joint probability density function under the H1 hypothesis and the joint probability density function under the H0 hypothesis

[0030]

[0031] Preferably, in step 3), the detection statistic λ of RAO is parameterized. PR-RAO for:

[0032]

[0033] Where, η PR-RAO This represents the detection threshold of the parameterized RAO. This represents the spacetime steering vector after whitening in the time domain. The time-domain whitened data to be detected satisfies the following formulas:

[0034]

[0035] Preferably, the cumulative maximum value function of the parameterized RAO-DP-TBD in step 4) satisfies the following equation:

[0036]

[0037] Where D={(l1,v1),...,(l K ,v K )} represents the distance-Doppler position of the target location in the distance-Doppler plane. This represents the space-time steering vector after temporal whitening during the k-th scan. This represents the maximum likelihood estimate of Q during the k-th scan. η represents the time-domain whitened data to be detected after the k-th scan. PR-RAO-DT-M This represents the detection threshold of parameterized RAO-DP-TBD.

[0038] Compared with the prior art, the advantages of the present invention are:

[0039] This invention provides a robust spatiotemporal adaptive pre-detection tracking method based on a parameterized model. It utilizes the MAR model to parameterize the reverberation in the target data and auxiliary data, transforming the problem of estimating the reverberation covariance matrix into estimating the MAR coefficient matrix and the spatial covariance matrix of the MAR model-driven noise. This reduces the number of unknown parameters and the dependence on auxiliary data, and can solve the problem of decreased target detection performance under small sample data conditions, effectively improving the active sonar detection capability. Attached Figure Description

[0040] Figure 1 It is K s The detection probability curves of the PR-RAO-DP-TBD method of the present invention and the prior art PS-RAO-DP-TBD method at a value of 45;

[0041] Figure 2 It is K s Accuracy tracking probability curves of the PR-RAO-DP-TBD method of the present invention and the prior art PS-RAO-DP-TBD method at a value of 45;

[0042] Figure 3 It is K s The detection probability curves of the PR-RAO-DP-TBD method of the present invention and the prior art PR-RAO-DP-TBD method when the value is 23;

[0043] Figure 4 It is K s Accuracy tracking probability curves of the PR-RAO-DP-TBD method of the present invention and the prior art PS-RAO-DP-TBD method when the accuracy is 23;

[0044] Figure 5 It is K s The detection probability curves of the PR-RAO-DP-TBD method of the present invention and the prior art PR-RAO-DP-TBD method when the value is 12;

[0045] Figure 6 It is K s Accuracy tracking probability curves of the PR-RAO-DP-TBD method of the present invention and the prior art PS-RAO-DP-TBD method when the value is 12. Detailed Implementation

[0046] Reverberation typically exhibits spatiotemporal correlation. When auxiliary data is insufficient to accurately estimate the reverberation covariance matrix, this correlation can be characterized using a parametric model. This invention aims to improve the robustness of the algorithm through reverberation parametric modeling. Therefore, how to improve the robustness of the underwater monopulse spatiotemporal adaptive pre-detection tracking method under limited auxiliary data is the core issue of this invention.

[0047] To address this issue and improve the robustness of the algorithm, this invention provides a spatiotemporal adaptive pre-detection tracking method based on a parameterized model. It utilizes a multi-channel autoregressive (MAR) model to parameterize the reverberation, transforming the estimation problem of the reverberation covariance matrix into the estimation problem of the MAR coefficient matrix and the spatial covariance matrix of the driving noise. This reduces the number of unknown parameters and effectively characterizes the spatiotemporal correlation of reverberation, thereby reducing the need for auxiliary data and improving the robustness of the STAD-DP-TBD algorithm under conditions of limited auxiliary data.

[0048] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0049] Example

[0050] The embodiments of the present invention propose a spatiotemporal adaptive pre-detection tracking method based on a parameterized model.

[0051] 1. Problem Modeling

[0052] Assume the active sonar receiver array is a uniform linear array with N elements and an element spacing of d. The transmitted pulse width is T. p L distance units, sampling frequency f s Then the number of sampling points in each distance unit is M = T p f s A sonar system transmits a single pulse signal to obtain MN×L dimensional space-time data, called one frame of data. Transmitting K single pulse signals, i.e., scanning the detection area K times, yields K frames of echo data. During the k-th scan of the l-th range cell, MN sampled data points are obtained, which together form an observation vector z. lk The detection problem under uniform reverberation background can be expressed as the following binary hypothesis test:

[0053]

[0054] Where H0 and H1 represent the hypotheses of no objective and having an objective, respectively; n lk ~CN(0,R k It follows a zero-mean, covariance matrix of R k The complex Gaussian distribution, α k Let l be the amplitude of the target signal during the k-th scan. k For the k-th scan, the distance cell containing the target is... Let s be the spacetime guiding vector, where s tk (v dk ) is the spatial guiding vector, s sk (v sk ) is the time-domain steering vector.

[0055] To simplify the analysis, we will analyze one frame of data from equation (1). For the k-th frame of data, the binary hypothesis test problem can be written in the following form:

[0056]

[0057] Where z represents the data of the unit to be detected; z l For auxiliary unit data; α is the unknown signal amplitude, which is a definite parameter; v is the signal space-time steering vector; K s Indicates the number of auxiliary distance units; n and n l Let be an independent and identically distributed complex Gaussian vector with mean 0 and covariance matrix R.

[0058] The parameterization method represents the reverberant signal received by the uniform linear array using a MAR model.

[0059]

[0060] in, Let κ represent the P-order MAR coefficient matrix. l (m) represents a multi-channel Gaussian process that whitens in the time domain and colors in the spatial domain, described as a complex Gaussian random vector with a mean of 0 and a covariance matrix of Q, where m = 1, ..., M; l = 1, ..., K s ;K s This represents the number of auxiliary distance units.

[0061] In equation (2), the data to be detected z and the auxiliary data z l The reverberation signal n in the data to be detected, and the reverberation signal n in the auxiliary data unit. l The spacetime steering vector v can be written in the following form

[0062] z = [z T (1),z T (2),...,z T (M)] T (4)

[0063]

[0064] n = [n T (1),n T (2),...,n T (M)] T (6)

[0065]

[0066] v = [v T (1),v T (2),...,v T (M)] T (8)

[0067] The binary hypothesis testing problem can then be rewritten as shown in the following equation.

[0068]

[0069] The detection data z and auxiliary data z in equation (9) l If the reverberation signal in the middle is modeled as a P-order MAR process according to equation (3), then we have

[0070]

[0071] Where, under the H0 assumption, α = 0, and under the H1 assumption, α ≠ 0. make

[0072]

[0073] but

[0074]

[0075] Data to be detected z and auxiliary data z l ,l=1,2,…K s The joint probability density function under the H1 assumption is:

[0076]

[0077] in

[0078]

[0079] here, κ l (m) is obtained from equation (14).

[0080] The probability density function under the H0 hypothesis is:

[0081]

[0082] in

[0083]

[0084] here,

[0085] 2. Algorithm Design

[0086] For the binary hypothesis test after transformation, a parameterized RAO-DP-TBD method is proposed under uniform reverberation background based on the RAO criterion, denoted as PR-RAO-DP-TBD.

[0087] In the binary hypothesis testing problem shown in equation (9), the target parameter vector θ to be estimated is... r =[α r ,α i ] T The redundant parameter vector θ s Includes unknown parameter A H And Q, can be written as Where a r =vec(Re(A H )), a i =vec(Im(A H )), q r The real part of q includes the elements diagonally opposite to Q and the elements below the diagonal. r It includes the imaginary part of the elements below the Q diagonal.

[0088] According to the RAO criterion shown in equation (19),

[0089]

[0090] Need to know Where θ r,0 =[0,0] T Therefore, the problem focuses on solving θ. s Maximum likelihood estimation under the H0 assumption And the Fisher information matrix of the first derivative of the log-likelihood function and the parameters under maximum likelihood estimation.

[0091] A can be obtained H Maximum likelihood estimation of Q

[0092]

[0093] in,

[0094]

[0095] t(m)=[v T (m-1),v T (m-2),...,v T (mP)] T (27)

[0096] The first derivative of the log-likelihood function under maximum likelihood estimation is:

[0097]

[0098] in, This represents the spacetime steering vector after whitening in the time domain. The time-domain whitened data to be detected is represented as

[0099]

[0100] Seek

[0101]

[0102] Under the assumption of H0, maximum likelihood estimation is performed on the coefficient matrix of the unknown MAR model using both primary and secondary data to obtain the detection statistic of the parameterized RAO (denoted as PR-RAO).

[0103]

[0104] Where, η PR-RAO This indicates the detection threshold for PR-RAO.

[0105] In the first scan, the detection statistic λ(l1,v1) of PR-RAO is assigned to the value function I(l1,v1) of the first scan; when 2≤k≤K, the value function is accumulated according to the following formula.

[0106]

[0107] Among them, I(l) k ,v k ) is the cumulative value function for the k-th scan, λ(l) k ,v k ) represents the detection statistic of PR-RAO in the k-th scan, (l k ,v k () represents the distance-Doppler position of the target in the k-th scan. The cumulative value function of PR-RAO-DP-TBD is obtained as follows:

[0108]

[0109] Where D={(l1,v1),...,(l K ,v K )} represents the distance-Doppler position of the target location in the distance-Doppler plane. This represents the space-time steering vector after temporal whitening during the k-th scan. This represents the maximum likelihood estimate of Q during the k-th scan. η represents the time-domain whitened data to be detected after the k-th scan. PR-RAO-DP-TBD This represents the detection threshold of the PR-RAO-DP-TBD algorithm.

[0110] The target detection result is obtained by comparing the final accumulated maximum value function with the threshold using equation (35), and then the trajectory is estimated by using the maximum value function of the last frame.

[0111] 3. Performance Analysis

[0112] Simulation parameter settings: number of array elements N = 3, number of sampling points per pulse M = 20, spatiotemporal dimension MN = 60, number of scans K = 6. To verify the performance of the proposed algorithm, scenarios with insufficient auxiliary data are divided into the following three scenarios: Scenario 1: Scene 2: Where [·] represents rounding; Scenario 3: The detection and tracking performance of the PR-RAO-DP-TBD algorithm is analyzed in three scenarios, and its performance is compared with that of the dual knowledge base RAO-DP-TBD algorithm (denoted as PS-RAO-DP-TBD).

[0113] Figure 1 and Figure 2 K sThe detection probability and accurate tracking probability curves of the PR-RAO-DP-TBD method and the PS-RAO-DP-TBD method are shown at a value of 45. The simulation results show that both PR-RAO-DP-TBD and PS-RAO-DP-TBD work normally, with PR-RAO-DP-TBD exhibiting better detection and tracking performance. Figure 3 and Figure 4 K s The detection probability and accurate tracking probability curves of the PR-RAO-DP-TBD method and the PS-RAO-DP-TBD method are shown at time 23. The simulation results show that both the PR-RAO-DP-TBD and PS-RAO-DP-TBD methods function normally, but the detection and tracking performance of the PS-RAO-DP-TBD method deteriorates significantly, while the PR-RAO-DP-TBD method shows slightly better detection and tracking performance. Figure 5 and Figure 6 K s The detection probability and accurate tracking probability curves of the PR-RAO-DP-TBD method are shown when the number of auxiliary data points is less than the spatiotemporal dimension. At this time, the PS-RAO-DP-TBD method cannot work properly because the amount of auxiliary data is less than the spatiotemporal dimension, while the PR-RAO-DP-TBD method still has good detection and tracking performance.

[0114] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A robust parameterized spatiotemporal adaptive pre-detection tracking method, the method comprising: Step 1) Receive the echo data collected by the uniform sonar line array, and use the parameterization method to represent the reverberation signal in the data of the unit to be detected and the auxiliary unit data using the MAR model based on the binary hypothesis test. Step 2) Based on the MAR model representation, obtain the joint probability density function under the two assumptions respectively; Step 3) Based on the RAO criterion, obtain the detection statistics of parameterized RAO; Step 4) Use the detection statistic as the value function to perform dynamic programming iteration and optimization to obtain the cumulative maximum value function of parameterized RAO-DP-TBD; Step 5) Compare the maximum value function of the parameterized RAO-DP-TBD accumulated in Step 4) with the detection threshold. If it does not meet the requirements, the target to be detected does not exist; otherwise, the target exists. Then, use the maximum value function of the last frame to backtrack the trajectory and estimate the trajectory of the target.

2. The robust parameterized spatiotemporal adaptive pre-detection tracking method according to claim 1, characterized in that, The uniform sonar line array in step 1) has N sonar array elements, M sampling points in each range unit, and L range units. Each time the uniform sonar line array emits a single pulse signal, it obtains MN×L dimensional space-time data as one frame of echo data. Emitting K single pulse signals yields K frames of echo data.

3. The robust parameterized spatiotemporal adaptive pre-detection tracking method according to claim 2, characterized in that, Step 1) Based on the binary hypothesis test, the reverberation signal in the data of the unit to be detected and the data of the auxiliary unit is represented by the MAR model using a parameterization method; include: For the k-th frame of echo data, based on the binary hypothesis test, H0 and H1 represent the no-target-signal hypothesis and the target-signal hypothesis, respectively, satisfying the following equation: Where z represents the data of the unit to be detected; z l For auxiliary unit data; α is the unknown signal amplitude, v is the signal space-time steering vector; K s Indicates the number of auxiliary distance units; n and n l , are independent and identically distributed complex Gaussian vectors with mean 0 and covariance matrix R, respectively, and are the reverberation signals in the data of the unit to be detected and the reverberation signals in the auxiliary data unit; The reverberation signal n is obtained by using a parameterization method. l (m) is represented using the MAR model: in, Denotes the P-order MAR coefficient matrix. Let A represent an N-dimensional complex number, P represent the total order, and A represent the total number of orders. H (p) represents the p-th order MAR coefficient matrix, where p = 1, ..., P. κ l (m) represents a multi-channel Gaussian process that is whitened in the time domain and colored in the spatial domain. It is described as a complex Gaussian random vector with a mean of 0 and a covariance matrix of Q, where m = 1, ..., M; m represents the m-th sampling point. The data of the unit to be detected z and the auxiliary unit data z l The reverberation signal n in the data of the unit to be detected, and the reverberation signal n in the auxiliary data unit. l The space-time steering vector v of the signal can be written in the following form: z=[z T (1),with T (2),...,with T (M)] T n=[n T (1),n T (2),...,n T (M)] T v=[v T (1),v T (2),...,v T (M)] T The binary hypothesis testing problem can then be rewritten in the following form:

4. The robust parameterized spatiotemporal adaptive pre-detection tracking method according to claim 3, characterized in that, Step 2) includes: The data of the unit to be detected z and the data of the auxiliary unit z l The reverberation signal in the image is modeled as a P-order MAR process, and z and z are obtained respectively. l The joint probability density function under the H1 hypothesis and the joint probability density function under the H0 hypothesis 5. The robust parameterized spatiotemporal adaptive pre-detection tracking method according to claim 4, characterized in that, Step 3) parameterizes the detection statistic λ of RAO. PR-RAO for: Where, η PR-RAO This represents the detection threshold of the parameterized RAO. This represents the spacetime steering vector after whitening in the time domain. The time-domain whitened data to be detected satisfies the following formulas:

6. The robust parameterized spatiotemporal adaptive pre-detection tracking method according to claim 3, characterized in that, The cumulative maximum value function of the parameterized RAO-DP-TBD in step 4) satisfies the following equation: Where D={(l1,v1),...,(l K ,v K )} represents the distance-Doppler position of the target location in the distance-Doppler plane. This represents the space-time steering vector after temporal whitening during the k-th scan. This represents the maximum likelihood estimate of Q during the k-th scan. η represents the time-domain whitened data to be detected after the k-th scan. PR-RAO-DP-TBD This represents the detection threshold of parameterized RAO-DP-TBD.

Images