Method for detecting small-volume moving obstacles based on entropy under condition of underwater dense jammer

Abstract

The present application relates to a kind of underwater dense jamming source condition based on entropy small volume movement obstacle detection method, which is first decomposed to time azimuth history matrix using LMD algorithm, obtain low rank matrix and sparse matrix;On this basis, respectively establish joint conditional entropy matrix and low rank similarity matrix;Finally, based on the pearson correlation coefficient of low rank similarity matrix and joint conditional entropy similarity matrix, the position of small target in matrix is located, the fast detection and tracking of mobile small target are realized.Compared with the traditional method, the proposed method significantly improves the computational efficiency and the generalization of model.The present application aims to solve the problem of small mobile obstacle detection under the shelter of underwater dense interference near the port.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of underwater acoustic engineering and underwater obstacle avoidance detection, and relates to a small-volume moving obstacle detection method based on entropy under the condition of underwater dense interference sources. In particular, the application relates to a low-rank sparse matrix decomposition algorithm based on joint conditional entropy similarity measurement, which can quickly detect small-volume moving obstacles under the condition of underwater dense interference sources, and is suitable for the near-port water area scene based on an active sonar array. BACKGROUND

[0002] In the face of the challenge of underwater traffic collision avoidance under the condition of dense obstacles, it is crucial to distinguish fixed obstacles from moving obstacles in the initial stage of underwater target detection while ensuring low computational complexity and high reliability. However, in the near-port water area application scenario relying on an active sonar array, it can be extremely difficult to extract the path of a small-volume moving target from the gap between fixed interference. By analyzing the active sonar echo signal in shallow water, it is found that the background interference mainly comes from sea surface, sea bottom reverberation, and scattering echo between underwater obstacles. Among them, the reverberation interference of multiple frames shows low-rank characteristics in the time-azimuth history matrix, while the echo of obstacles has significant sparse characteristics due to the limited space occupied by the beam scanning. Based on the difference between reverberation interference and targets, low-rank matrix decomposition (LMD) can effectively suppress reverberation interference and extract target echoes to a certain extent. See “Chu Wenhua, Wang Weiguo, Zeng Xueying. A non-convex model of sparse low-rank matrix decomposition [J]. Journal of Ocean University of China (Natural Science Edition), 2018, 48(S2): 223-227.” However, this method has poor suppression effect on dense interference sources in complex environments, and is sensitive to parameters. Its dereverberation effect and target detection performance are severely dependent on manual parameter tuning. In addition, the LMD method requires multi-frame data association calculation, which has extremely high computational complexity and takes a long time. Therefore, it is necessary to design a more efficient post-processing algorithm for fast small target detection under the condition of underwater dense interference sources based on the non-optimal suppression result of single-frame LMD. SUMMARY

[0003] Technical problems to be solved

[0004] To overcome the shortcomings of existing technologies, this invention proposes an entropy-based method for detecting small-volume moving obstacles under conditions of dense underwater interference sources. To detect small-volume moving targets amidst interference from numerous fixed obstacles in a background of strong reverberation, a target detection method based on joint conditional entropy similarity measure (JCESM) is proposed. Unlike the multi-frame correlation LMD algorithm, this invention uses only the temporal and azimuth history matrix of the first frame echo as a reference for moving target detection in subsequent single-frame echoes.

[0005] Technical solution

[0006] A method for detecting small-volume moving obstacles based on entropy under conditions of dense underwater interference sources, characterized by the following steps:

[0007] Step 1: Perform beamforming on the active echo signal to obtain the time-azimuth history of the i-th frame echo.

[0008] Step 2: Use the LMD algorithm to perform low-rank sparse decomposition on the beam data of each frame of the time-azimuth history matrix to obtain the low-rank matrix L. i and sparse matrix S i ;

[0009] B i =L i +S i ;

[0010] Step 3: Optimize the solution of low-rank sparse matrix decomposition using the alternating direction multi-multiplier method;

[0011] Through steps 2 to 3, the low-rank matrix L1 and sparse matrix S1 of the time orientation history of the first frame reference signal are obtained as B1.

[0012] The time-position history of the reference signal in the i-th frame is obtained as B. i The low-rank matrix L i sparse matrix

[0013] Step 4: For S i First, vectorize S1 and calculate vec(S i Joint conditional entropy of ) and vec(S1)

[0014] For L i and S i First, perform vectorization and then calculate matrix L. i Sparse matrix S i joint conditional entropy

[0015] H(vec(S i )|vec(S i )|vec(L i )) is reconverted into an n1*n2 size matrix, defined as H(X i |X1), H(X i |L i );

[0016] Step 5: Calculate the Euclidean distance E H of H(S i |S1) and H(S i |L i ), and the relevant Euclidean distance E L of L1 and the matrix L i ;

[0017] Step 6: Calculate the Pearson correlation coefficient of E H and , to obtain the target bright spot direction under the condition of dense interference source:

[0018] The expression of the time direction history of the i-th frame echo is an n1*n2 size matrix, where n1 represents the dimension in the time direction, and n2 represents the dimension in the direction, and the expression is as follows:

[0019]

[0020] Wherein: corresponds to the value at the n1 time and the n2 angle in the direction history matrix B i .

[0021] The decomposition process of the step 2 is the robust principal component analysis (RPCA), and the constraint condition follows:

[0022]

[0023] s.t.B i =L i +S i

[0024] Wherein, ||L i || * The sum of the singular values of the matrix L i is the nuclear norm; ||S i ||1 is used to calculate the sum of the absolute values of all elements of the matrix S i , which is the L1 norm; λ represents the balance parameter between the low-rank matrix and the sparse matrix; since the matrix L iThe low-rank property is characterized by the nuclear norm of the low-rank matrix L i The sparse property is characterized by the L1 norm of the sparse matrix S i The relaxation representation is performed.

[0025] The step 3 is to solve the optimization of the matrix low-rank sparse decomposition by using the alternating direction multi-multiplier method, and the solution is as follows:

[0026] The matrix variable ||L i || * and ||S i ||1 is f(L i ) and g(S i ), and the constraint condition is expressed as:

[0027]

[0028] s.t.B i =L i +S i

[0029] The augmented Lagrange multiplier expression of the above formula is expressed as:

[0030]

[0031] Where Y i is the dual variable, ρ is the penalty factor, and k is the iteration number of the optimization calculation;

[0032] In the alternating variable solving process, the matrix corresponding to the kth iteration is as follows:

[0033]

[0034] Y i,k =Y i,k-1 +L i,k +S i,k -B i,k

[0035] Where, The formula L i,k and the formula S i,k are solved by the singular value soft threshold operator and the soft threshold operator.

[0036] The penalty factor ρ is set as a variable, and the expression is as follows:

[0037]

[0038] Se i,k =||S i.k -S i,k-1 || F / ||S i.k ||F

[0039] Le i,k =||L i.k -L i,k-1 || F / ||L i.k || F

[0040] where τ1,τ2 and μ are small constants, Le i,k and Se i,k represent the iteration residual of the kth low-rank matrix and sparse matrix and the (k-1)th low-rank matrix and sparse matrix, respectively; the smaller the residual, the closer the obtained matrix decomposition result is to the convergence threshold; ε, Se i,k , Le i,k < ε.

[0041] The value range of τ1,τ2 and μ is usually between 0 and 10.

[0042] The joint conditional entropy of the sparse matrix S i and the sparse matrix S1 is calculated as follows: First, vec(S i ) and vec(S1) are vectorized to obtain column vectors vec(S i ) and vec(S1) with n1×n2 dimensions in columns and 1 dimension in rows:

[0043]

[0044] The joint conditional entropy of vec(S i ) and vec(S1) is calculated as follows:

[0045]

[0046] where s i and s 1 correspond to the elements of vec(S i ) and vec(S1) in the formula, respectively.

[0047] The joint conditional entropy of the matrix L i and the sparse matrix S i is calculated as follows: First, vec(L i ) and vec(S i ) are vectorized to obtain column vectors vec(L i ) and vec(S1) with n1×n2 dimensions in columns and 1 dimension in rows:

[0048]

[0049] The calculation expression of the joint conditional entropy H(L ) is as follows:

[0050]

[0051] Among them, l i For vector vec(L) i The elements in ) vec(L i ) represents matrix L i The transformed columns are n1×n2 dimensional, and the rows are 1-dimensional column vectors.

[0052] The Euclidean distance expression for step 5 is as follows:

[0053]

[0054] Step 1 involves beamforming the active echo signal using a conventional beamforming algorithm (CBF) to obtain the time-azimuth history.

[0055] Beneficial effects

[0056] This invention proposes an entropy-based method for detecting small-volume moving obstacles under conditions of dense underwater interference. First, the LMD algorithm is used to decompose the temporal orientation history matrix to obtain a low-rank matrix and a sparse matrix. Based on this, a joint conditional entropy matrix and a low-rank similarity matrix are established. Finally, based on the Pearson correlation coefficient of the low-rank similarity matrix and the joint conditional entropy similarity matrix, the position of small targets in the matrix is ​​located, enabling rapid detection and tracking of moving small targets.

[0057] Compared with traditional methods, the proposed method significantly improves computational efficiency and model generalization. It aims to solve the challenge of detecting small moving obstacles under dense underwater obstruction near ports. This invention overcomes the problem of excessive cost caused by the need for multi-frame continuous computation in LMD by combining Variational Mode Decomposition (VMD) and Joint Conditional Entropy Matching Optimization Low-Rank Matrix Factorization (LMD). It achieves rapid suppression of reverberation and dynamic background in a single frame, and the target detection performance is superior to conventional LMD algorithms. The average computation time of this invention is within 12-14 seconds, which is more than 5 times more efficient than the continuous multi-frame LMF algorithm that takes more than one minute.

[0058] Compared to existing technologies, it has the following beneficial effects:

[0059] a) Compared with the traditional LMD method, the present invention does not require multi-frame correlation calculation, which greatly reduces the computational complexity and saves computation time.

[0060] b) Compared with the traditional LMD method, the adaptive post-processing method based on joint conditional entropy and Euclidean distance similarity measure is adopted, which reduces the sensitivity of the algorithm to parameter selection and improves the robustness of the method.

[0061] c) The invention overcomes the influence of fixed position dense interference source while suppressing reverberation, effectively realizing the detection of small target azimuth in motion. BRIEF DESCRIPTION OF DRAWINGS

[0062] Figure 1 Target detection method based on joint conditional entropy similarity measure schematic diagram;

[0063] Figure 2 Time azimuth history diagram of the 1st frame reference signal and the 233rd frame echo;

[0064] (a) Azimuth history diagram of the 1st frame reference signal;

[0065] (b) Azimuth history diagram of the 233rd frame reference signal;

[0066] Figure 3 Low-rank matrix and sparse matrix obtained by low-rank sparse decomposition of the 233rd frame time azimuth history matrix;

[0067] (a) Low-rank matrix; (b) Sparse matrix;

[0068] Figure 4 Joint conditional entropy matrix H(S i |S1) and H(S i |L i );

[0069] (a) H(S i |S1); (b) H(S i |L i );

[0070] Figure 5 Similarity measure matrix E H and

[0071] (a) E H ; (b)

[0072] Figure 6 Pearson correlation coefficient matrix, and the bright spot in the figure is the target bright spot echo under the condition of dense interference source;

[0073] (a) Single frame JCESM algorithm detects target, and the red circle frames the target bright spot echo;

[0074] (b) Interference suppression result of 4 frames of conventional LMD correlation. Detailed Implementation

[0075] The present invention will now be further described in conjunction with the embodiments and accompanying drawings:

[0076] A target detection method based on Joint Conditional Entropy Similarity Measure (JCESM) is characterized by the following steps: First, the LMD algorithm is used to decompose the time-location history matrix to obtain a low-rank matrix and a sparse matrix. Then, a joint conditional entropy matrix is ​​established between the sparse matrix of the reference signal and the sparse matrix of the echo signal, a low-rank similarity matrix is ​​established between the low-rank matrix of the reference signal and the low-rank matrix of the echo signal, and a joint conditional entropy matrix is ​​established between the low-rank matrix of the echo signal and the sparse matrix. Next, the similarity between the two joint conditional entropy matrices is measured using Euclidean distance to obtain a joint conditional entropy similarity matrix. Finally, the correlation coefficient between the low-rank similarity matrix and the joint conditional entropy similarity matrix is ​​calculated to find the location of the moving target corresponding to a fixed interference source that deviates from the entropy approximation. The steps can be summarized as follows:

[0077] Step 1: Perform beamforming processing on the active echo signal. For the echo signal of the i-th active sonar pulse, define its beamforming result as a matrix of size n1×n2. Where n1 represents the dimension in the time direction (which can be converted to distance by multiplying by the speed of sound), and n2 represents the dimension in the orientation direction, as expressed below:

[0078]

[0079] Here, B i This represents the time-azimuth history of the i-th frame echo. Similarly, the time-azimuth history of the first frame of data, which serves as the reference signal, is defined as B1. The corresponding representation is the azimuth history matrix B. i The values ​​at the n1-th time and the n2-th angle.

[0080] Step 2: Perform low-rank sparse decomposition on the beamforming data of each frame of echo. Assuming there is a moving target in the active sonar echo, the target's azimuth-range spatial spectrum exists in matrix B. i It is also sparsity-dependent, and B i It also includes relatively stable reverberation fluctuations. For matrix B... i Perform low-rank matrix L i and sparse matrix S i :

[0081] B i =L i +S i (2)

[0082] The decomposition process described above is also known as robust principal component analysis (RPCA), and its constraints follow:

[0083]

[0084] where ||L i || * The matrix L i is calculated i The sum of singular values, also known as the nuclear norm, ||S i is calculated i The sum of absolute values of all elements, also known as the L1 norm. λ represents a balance parameter between low-rank matrix and sparse matrix. Since matrix L i has low-rank characteristics, the nuclear norm is used to relax the representation of low-rank matrix L i has sparse characteristics, the L1 norm is used to relax the representation of sparse matrix S

[0085] Step three: optimization solution of matrix low-rank sparse decomposition by using alternating direction multipliers method. Define ||L i || * and ||S i ||1as f(L i ) and g(S i ), and re-express equation (3) as:

[0086]

[0087] The augmented Lagrange multiplier expression of equation (4) can be expressed as:

[0088]

[0089] where Y i is the dual variable, ρ is the penalty factor, and k is the iteration number of optimization calculation. In the alternating variable solution process, the matrix corresponding to the kth iteration is as follows:

[0090]

[0091]

[0092] Y i,k = Y i,k-1 + L i,k + S i,k - B i,k (8)

[0093] where, Equations (6) and (7) can be solved by singular value soft threshold operator and soft threshold operator. In order to converge to the optimal solution faster, the penalty factor ρ k is usually set as a variable, and the expression is as follows:

[0094]

[0095] Among them, τ1, τ2 and μ are small constants, and empirically, their values ​​usually range from 0 to 10. i,k and Se i,k ε,Se represent the iterative residuals of the k-th low-rank and sparse matrices and the (k-1)-th low-rank and sparse matrices, respectively. The smaller the residual, the closer the obtained matrix decomposition result is to the convergence threshold. i,k Le i,k <ε

[0096] Step 4: Define the time-position history of the reference signal in frame 1 as B1. After steps 2 and 3, the low-rank matrix obtained by decomposition is L1, and the sparse matrix is ​​S1. Correspondingly, the time-position history of the reference signal in frame i is B. i After steps two and three, the low-rank matrix L is obtained. i sparse matrix

[0097] First, for S i First, vectorize S1 to obtain a column vector vec(S) with n1×n2 dimensions and 1-dimensional rows. i ) and vec(S1):

[0098]

[0099] Next, calculate vec(S) i The joint conditional entropy of ) and vec(S1):

[0100]

[0101] Among them, s i ,s 1 Corresponding to vec(S) in equation (11) i The elements of ) and vec(S1).

[0102] Similarly, calculate matrix L i Sparse matrix S i The joint conditional entropy, in its specific form, is as follows:

[0103]

[0104] Joint conditional entropy The calculation expression is as follows:

[0105]

[0106] Among them, l i For vector vec(L) i The elements in ) vec(Li ) represents matrix L i The transformed columns are n1×n2 dimensional, and the rows are 1-dimensional column vectors.

[0107] Then, H(vec(S) i )|vec(S1)) and H(vec(S i )|vec(L i The matrix is ​​reconverted into an n1*n2 matrix, defined as H(X). i |X1), H(X) i |L i ).

[0108] Step 5: Calculate H(S) i |S1) and H(S) i |L i Euclidean distance E) H , and L1 and matrix L i Related Euclidean distance E L The expression is as follows:

[0109]

[0110] Step Six: Calculate E H and The Pearson correlation coefficient was used to obtain the location of the target bright spot under conditions of dense interference sources:

[0111]

[0112] This invention aims to solve the challenge of detecting small moving obstacles under dense underwater obstruction near ports. By combining Variational Mode Decomposition (VMD) and Joint Conditional Entropy Matching Optimized Low-Rank Matrix Factorization (LMD), this invention overcomes the high cost of multi-frame continuous computation required by LMD, achieving rapid suppression of reverberation and dynamic background in a single frame, and outperforming conventional LMD algorithms in target detection. The average computation time of this invention is within 12-14 seconds, which is more than 5 times more efficient than the continuous multi-frame LMD algorithm that takes more than one minute.

[0113] Table 1. Comparison of average computation time between single-frame JCESM and multi-frame LMD (Unit: seconds)

[0114] Method Frame number 1 Frame number 4 Frame number 6 Frame number 8 Frame number 10 JCESM 12.69 \ \ \ \ LMD \ 65.44 106.85 167.53 197.2

[0115] Table 1 shows the comparison results between the present invention and the conventional LMD algorithm. To achieve reverberation suppression, LMD requires correlation processing of at least 4 frames of matrices, and the computation time is much longer than that of the single-frame JCESM algorithm. Moreover, the computational cost continues to increase as the number of correlated frames increases. Figure 6In contrast, it is obvious that the JCESM algorithm used in the patent can obtain the complete target moving track, while the conventional LMD algorithm is difficult to find the target bright spot and needs further processing to detect the target, and the calculation time is much higher than the present application.

[0116] The present application achieves obvious implementation effects in typical embodiments, Figure 6 In the red box of (a), the continuous target track tailing can be obviously detected, while the LMD method cannot obtain obvious target echo bright spots. Compared with the prior art (the operation time of the LMD of 4 frames is usually more than 1 min), the calculation time of the JCESM algorithm proposed in the present application is only 5.4 s for a single frame, and the superiority lies in that the target can be quickly positioned under the shielding of dense interference sources.

Claims

1. A method for detecting small volume motion obstacles based on entropy under underwater dense jammer conditions, characterized in that The steps are as follows: Step 1: Beamform the active echo signal to obtain the time-azimuth history of the i-th frame of echo Step 2: Perform low-rank and sparse decomposition on the beam data of each frame of echo of the time-azimuth history matrix using the LMD algorithm to obtain a low-rank matrix L i and a sparse matrix S i ; B i = L i + S i ; Step 3: optimization solution of matrix low rank sparse decomposition by using an alternating direction multiple multiplier method; Through steps 2-3, the time and azimuth history of the first frame of reference signals is obtained as a low rank matrix L1 and a sparse matrix S1 of B1; The time direction history of the ith frame reference signal is B i a low rank matrix L i and a sparse matrix Step 4: Vectorizing the sparse matrix S i and S1 first, and calculating the joint conditional entropy of vec(S i ) and vec(S1) a low-rank matrix L i and a sparse matrix S i First, vectorization processing is performed, and the joint conditional entropy i of the low-rank matrix L i and the sparse matrix S H(vec(S i )|vec(S1)) and H(vec(S i )|vec(L i )) are reconverted into n1*n2 size matrices, defined as H(S i |S1), H(S i |L i ); Step 5: Compute the Euclidean distance E i |S1) and H(S i |L i ) of H(S i,H , and the relevant Euclidean distance E i |L1 and the low-rank matrix L i,L ; Step 6: Calculate E i,H and the Pearson correlation coefficient of E i,L to get the target bright spot azimuth under the condition of dense interference sources:

2. The method of claim 1, wherein the method is based on entropy under the condition of underwater dense jammer. a temporal azimuth profile of the ith frame echo The expression is a matrix of size n1x n2, where n1 represents the dimension in the temporal direction and n2 represents the dimension in the azimuth direction, and is expressed as follows: wherein: corresponding to the value at the nth1 time, the nth2 angle in the bearing history matrix B i corresponding to the value at the nth1 time, the nth2 angle in the bearing history matrix B 3. The method of claim 1, wherein the method is based on entropy under the condition of underwater dense jammer. The decomposition process of step 2 is robust principal component analysis (RPCA), and the constraint condition is as follows: s.t.B i = L i + S i wherein, ||L i || * The singular value sum of the low-rank matrix L i is the nuclear norm; ||S i The sum of the absolute values of all elements of the sparse matrix S i is the L1 norm; λ represents a balance parameter between the low-rank matrix and the sparse matrix; since the matrix L i has a low-rank characteristic, the nuclear norm is used to relax the representation of the low-rank matrix L i , and the L1 norm is used to relax the representation of the sparse matrix S i .

4. The method of claim 1, wherein the method is based on entropy under dense jammer conditions. The optimization solution of matrix low rank sparse decomposition by using an alternating direction multiple multiplier method in step 3 is as follows: Definition ||L i || * and ||S i The matrix variables for ||1 are f(L i ) and g(S i ), which are expressed as: s.t. B i = L i + S i The augmented Lagrange multiplier expression of the above formula is as follows: where Y i is the dual variable, p is the penalty factor, and k is the number of iterations for the optimization calculation. In the alternating variable solving process, the matrix corresponding to the kth iteration is as follows: Y i,k = Y i,k-1 + L i,k + S i,k - B i,k wherein Formula L i,k and Formula S i,k Solved by singular value soft threshold operator and soft threshold operator.

5. The method of claim 4, wherein the method is based on entropy under the condition of underwater dense jammer. The penalty factor ρ is set as a variable, and the expression is as follows: Se i,k =||S i.k -S i,k-1 || F / ||S i.k || F Le i,k =||L i.k -L i,k-1 || F / ||L i.k || F where τ1, τ2 and μ are constants, Le i,k and Se i,k respectively represent the iteration residual of the kth low-rank matrix and sparse matrix and the (k-1)th low-rank matrix and sparse matrix; the smaller the residual, the closer the obtained matrix decomposition result is to the convergence threshold.

6. The method of claim 5, wherein the method is based on entropy under conditions of dense underwater jammer sources. The value range of τ1, τ2 and μ is usually between 0-10.

7. The method of claim 1, wherein: The calculated sparse matrix S i and the joint conditional entropy H(S i |S1) of the sparse matrix S i and S1, first vectorize the sparse matrix S i and vec(S1) with the column being n1 x n2 dimension and the row being 1 dimension: Compute the joint conditional entropy of vec(S i ) and vec(S1): where s i , s 1 correspond to the elements of vec(S i ) and vec(S1) respectively.

8. The method of claim 1, wherein: The calculation of the low-rank matrix L i and the joint conditional entropy H(S i |L i ) of the sparse matrix S i First, the low-rank matrix L i and the sparse matrix S i are subjected to vectorization to obtain a column vector vec(L i ) with n1×n2 dimensions and a row vector vec(S1) with 1 dimension. Joint conditional entropy H Si|Li The computational expression for H is as follows: where l i is an element in the vector vec(L i ) which represents the columns of the matrix L i ) is an n1 x n2 dimensional column vector whose elements are the columns of the matrix L i ) is an 1 dimensional column vector whose elements are the columns of the matrix L 9. The method of claim 1, wherein: The Euclidean distance expression of step 5 is as follows:

10. The method of claim 1, wherein the method is based on entropy under dense source of interference conditions in underwater. The step 1 adopts a conventional beam forming algorithm to perform beam processing on the active echo signal to obtain a time-azimuth history

Images