Coherent signal DOA estimation method based on tensor decomposition

Abstract

The invention provides a coherent signal DOA estimation method based on tensor decomposition, and belongs to the technical field of signal processing, and the coherent signal DOA estimation method comprises the following steps: S1, carrying out the forward and backward subarray division of a two-dimensional area array, so as to construct a three-order tensor model; s2, performing parallel factorization on the third-order tensor model to estimate an array manifold matrix corresponding to the first sub-array; and S3, performing two-dimensional DOA estimation by using an estimation result of the array manifold matrix corresponding to the first sub-array. According to the method, the two-dimensional DOA of the coherent signal can be estimated without rank recovery under the conditions of low signal-to-noise ratio and small snapshot, and the two-dimensional DOA is high in estimation precision and good in noise robustness.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and in particular relates to a coherent signal DOA estimation method based on tensor decomposition. Background Art

[0002] Due to the influence of complex electromagnetic environment, multipath propagation and mutual coupling between array elements, the signals received by array elements are often correlated. However, the received covariance matrix of the correlated signal is usually rank-deficient, which makes it impossible to correctly divide the signal subspace and the noise subspace. Therefore, the impact on traditional subspace algorithms such as Music and Esprit is particularly obvious. In order to solve the problem of rank deficiency of the signal covariance matrix, many algorithms for recovering the rank of the covariance matrix of the correlated signal have been generated, and then estimating the DOA of the signal from the recovered full-rank covariance matrix, such as forward and backward spatial smoothing. However, the traditional forward and backward spatial smoothing algorithm has a relatively high requirement on the signal-to-noise ratio. At low signal-to-noise ratio, the algorithm accuracy is seriously reduced and the robustness to noise is low. Summary of the invention

[0003] The purpose of the present invention is to provide a coherent signal DOA estimation method based on tensor decomposition, which can estimate the two-dimensional DOA of the coherent signal without the need for covariance matrix rank recovery under low signal-to-noise ratio and small snapshot conditions, and the two-dimensional DOA estimation has high accuracy and good robustness to noise.

[0004] In order to achieve the above object, the present invention adopts the following technical solutions:

[0005] A coherent signal DOA estimation method based on tensor decomposition, the coherent signal DOA estimation method comprising the following steps:

[0006] Step S1, dividing the two-dimensional array into forward and backward sub-arrays to construct a third-order tensor model;

[0007] Step S2, performing parallel factor decomposition on the third-order tensor model to estimate the array popularity matrix corresponding to the first sub-array;

[0008] Step S3: perform two-dimensional DOA estimation using the estimation result of the array popularity matrix corresponding to the first sub-array.

[0009] Furthermore, the specific implementation process of step S1 includes:

[0010] Step S11, determining the first sub-array in the two-dimensional array, and moving along the forward direction and the backward direction of the two-dimensional array respectively, so as to divide the two-dimensional array into a plurality of sub-arrays;

[0011] The number of rows and columns of each sub-array is the same, and any two adjacent sub-arrays partially overlap, and the number of array elements in the overlapping part is the same;

[0012] Step S12: acquiring the coherent signal data received by each sub-array to determine the covariance data of each sub-array;

[0013] Step S13: Arrange the covariance data of the multiple sub-matrices into a third-order tensor model in a forward slicing manner.

[0014] Furthermore, in step S2, the specific process of the parallel factor decomposition includes:

[0015] Step S21, performing modulo 1, modulo 2 and modulo 3 expansion on the third-order tensor model respectively to determine a modulo 1 expansion matrix, a modulo 2 expansion matrix and a modulo 3 expansion matrix;

[0016] Step S22: using the module 1 expansion matrix, the module 2 expansion matrix and the module 3 expansion matrix, three linear least squares solutions are performed on the three factor matrices of the third-order tensor model to determine the estimation result of the array manifold matrix corresponding to the first sub-array.

[0017] Furthermore, in step S21, the modulo 1 expansion matrix, the modulo 2 expansion matrix and the modulo 3 expansion matrix are respectively:

[0018] Z1=(A * ☉B)A T +N1;

[0019] Z2=(B☉A)(A * ) T +N2;

[0020] Z3=(A☉A * )B T +N3;

[0021] Among them, Z1, Z2 and Z3 are modulo 1 expansion matrix, modulo 2 expansion matrix and modulo 3 expansion matrix respectively; A, A * and B are the first factor matrix, the second factor matrix and the third factor matrix respectively; A T ,(A * ) T and B T are the transposed matrices corresponding to the first factor matrix, the second factor matrix and the third factor matrix respectively; N1, N2 and N3 are the first noise matrix, the second noise matrix and the third noise matrix corresponding to the expansion of modulo 1, modulo 2 and modulo 3 respectively.

[0022] Furthermore, in step S22, the specific process of the trilinear least squares solution includes:

[0023] Step S221, performing Tuker decomposition compression on the third-order tensor to obtain a core tensor;

[0024] Step S222, performing parallel factor decomposition on the core tensor to obtain initial matrices of the first factor matrix, the second factor matrix and the third factor matrix;

[0025] Step S223, setting the initial value of the number of iterations k to 1;

[0026] Step S224: using the initial matrices of two of the factor matrices and the corresponding unfolded matrices, estimate the remaining factor matrix to obtain estimated values ​​of the first factor matrix, the second factor matrix and the third factor matrix;

[0027] Step S225, determine whether the number of iterations k is less than the threshold value. If so, add 1 to the number of iterations k and assign it to k, and use the estimated values ​​of the three factor matrices as the initial three factor matrices, and return to step S224; if not, use the estimated value of the first factor matrix as the estimated value of the array popularity matrix of the first sub-array.

[0028] Further, in step S224, when the remaining factor matrix is ​​the first factor matrix, the transposed matrix estimation result of the first factor matrix is:

[0029]

[0030] in, is the estimated result of the transposed matrix of the first factor matrix; represents the pseudo-inverse operation of the matrix; ⊙ is the KhatriRao product operation.

[0031] Further, in step S224, when the remaining factor matrix is ​​the second factor matrix, the transposed matrix estimation result of the second factor matrix is:

[0032]

[0033] in, is the estimated result of the transposed matrix of the second factor matrix; represents the pseudo-inverse operation of the matrix; ⊙ is the KhatriRao product operation.

[0034] Further, in step S224, when the remaining factor matrix is ​​the third factor matrix, the transposed matrix estimation result of the third factor matrix is:

[0035]

[0036] in, is the estimated result of the transposed matrix of the third factor matrix; represents the pseudo-inverse operation of the matrix; ⊙ is the KhatriRao product operation.

[0037] Furthermore, in step S3, the specific process of the two-dimensional DOA estimation includes:

[0038] Step S31, calculating the product matrix of the array popularity matrix corresponding to the estimated first sub-matrix and its corresponding conjugate transposed matrix;

[0039] Step S32: Use the product matrix to perform direction finding estimation to obtain DOA estimation results of each coherent signal.

[0040] In summary, the technical solution of the present invention has the following technical effects:

[0041] The present invention realizes the construction of a third-order tensor model by dividing a two-dimensional array into a forward sub-array and a backward sub-array; estimates the array popularity matrix corresponding to the first sub-array by utilizing the parallel factor decomposition of the third-order tensor model; performs two-dimensional DOA estimation by utilizing the rotational invariance of the estimation result of the array popularity matrix corresponding to the first sub-array, and realizes that a high-precision DOA estimation value can be obtained without rank recovery in the case of low signal-to-noise ratio and small snapshots, and the estimation accuracy is high and the robustness to noise is high. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0043] Figure 1 It is a flow chart of a coherent signal DOA estimation method based on tensor decomposition of the present invention;

[0044] Figure 2 Schematic diagram of forward and backward movement of a one-dimensional subarray;

[0045] Figure 3 (a) and (b) are respectively a schematic diagram of a scatter point of a one-dimensional coherent signal DOA estimation and a schematic diagram of a root mean square error curve of a one-dimensional coherent signal DOA estimation of the method of the present invention and the traditional method;

[0046] Figure 4 (a) and (b) are schematic diagrams of a scatter diagram of two-dimensional coherent signal DOA estimation and a root mean square error curve of two-dimensional coherent signal DOA estimation of the method of the present invention and the traditional method, respectively. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0048] This embodiment provides a coherent signal DOA estimation method based on tensor decomposition. Figure 1 , the coherent signal DOA estimation method comprises the following steps:

[0049] Step S1, dividing the two-dimensional array into forward and backward sub-arrays to construct a third-order tensor model.

[0050] This embodiment adopts a spatial smoothing algorithm to realize the forward and backward sub-array division of the two-dimensional array, and stacks the covariance data of each sub-array into a third-order tensor. The specific implementation process includes:

[0051] Step S11, determining the first sub-array in the two-dimensional array, and moving along the forward direction and the backward direction of the two-dimensional array respectively, so as to divide the two-dimensional array into a plurality of sub-arrays;

[0052] This embodiment first determines the first subarray 1, and then follows Figure 2 The forward movement and backward movement modes shown in the figure obtain M forward sub-arrays and M backward sub-arrays, wherein the number of rows a (number of antenna elements) and the number of columns b (number of antenna elements) of each sub-array are the same, and any two adjacent sub-arrays overlap, and the number of array elements in the overlapping part is the same, a and b are both greater than or equal to the number of incident signals, and the total number of sub-arrays is greater than or equal to the number of incident signals.

[0053] Step S12: acquiring the coherent signal data received by each sub-array to determine the covariance data of each sub-array;

[0054] Step S13: Arrange the covariance data of the multiple sub-matrices into a third-order tensor model in a forward slicing manner.

[0055] Step S2: performing parallel factorization on the third-order tensor model to estimate an array manifold matrix corresponding to the first sub-array.

[0056] This embodiment uses the construction method of the third-order tensor to achieve the uniqueness of parallel factor decomposition, and finally obtains the array manifold matrix corresponding to the first sub-array. The specific process of parallel factor decomposition includes:

[0057] Step S21, performing modulo 1, modulo 2 and modulo 3 expansion on the third-order tensor model respectively to determine a modulo 1 expansion matrix, a modulo 2 expansion matrix and a modulo 3 expansion matrix;

[0058] In this embodiment, the modulo 1 expansion matrix, the modulo 2 expansion matrix and the modulo 3 expansion matrix are respectively:

[0059] Z1=(A * ☉B)A T +N1;

[0060] Z2=(B☉A)(A * ) T +N2;

[0061] Z3=(A☉A * )B T +N3;

[0062] Among them, Z1, Z2 and Z3 are modulo 1 expansion matrix, modulo 2 expansion matrix and modulo 3 expansion matrix respectively; A, A * and B are the first factor matrix, the second factor matrix, and the third factor matrix, respectively (ideally, A and A * are mutually conjugate matrices); A T ,(A * ) T and B T are the transposed matrices corresponding to the first factor matrix, the second factor matrix and the third factor matrix respectively; N1, N2 and N3 are the first noise matrix, the second noise matrix and the third noise matrix corresponding to the expansion of modulo 1, modulo 2 and modulo 3 respectively.

[0063] Step S22: using the module 1 expansion matrix, the module 2 expansion matrix and the module 3 expansion matrix, three linear least squares solutions are performed on the three factor matrices of the third-order tensor model to determine the estimation result of the array manifold matrix corresponding to the first sub-array.

[0064] The three factor matrices in this embodiment are the first factor matrix, the second factor matrix and the third factor matrix. The trilinear least squares solution in this embodiment is to fix all the factor matrices except one factor matrix, and solve each factor matrix through iteration, such as fixing A * and B, use the following formula to find A:

[0065]

[0066] Among them, ||·|| F represents the Frobenius norm.

[0067] If A and B are fixed, use the following formula to calculate A * :

[0068]

[0069] Among them, ||·|| F represents the Frobenius norm.

[0070] If A and A are fixed * , use the following formula to calculate B:

[0071]

[0072] Among them, ||·|| F represents the Frobenius norm.

[0073] In summary, the specific process of trilinear least squares solution in this embodiment includes:

[0074] Step S221, performing Tuker decomposition compression on the third-order tensor to obtain a core tensor;

[0075] Step S222, performing parallel factor decomposition on the core tensor to obtain initial matrices of the first factor matrix, the second factor matrix and the third factor matrix;

[0076] Step S223, setting the initial value of the number of iterations k to 1;

[0077] Step S224: using the initial matrices of two of the factor matrices and the corresponding unfolded matrices, estimate the remaining factor matrix to obtain estimated values ​​of the first factor matrix, the second factor matrix and the third factor matrix.

[0078] In this embodiment, when the remaining factor matrix is ​​the first factor matrix, the transposed matrix estimation result of the first factor matrix is:

[0079]

[0080] in, is the estimated result of the transposed matrix of the first factor matrix; represents the pseudo-inverse operation of the matrix; ⊙ is the KhatriRao product operation.

[0081] When the remaining factor matrix is ​​the second factor matrix, the transposed matrix estimation result of the second factor matrix is:

[0082]

[0083] in, is the estimated result of the transposed matrix of the second factor matrix; represents the pseudo-inverse operation of the matrix; ⊙ is the KhatriRao product operation.

[0084] When the remaining factor matrix is ​​the third factor matrix, the transposed matrix estimation result of the third factor matrix is:

[0085]

[0086] in, is the estimated result of the transposed matrix of the third factor matrix; represents the pseudo-inverse operation of the matrix; ⊙ is the KhatriRao product operation.

[0087] Step S225, determine whether the number of iterations k is less than the threshold value. If so, add 1 to the number of iterations k and assign it to k, and use the estimated values ​​of the three factor matrices as the initial three factor matrices, and return to step S224; if not, use the estimated value of the first factor matrix as the estimated value of the array popularity matrix of the first sub-array.

[0088] Step S3: perform two-dimensional DOA estimation using the estimation result of the array popularity matrix corresponding to the first sub-array.

[0089] The array popularity matrix corresponding to the first sub-array of this embodiment has a Vandermonde structure. The rotation invariance of the array popularity matrix corresponding to the first sub-array is utilized, and the ESPRIT algorithm is used to perform two-dimensional DOA estimation. The specific process of two-dimensional DOA estimation includes:

[0090] Step S31, calculating the product matrix of the array manifold matrix corresponding to the estimated first sub-matrix and its corresponding conjugate transposed matrix.

[0091] The product matrix in this embodiment is:

[0092]

[0093] Where R is the product matrix; is the estimated result of the array popularity matrix A corresponding to the first sub-array; It is the conjugate transposed matrix corresponding to the estimated result of the array popularity matrix A corresponding to the first sub-matrix.

[0094] Step S32: Use the product matrix to perform direction finding estimation to obtain DOA estimation results of each coherent signal.

[0095] In this embodiment, the DOA estimation result of each coherent signal is:

[0096]

[0097] in, is the estimated result of the kth coherent signal DOA; θ k and is the phase information (i.e., elevation angle and azimuth angle) of the kth coherent signal in the product matrix R.

[0098] from Figure 3 DOA estimation of coherent signals in a one-dimensional array and Figure 4 It can be seen from the Monte Carlo simulation experimental results of the coherent signal DOA estimation of the two-dimensional array in that the method of the present invention can accurately estimate the coherent signal. Under low signal-to-noise ratio conditions, the performance of both one-dimensional and two-dimensional DOA estimation is better than the traditional forward and backward spatial smoothing, and the DOA estimation accuracy is high.

[0099] This embodiment realizes the construction of a third-order tensor model by dividing the two-dimensional array into a forward sub-array and a backward sub-array; estimates the array manifold matrix corresponding to the first sub-array by utilizing the parallel factor decomposition of the third-order tensor model; performs two-dimensional DOA estimation by utilizing the rotational invariance of the estimated result of the array manifold matrix corresponding to the first sub-array, and realizes that in the case of low signal-to-noise ratio and small snapshots, a high-precision DOA estimation value can be obtained without rank recovery, and the estimation accuracy is high and the robustness to noise is high.

[0100] Please note that the technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, all possible combinations of the technical features in the above embodiments are not described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification. The above embodiments only express several implementation methods of the present application, and their descriptions are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that for ordinary technicians in this field, without departing from the concept of the present application, several variations and improvements can be made, which all belong to the scope of protection of the present application. Therefore, the scope of protection of the patent in this application shall be based on the attached claims.

Claims

1. A coherent signal DOA estimation method based on tensor decomposition, characterized in that: The coherent signal DOA estimation method comprises the following steps: Step S1, dividing the two-dimensional array into forward and backward sub-arrays to construct a third-order tensor model; Step S2, performing parallel factor decomposition on the third-order tensor model to estimate the array popularity matrix corresponding to the first sub-array; Step S3: perform two-dimensional DOA estimation using the estimation result of the array popularity matrix corresponding to the first sub-array.

2. The coherent signal DOA estimation method according to claim 1, characterized in that: The specific implementation process of step S1 includes: Step S11, determining the first sub-array in the two-dimensional array, and moving along the forward direction and the backward direction of the two-dimensional array respectively, so as to divide the two-dimensional array into a plurality of sub-arrays; The number of rows and columns of each sub-array is the same, and any two adjacent sub-arrays partially overlap, and the number of array elements in the overlapping part is the same; Step S12: acquiring the coherent signal data received by each sub-array to determine the covariance data of each sub-array; Step S13: Arrange the covariance data of the multiple sub-matrices into a third-order tensor model in a forward slicing manner.

3. The coherent signal DOA estimation method according to claim 2, characterized in that: In step S2, the specific process of the parallel factor decomposition includes: Step S21, performing modulo 1, modulo 2 and modulo 3 expansion on the third-order tensor model respectively to determine a modulo 1 expansion matrix, a modulo 2 expansion matrix and a modulo 3 expansion matrix; Step S22: using the module 1 expansion matrix, the module 2 expansion matrix and the module 3 expansion matrix, three linear least squares solutions are performed on the three factor matrices of the third-order tensor model to determine the estimation result of the array manifold matrix corresponding to the first sub-array.

4. The coherent signal DOA estimation method according to claim 3, characterized in that: In step S21, the modulo 1 expansion matrix, the modulo 2 expansion matrix and the modulo 3 expansion matrix are respectively: Z1=(A * ☉B)A T +N1; Z2=(B☉A)(A * ) T +N2; <h2 style=";text-align:left;direction:ltr">Z3=(A☉A<h2 style=";text-align:left;direction:ltr"> * <h2 style=";text-align:left;direction:ltr"> B)<h2 style=";text-align:left;direction:ltr"> T <h2 style=";text-align:left;direction:ltr"> +N3; Among them, Z1, Z2 and Z3 are modulo 1 expansion matrix, modulo 2 expansion matrix and modulo 3 expansion matrix respectively; A, A * and B are the first factor matrix, the second factor matrix and the third factor matrix respectively; A T ,(A * ) T and B T are the transposed matrices corresponding to the first factor matrix, the second factor matrix and the third factor matrix respectively; N1, N2 and B3 are the first noise matrix, the second noise matrix and the third noise matrix corresponding to the expansion of modulo 1, modulo 2 and modulo 3 respectively.

5. The coherent signal DOA estimation method according to claim 4, characterized in that: In step S22, the specific process of the trilinear least squares solution includes: Step S221, performing Tuker decomposition compression on the third-order tensor to obtain a core tensor; Step S222, performing parallel factor decomposition on the core tensor to obtain initial matrices of the first factor matrix, the second factor matrix and the third factor matrix; Step S223, setting the initial value of the number of iterations k to 1; Step S224: using the initial matrices of two of the factor matrices and the corresponding unfolded matrices, estimate the remaining factor matrix to obtain estimated values ​​of the first factor matrix, the second factor matrix and the third factor matrix; Step S225, determine whether the number of iterations k is less than the threshold value. If so, add 1 to the number of iterations k and assign it to k, and use the estimated values ​​of the three factor matrices as the initial three factor matrices, and return to step S224; if not, use the estimated value of the first factor matrix as the estimated value of the array popularity matrix of the first sub-array.

6. The coherent signal DOA estimation method according to claim 5, characterized in that: In step S224, when the remaining factor matrix is ​​the first factor matrix, the transposed matrix estimation result of the first factor matrix is: in, is the estimated result of the transposed matrix of the first factor matrix; represents the pseudo-inverse operation of the matrix; ⊙ is the KhatriRao product operation.

7. The coherent signal DOA estimation method according to claim 5, characterized in that: In step S224, when the remaining factor matrix is ​​the second factor matrix, the transposed matrix estimation result of the second factor matrix is: in, is the estimated result of the transposed matrix of the second factor matrix; represents the pseudo-inverse operation of the matrix; ⊙ is the KhatriRao product operation.

8. The coherent signal DOA estimation method according to claim 5, characterized in that: In step S224, when the remaining factor matrix is ​​the third factor matrix, the transposed matrix estimation result of the third factor matrix is: in, is the estimated result of the transposed matrix of the third factor matrix; represents the pseudo-inverse operation of the matrix; ⊙ is the KhatriRao product operation.

9. The coherent signal DOA estimation method according to any one of claims 1 to 8, characterized in that: In step S3, the specific process of the two-dimensional DOA estimation includes: Step S31, calculating the product matrix of the array popularity matrix corresponding to the estimated first sub-matrix and its corresponding conjugate transposed matrix; Step S32: Use the product matrix to perform direction finding estimation to obtain DOA estimation results of each coherent signal.

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