Robust parameterized space-time adaptive track-before-detect method

Abstract

The invention discloses a robust parameterized space-time adaptive track-before-detect method, which comprises the following steps of: receiving echo data acquired by a uniform sonar linear array, and representing reverberation signals in to-be-detected unit data and auxiliary unit data by using an MAR model by adopting a parameterization method based on binary hypothesis testing; respectively obtaining joint probability density functions under the two assumptions according to MAR model representation; obtaining detection statistics of parameterized RAO according to an RAO criterion; performing dynamic programming iteration and optimization by using the detection statistics as a value function to obtain a cumulative maximum function of the parameterized RAO-DP-TBD; comparing the finally accumulated maximum value function of the parameterized RAO-DP-TBD with a detection threshold, and if the maximum value function does not meet the requirement, determining that the target to be detected does not exist; otherwise, the target exists, track backtracking is achieved through the maximum value function of the last frame, and the track of the target is obtained through estimation.

Description

Technical Field

[0001] The invention belongs to the technical field of active sonar detection, and in particular relates to a robust parameterized space-time adaptive tracking-before-detection method. Background Art

[0002] In the complex hydrological environment of shallow waters, reverberation seriously affects the detection performance of active sonar. Especially when the sonar carrier has a certain speed, the reverberation will be incident from different cone angles, causing its power spectrum to expand significantly in the two-dimensional space-time plane, showing the space-time coupling characteristics. At present, underwater targets represented by underwater vehicles have the characteristics of small target intensity, low speed, and strong concealment. They are easily submerged in reverberation, which brings new challenges to active sonar target detection. To address this problem, an effective solution is to adopt an underwater single pulse space-time adaptive detection-before-tracking algorithm (STAD-DP-TBD) based on dynamic programming. By effectively suppressing reverberation in the space-time domain and accumulating multiple frames of target signals in the time domain, the signal-to-mixing ratio of the active sonar receiving signal can be improved, thereby achieving reliable detection of low-speed weak targets.

[0003] Due to the complexity and changeability of the underwater environment, especially in the shallow sea environment, it is difficult to obtain sufficient independent and identically distributed auxiliary data, resulting in a significant decrease in the estimation performance of the reverberation covariance matrix of the STAD-DP-TBD algorithm, which greatly affects the detection performance. According to the RMB criterion, in order to ensure that the algorithm detection loss does not exceed 3dB, the number of auxiliary data is required to be no less than twice the space-time dimension of the system. Insufficient auxiliary data will cause inaccurate estimation of the covariance matrix, thereby affecting the accuracy of the algorithm.

[0004] The existing space-time adaptive detection-before-tracking method based on dual knowledge base has good detection and tracking performance when the number of auxiliary data is greater than or equal to 1 / 2 of the space-time dimension, and can work normally when the number of auxiliary data is between 1 / 4 of the system space-time dimension and 1 / 2 of the system space-time dimension. However, as the number of auxiliary data decreases, its detection and tracking performance decreases significantly, and it cannot work normally when the number of auxiliary data is less than 1 / 4 of the space-time dimension. Summary of the invention

[0005] The purpose of the present invention is to overcome the defects of the prior art and propose a robust parameterized space-time adaptive tracking-before-detection method.

[0006] In order to achieve the above object, the present invention proposes a robust parameterized space-time adaptive tracking-before-detection method, the method comprising:

[0007] Step 1) receiving echo data collected by a uniform sonar line array, and based on a binary hypothesis test, using a parameterized method to represent the reverberation signal in the unit data to be detected and the auxiliary unit data using a MAR model;

[0008] Step 2) According to the MAR model representation, the joint probability density functions under the two assumptions are obtained respectively;

[0009] Step 3) according to the RAO criterion, obtain the detection statistic of the 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 function of parameterized RAO-DP-TBD

[0011] Step 5) Compare the maximum value function of the parameterized RAO-DP-TBD finally 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, and the maximum value function of the last frame is used to realize trajectory backtracking and estimate the trajectory of the target.

[0012] Preferably, the number of sonar array elements of the uniform sonar line array in step 1) is N, the number of sampling points in each distance unit is M, and there are L distance units. Each time the uniform sonar line array transmits a single pulse signal, MN×L-dimensional space-time data is obtained as a frame of echo data, and K frames of echo data are obtained by transmitting K single pulse signals.

[0013] Preferably, the step 1) is based on a binary hypothesis test and uses a parameterized method to represent the reverberation signal in the unit data to be detected and the auxiliary unit data using a MAR model; comprising:

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

[0015]

[0016] Among them, z is the unit data to be detected; z l is the 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 a mean of 0 and a covariance matrix of R, which are the reverberation signal in the unit data to be detected and the reverberation signal in the auxiliary data unit respectively;

[0017] The reverberation signal n is parametrically transformed l (m) is expressed by the MAR model:

[0018]

[0019] in, represents the P-order MAR coefficient matrix, represents an N-dimensional complex number, P represents the total order, AH (p) represents the p-th order MAR coefficient matrix, p = 1, ..., P, k l (m) represents a multi-channel Gaussian process with whitening in time domain and coloring in space domain, which is described as a complex Gaussian random vector with mean 0 and covariance matrix Q, m = 1, ..., M; m represents the mth sampling point;

[0020] The unit data z to be detected and the auxiliary unit data z l , the reverberation signal n in the unit data to be detected, the reverberation signal n in the auxiliary data unit l The sum signal space-time steering vector v is written as follows:

[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] Then the binary hypothesis testing problem can be rewritten as follows:

[0027]

[0028] Preferably, the step 2) comprises:

[0029] The unit data z to be detected and the auxiliary unit data z l The reverberation signal in 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, the step 3) parameterizes the detection statistic λ of RAO PR-RAO for:

[0032]

[0033] Among them, η PR-RAO represents the detection threshold of parameterized RAO, represents the space-time steering vector after whitening in the time domain, Represents the data to be detected after time domain whitening, which satisfies the following formulas:

[0034]

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

[0036]

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

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

[0039] The present invention provides a robust space-time adaptive pre-detection tracking method based on a parameterized model. The MAR model is used to perform parameterized modeling on the reverberation in the data to be detected and the auxiliary data, and the reverberation covariance matrix estimation problem is converted into the estimation problem of the MAR coefficient matrix and the MAR model-driven noise spatial domain covariance matrix, which reduces the number of unknown parameters and the dependence on auxiliary data, can solve the problem of decreased target detection performance in the case of small sample data, and effectively improves the active sonar detection capability. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It's K s =45, the detection probability curves of the PR-RAO-DP-TBD method of the present invention and the PS-RAO-DP-TBD method of the prior art;

[0041] Figure 2 It's K s =45, the accurate tracking probability curve of the PR-RAO-DP-TBD method of the present invention and the PS-RAO-DP-TBD method of the prior art;

[0042] Figure 3 It's K s =23, the detection probability curves of the PR-RAO-DP-TBD method of the present invention and the PR-RAO-DP-TBD method of the prior art;

[0043] Figure 4 It's K s =23, the accurate tracking probability curve of the PR-RAO-DP-TBD method of the present invention and the PS-RAO-DP-TBD method of the prior art;

[0044] Figure 5 It's K s =12, the detection probability curves of the PR-RAO-DP-TBD method of the present invention and the PR-RAO-DP-TBD method of the prior art;

[0045] Figure 6 It's K s =12, the accurate tracking probability curves of the PR-RAO-DP-TBD method of the present invention and the PS-RAO-DP-TBD method of the prior art. DETAILED DESCRIPTION

[0046] Reverberation usually exhibits space-time correlation. When the auxiliary data is insufficient to accurately estimate the reverberation covariance matrix, this correlation can be characterized by a parameterized model. The present invention aims to improve the robustness of the algorithm through reverberation parameterized modeling. Therefore, how to improve the robustness of the underwater single pulse space-time adaptive detection and tracking method under small auxiliary data is the core problem of the present invention.

[0047] To address this problem, in order to improve the robustness of the algorithm, the present invention provides a space-time adaptive pre-detection tracking method based on a parameterized model, which uses a multi-channel autoregression (MAR) model to parameterize the reverberation, and converts the estimation problem of the reverberation covariance matrix into the estimation problem of the MAR coefficient matrix and the driving noise spatial covariance matrix, thereby reducing the number of unknown parameters and being able to well characterize the space-time correlation of reverberation, thereby reducing the demand for the amount of auxiliary data and improving the robustness of the STAD-DP-TBD algorithm in the case of small auxiliary data.

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

[0049] Example

[0050] The embodiment of the present invention proposes a space-time adaptive tracking-before-detection method based on a parameterized model.

[0051] 1. Problem Modeling

[0052] Assume that the receiving array of active sonar is a uniform linear array with N array elements and d array element spacing. The pulse width of the transmission is T p , L distance units, sampling frequency is f s , then the number of sampling points in each distance unit is M = T p f s The sonar system emits a single pulse signal to obtain MN×L-dimensional space-time data, which is called a frame of data. It emits K single pulse signals, that is, it scans the detection area K times to obtain K frames of echo data. When the k-th scan of the l-th distance unit is performed, MN sampling data can be obtained. These MN data form an observation vector z lk The detection problem in a uniform reverberation background can be expressed as the following binary hypothesis test:

[0053]

[0054] Among them, H0 and H1 represent the hypothesis without target and with target respectively; n lk ~CN(0,R k ) has zero mean and the covariance matrix is ​​R k The complex Gaussian distribution of k is the amplitude of the target signal at the kth scan, l k is the distance unit with target in the kth scan, is the space-time steering vector, where s tk (v dk ) is the spatial steering vector, s sk (v sk ) is the time domain steering vector.

[0055] To simplify the analysis, we take one frame of data from equation (1) for analysis. For the kth frame of data, the binary hypothesis test problem can be written as follows:

[0056]

[0057] Among them, z is the unit data to be detected; z l is the 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 are independent and identically distributed complex Gaussian vectors with mean 0 and covariance matrix R.

[0058] The parameterization method is to represent the reverberation signal received by the uniform linear array using the MAR model.

[0059]

[0060] in, represents the P-order MAR coefficient matrix, κ l (m) represents a multi-channel Gaussian process with whitening in time domain and coloring in space domain, which is described as a complex Gaussian random vector with mean 0 and covariance matrix Q, m = 1, ..., M; l = 1, ..., K s ; K s is the number of auxiliary distance units.

[0061] The data to be detected z and auxiliary data z in formula (2) are l , the reverberation signal n in the data to be detected, the reverberation signal n in the auxiliary data unit l and the space-time steering vector v is written as follows

[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] Then the binary hypothesis testing problem can be rewritten as shown below

[0068]

[0069] The detection data z and auxiliary data z in formula (9) are l The reverberation signal in is modeled as a P-order MAR process according to formula (3), then

[0070]

[0071] Among them, under the H0 hypothesis, α=0, and under the H1 hypothesis, 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 by formula (14).

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

[0081]

[0082] in

[0083]

[0084] here,

[0085] 2. Algorithm Design

[0086] For the converted binary hypothesis test, according to the RAO criterion, a parameterized RAO-DP-TBD method is proposed in the uniform reverberation background, denoted as PR-RAO-DP-TBD.

[0087] In the binary hypothesis testing problem shown in formula (9), the target parameter vector θ to be estimated is r =[α r ,α i ] T , the redundant parameter vector θ s Contains unknown parameters A H and Q, can be written as where a r =vec(Re(A H )), a i =vec(Im(A H )),q r Contains the real parts of the diagonal elements of Q and the elements below the diagonal, q r Contains the imaginary parts of the elements below the diagonal of Q.

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

[0089]

[0090] Need to know where θ r,0 =[0,0] T , so the problem focuses on solving θ s Maximum likelihood estimation under the H0 hypothesis As well as the first derivative of the log-likelihood function and the Fisher information matrix of the parameters under maximum likelihood estimation.

[0091] You can get A H and the maximum likelihood estimate 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-order derivative of the log-likelihood function under maximum likelihood estimation is:

[0097]

[0098] in, represents the space-time steering vector after whitening in the time domain, It represents the data to be detected after time domain whitening, expressed as

[0099]

[0100] Obtain

[0101]

[0102] Under the H0 hypothesis, the unknown MAR model coefficient matrix is ​​estimated by maximum likelihood using both the primary and secondary data to obtain the test statistic of parameterized RAO (denoted as PR-RAO)

[0103]

[0104] Among them, η PR-RAO Indicates the detection threshold of 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 accumulation is performed according to the following formula

[0106]

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

[0108]

[0109] Where D = {(l1,v1),...,(l K ,v K )} represents the range-Doppler position of the target in the range-Doppler plane, represents the space-time steering vector after time domain whitening for the kth scan, represents the maximum likelihood estimate of Q at the kth scan, represents the data to be detected after whitening in the time domain for the kth scan, η PR-RAO-DP-TBD Indicates the detection threshold of the PR-RAO-DP-TBD algorithm.

[0110] The final accumulated maximum function is compared with the threshold using formula (35) to obtain the target detection result, and then the maximum function of the last frame is used to realize trajectory backtracking and estimate the trajectory of the target.

[0111] 3. Performance Analysis

[0112] Simulation parameter settings: number of array elements N = 3, number of single pulse sampling points M = 20, space-time dimension MN = 60, number of scans K = 6. In order to verify the performance of the proposed algorithm, the scene with insufficient auxiliary data is divided into the following three scenes, scene 1: Scenario 2: [·] indicates rounding; Scenario 3: The detection and tracking performance of the PR-RAO-DP-TBD algorithm in three scenarios is analyzed and compared with the performance of the dual knowledge base RAO-DP-TBD (denoted as PS-RAO-DP-TBD) algorithm.

[0113] Figure 1 and Figure 2 Respectively represent K sDetection probability and accurate tracking probability curves of PR-RAO-DP-TBD method and PS-RAO-DP-TBD method when =45. It can be seen from the simulation diagram that both PR-RAO-DP-TBD and PS-RAO-DP-TBD can work normally, and PR-RAO-DP-TBD has better detection and tracking performance. Figure 3 and Figure 4 Respectively represent K s = 23. The detection probability and accurate tracking probability curves of the PR-RAO-DP-TBD method and the PS-RAO-DP-TBD method. It can be seen from the simulation diagram that both the PR-RAO-DP-TBD and PS-RAO-DP-TBD methods can work normally, but the detection and tracking performance of the PS-RAO-DP-TBD method decreases significantly, while the detection and tracking performance of the PR-RAO-DP-TBD method decreases slightly, and has better detection and tracking performance. Figure 5 and Figure 6 Respectively represent K s = 12. At this time, the PS-RAO-DP-TBD method cannot work properly because the amount of auxiliary data is less than the space-time 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 the present invention. Although the present invention is described in detail with reference to the embodiments, it should be understood by those skilled in the art that any modification or equivalent replacement of the technical solutions of the present invention does not depart from the spirit and scope of the technical solutions of the present invention and should be included in the scope of the claims of the present invention.

Claims

1. A robust parameterized space-time adaptive tracking-before-detection method, the method comprising: Step 1) receiving echo data collected by a uniform sonar line array, and based on a binary hypothesis test, using a parameterized method to represent the reverberation signal in the unit data to be detected and the auxiliary unit data using a MAR model; Step 2) According to the MAR model representation, the joint probability density functions under the two assumptions are obtained respectively; Step 3) according to the RAO criterion, obtain the detection statistic of the parameterized RAO; Step 4) Using the detection statistic as the value function, dynamic programming is iterated and optimized to obtain the cumulative maximum function of the parameterized RAO-DP-TBD; Step 5) Compare the maximum value function of the parameterized RAO-DP-TBD finally 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, and the maximum value function of the last frame is used to realize trajectory backtracking and estimate the trajectory of the target.

2. The robust parameterized space-time adaptive tracking-before-detection method according to claim 1, characterized in that: The number of sonar array elements of the uniform sonar line array in step 1) is N, the number of sampling points in each distance unit is M, and there are L distance units. Each time the uniform sonar line array transmits a single pulse signal, MN×L-dimensional space-time data is obtained as a frame of echo data, and K frames of echo data are obtained by transmitting K single pulse signals.

3. The robust parameterized space-time adaptive tracking-before-detection method according to claim 2, characterized in that: The step 1) uses a parameterized method to represent the reverberation signal in the unit data to be detected and the auxiliary unit data using a MAR model based on a binary hypothesis test; include: For the k-th frame echo data, based on the binary hypothesis test, H0 and H1 are used to represent the hypothesis of no target signal and the hypothesis of target signal, respectively, satisfying the following formula: Among them, z is the unit data to be detected; z l is the 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 a mean of 0 and a covariance matrix of R, which are the reverberation signal in the unit data to be detected and the reverberation signal in the auxiliary data unit respectively; The reverberation signal n is parametrically transformed l (m) is expressed by the MAR model: in, represents the P-order MAR coefficient matrix, represents an N-dimensional complex number, P represents the total order, A H (p) represents the p-th order MAR coefficient matrix, p = 1, ..., P, κ l (m) represents a multi-channel Gaussian process with whitening in time domain and coloring in space domain, which is described as a complex Gaussian random vector with mean 0 and covariance matrix Q, m = 1, ..., M; m represents the mth sampling point; The unit data z to be detected and the auxiliary unit data z l , the reverberation signal n in the unit data to be detected, the reverberation signal n in the auxiliary data unit l The sum signal space-time steering vector v is written as follows: from=[from T (1),with T (2),...,of 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 Then the binary hypothesis testing problem can be rewritten as follows:

4. The robust parameterized space-time adaptive tracking-before-detection method according to claim 3, characterized in that: The step 2) comprises: The unit data z to be detected and the auxiliary unit data z l The reverberation signal in 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 space-time adaptive tracking-before-detection method according to claim 4, characterized in that: Step 3) parameterizes the detection statistic λ of RAO PR-RAO for: Among them, η PR-RAO represents the detection threshold of parameterized RAO, represents the space-time steering vector after whitening in the time domain, Represents the data to be detected after time domain whitening, which satisfies the following formulas:

6. The robust parameterized space-time adaptive tracking-before-detection 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 formula: Where D = {(l1,v1),...,(l K ,v K )} represents the range-Doppler position of the target in the range-Doppler plane, represents the space-time steering vector after time domain whitening for the kth scan, represents the maximum likelihood estimate of Q at the kth scan, represents the data to be detected after whitening in the time domain for the kth scan, η PR-RAO-DP-TBD Represents the detection threshold of parameterized RAO-DP-TBD.

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