ALS-based RGSVD distributed MIMO radar direction finding method

Abstract

This invention proposes an ALS-based RGSVD distributed MIMO radar direction finding method, belonging to the field of radar direction finding technology. Starting from the perspective of improving the direction finding accuracy of the system under low signal-to-noise ratio conditions, this invention designs a direction finding algorithm for distributed MIMO radar systems. It mainly utilizes generalized singular value decomposition (SVO) technology to jointly decompose the covariance matrices of the echo signals from multiple receiving arrays of the system. This effectively applies the intrinsic correlation of the data to achieve better denoising performance. The more accurate signal subspace obtained from the decomposition is then input into the ESPRIT algorithm to achieve joint high-precision direction finding of multiple targets' DOA and DOD.

Description

Technical Field

[0001] This invention belongs to the field of radar direction finding technology, and particularly relates to an ALS-based RGSVD distributed MIMO radar direction finding method. Background Technology

[0002] With the rapid development of modern penetration methods such as hypersonic vehicles, stealth aircraft, and cruise missiles, national strategic early warning systems have placed new and higher demands on radar detection technology. In order to meet the requirements of radar anti-stealth, anti-jamming, and anti-destruction, MIMO radar based on distributed sub-platforms has emerged and achieved significant development.

[0003] From a signal processing perspective, radar functions primarily include detection, estimation, tracking, imaging, and identification. Radar direction finding is a major aspect of parameter estimation and the foundation for target localization and tracking, thus making it one of the core technologies of radar. Improving the direction finding accuracy of radar systems is a key direction for enhancing radar performance, and distributed array MIMO radar can effectively improve the joint estimation accuracy of target DOA and DOD under low signal-to-noise ratio conditions through joint optimization processing of data.

[0004] From the perspective of existing MIMO radar direction finding technology: For bistatic MIMO radar, the algorithm of using truncated singular value decomposition to process the cross-covariance matrix of the two arrays to obtain the signal subspace and then using the classic ESPRIT algorithm for direction finding is similar to that of this patent. However, it is only applicable to bistatic MIMO radar systems. Moreover, since it only utilizes the cross-covariance matrix, the data information extraction is insufficient, making it difficult to achieve central fusion processing and noise reduction of multi-array received echo data. Under low signal-to-noise ratio conditions, the direction finding accuracy is low.

[0005] The following is a flowchart of bistatic MIMO radar direction finding implemented by processing the cross-covariance matrix using TSVD and then inputting it into the ESPRIT algorithm. Figure 1 As shown: This technique is a classic algorithm for joint DOA and DOD direction finding of bistatic MIMO radar. The algorithm performs singular value decomposition on the cross-covariance matrix of the echo signals from the two receiving arrays of the bistatic MIMO radar to obtain the signal subspace of each receiving array. This subspace is then fed into the ESPRIT algorithm to measure the DOA of the target relative to the receiving array. Next, the receiving subspace is permuted to obtain the signal subspace of the transmitting array, and the DOD of the target relative to the transmitting array is calculated similarly. Finally, the direction finding is completed by matching the angles of multiple targets.

[0006] This implementation method can achieve high-precision estimation of target DOA and DOD under high signal-to-noise ratio conditions. However, under low signal-to-noise ratio and low snapshot number conditions, the direction-finding accuracy of the algorithm will be affected, which in turn will affect the subsequent positioning and tracking functions of the radar. In addition, the algorithm is mainly applicable to bistatic MIMO radar systems with a relatively limited array size and insufficient data extraction. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention proposes an ALS-based RGSVD distributed MIMO radar direction finding scheme.

[0008] The first aspect of this invention proposes a distributed MIMO radar direction finding method based on Alternating Least Squares (ALS) and RGSVD. ALS stands for Alternating Least Squares Algorithm, RGSVD for Low-Complexity Generalized Singular Value Decomposition, and MIMO radar for Multiple Input Multiple Output radar. The method includes:

[0009] Step S1: By performing matched filtering and vectorization processing on the echo signal of the receiving array of the distributed MIMO radar, the echo signal model η of the distributed MIMO radar is constructed. (l) And according to the echo signal model η (l) Calculate the covariance matrix R of the echo signal. ηη ;

[0010] Step S2: Apply RGSVD to the covariance matrix R of the echo signal. ηη The signal subspace of the receiving array is obtained by decomposition. The joint matrix decomposition is achieved by iterative update using ALS. The signal subspace of the transmitting array is obtained by permutation matrix.

[0011] Step S3: Substitute the calculated receiver array signal subspace and transmitter array signal subspace into the ESPRIT algorithm to perform joint estimation and matching of multiple DOAs and DODs for each target;

[0012] Where DOA represents the angle of arrival and DOD represents the angle of departure.

[0013] According to the method of the first aspect of the present invention, in step S1, the distributed MIMO radar includes m sub-transmit arrays and n sub-receive arrays, each sub-array being arranged in a uniform linear array configuration; wherein:

[0014] The number of elements in each of the sub-emission arrays are M1, M2…M m The element spacing is d t Then the total number of transmitting array elements is M = M1 + M2 + ... + M m The number of array elements in each of the sub-receiver arrays are N1, N2…N n The element spacing is dr Then the total number of receiving array elements is N = N1 + N2 + ... + N n And the element spacing satisfies d. t (d r )≤λ / 2, where λ represents the wavelength of the transmitted signal;

[0015] All transmitted signals are reflected by P targets and then received by the sub-receiving array. The DOA of the p-th target with respect to the i-th receiving sub-array is denoted as φ. ip The DOD of the i-th emitter subarray is denoted as θ. ip The target reflectance coefficient is β p Then the vectors of DOD and DOA of P targets with respect to the i-th array are represented as θ. i =[θ i1 θ i2 …θ iP ] T and φ i =[φ i1 φ i2 …φ iP ] T ;

[0016] The steering vector of the i-th sub-receiver array about the p-th target is:

[0017]

[0018] The manifold matrix of the i-th sub-receiver array is:

[0019] A ri (φ i )=[a ri (φ i1 ) a ri (φ i2 ...a ri (φ iP )]

[0020] The steering vector of the i-th sub-emission array about the p-th target is:

[0021]

[0022] The manifold matrix of the i-th sub-emission array is:

[0023] A ti (θ i )=[a ti (θ i1 ) a ti (θ i2 ...a ti (θ iP )]

[0024] by The m-th sub-emission matrix represents the i-th sub-emission matrix. i If each element of the array emits a pulse, and each pulse contains K symbols with a dimension of K×1, then the transmitted waveform of the i-th sub-array is an M-shaped waveform. i A matrix of size ×K, and:

[0025]

[0026] The received signal matrix formed by each of the sub-receiver arrays is represented as follows:

[0027]

[0028] in, This represents the l-th snapshot signal received by the n sub-receiver arrays. Let P be the reflection coefficients of P targets, following a distribution. Z (l) This represents zero-mean complex Gaussian white noise, following the distribution CN~(0,σ). 2 I N ), transmit signal and:

[0029]

[0030]

[0031] After performing matched filtering and vectorization on the received signal, we obtain:

[0032]

[0033] in, ζ (l) Represents the noise vector. Represents the Kronecker product;

[0034] R ζζ =σ 2 I MN

[0035] Because of A i1 A i2 ,...,A im Each contains the DOA information of the i-th sub-receiver array, which is used to extract φ. i The information is obtained by combining m matrices:

[0036]

[0037] With K i (φ i ) represents K i(φ i ,θ1,...,θ m If the data vectors of the n sub-receiver arrays are combined, then:

[0038]

[0039] in, The covariance matrix of the received signal represents the combination of received data vectors of the i-th sub-receiver array.

[0040]

[0041]

[0042] Among them, R b =E[b (l) b (l)H ], Let represent the noise covariance matrix of the i-th sub-receiver array.

[0043] According to the method of the first aspect of the present invention, in step S2, the covariance matrix of the received signal is divided into n matrices with the same number of columns:

[0044]

[0045] …

[0046]

[0047] H i Represented as:

[0048]

[0049] The above n matrices are tensors The mode-3 slice, and J = max(MN1,...,MN) n The tensor is represented by slices after multithreaded generalized singular value decomposition (GSVD) and zero-padding for undefined elements.

[0050]

[0051] Where k∈{1,...,n} is a tensor The k-th slice, P is the number of targets to be detected. It is a non-negative diagonal matrix; diagonal matrix C k The diagonal elements are stacked to form a row vector of matrix C, C k =diag(C(k,:)); then the optimization problem is obtained:

[0052]

[0053] Using the ALS algorithm, in C k With A fixed, B k Optimize in B k Under fixed conditions, for C k Optimize with A, iterate multiple times to find the required signal subspace B. k =A((MN) k-1 +1):MN k ,:).

[0054] According to the method of the first aspect of the present invention, in step S2, the variables in the ALS algorithm are initialized, and A is initialized to... The left singular matrices, C1,...,C k All initialized to I P By adding l1 norm constraints to the optimization problem expression, the following equation is solved to update B. k :

[0055]

[0056] The following was obtained through an iterative shrinkage threshold algorithm:

[0057] B k =soft λt (B k (old) +α k (H k H -AC k (B k (old) ) H ) H AC k )

[0058] Among them, soft λt (·) is the soft thresholding operation function, B k (old) Indicates B in the previous iteration k matrix, Indicates a fixed step value;

[0059] set up Fixed B k Update matrices A and C k The specific steps are as follows:

[0060] Use n Tensors are stacked as mode-3 slices. tensor The constrained CP decomposition of the front slice can be expressed as:

[0061]

[0062] tensor The mode-1 and mode-3 expansions satisfy:

[0063]

[0064]

[0065] Where, the row vectors of C contain matrix C k The least-squares solution for the diagonal elements of matrices A and C is expressed as follows:

[0066]

[0067]

[0068] When the number of iterations exceeds the preset maximum number of iterations or the residual When the value falls below a predefined threshold, it indicates that the loop has entered a convergence state and stops. Let B be the residual from the previous iteration. k =A((MN) k-1 +1):MN k ,:) represents the signal subspace of the k-th sub-receiver array.

[0069] A second aspect of this invention proposes an ALS-based RGSVD distributed MIMO radar direction finding system. ALS stands for Alternating Least Squares Algorithm, RGSVD for Low-Complexity Generalized Singular Value Decomposition, and MIMO radar for Multiple-Input Multiple-Output radar. The system includes a processing unit configured to execute:

[0070] Step S1: By performing matched filtering and vectorization processing on the echo signal of the receiving array of the distributed MIMO radar, the echo signal model η of the distributed MIMO radar is constructed. (l) And according to the echo signal model η (l) Calculate the covariance matrix R of the echo signal. ηη ;

[0071] Step S2: Apply RGSVD to the covariance matrix R of the echo signal. ηη The signal subspace of the receiving array is obtained by decomposition. The joint matrix decomposition is achieved by iterative update using ALS. The signal subspace of the transmitting array is obtained by permutation matrix.

[0072] Step S3: Substitute the calculated receiver array signal subspace and transmitter array signal subspace into the ESPRIT algorithm to perform joint estimation and matching of multiple DOAs and DODs for each target;

[0073] Where DOA represents the angle of arrival and DOD represents the angle of departure.

[0074] According to the system of the second aspect of the present invention, in step S1, the distributed MIMO radar includes m sub-transmit arrays and n sub-receive arrays, each sub-array being arranged in a uniform linear array configuration; wherein:

[0075] The number of elements in each of the sub-emission arrays are M1, M2…M m The element spacing is d t Then the total number of transmitting array elements is M = M1 + M2 + ... + M m The number of array elements in each of the sub-receiver arrays are N1, N2…N n The element spacing is d r Then the total number of receiving array elements is N = N1 + N2 + ... + N n And the element spacing satisfies d. t (d r )≤λ / 2, where λ represents the wavelength of the transmitted signal;

[0076] All transmitted signals are reflected by P targets and then received by the sub-receiving array. The DOA of the p-th target with respect to the i-th receiving sub-array is denoted as φ. ip The DOD of the i-th emitter subarray is denoted as θ. ip The target reflectance coefficient is β p Then the vectors of DOD and DOA of P targets with respect to the i-th array are represented as θ. i =[θ i1 θ i2 …θ iP ] T and φ i =[φ i1 φ i2 …φ iP ] T ;

[0077] The steering vector of the i-th sub-receiver array about the p-th target is:

[0078]

[0079] The manifold matrix of the i-th sub-receiver array is:

[0080] A ri (φ i )=[a ri (φi1 ) a ri (φ i2 ...a ri (φ iP )]

[0081] The steering vector of the i-th sub-emission array about the p-th target is:

[0082]

[0083] The manifold matrix of the i-th sub-emission array is:

[0084] A ti (θ i )=[a ti (θ i1 ) a ti (θ i2 ...a ti (θ iP )]

[0085] by The m-th sub-emission matrix represents the i-th sub-emission matrix. i If each element of the array emits a pulse, and each pulse contains K symbols with a dimension of K×1, then the transmitted waveform of the i-th sub-array is an M-shaped waveform. i A matrix of size ×K, and:

[0086]

[0087] The received signal matrix formed by each of the sub-receiver arrays is represented as follows:

[0088]

[0089] in, This represents the l-th snapshot signal received by the n sub-receiver arrays. Let P be the reflection coefficients of P targets, following a distribution. Z (l) This represents zero-mean complex Gaussian white noise, following the distribution CN~(0,σ). 2 I N ), transmit signal and:

[0090]

[0091]

[0092] After performing matched filtering and vectorization on the received signal, we obtain:

[0093]

[0094] in, ζ (l) Represents the noise vector. Represents the Kronecker product;

[0095] R ζζ =σ 2 I MN

[0096] Because of A i1 A i2 ,...,A im Each contains the DOA information of the i-th sub-receiver array, which is used to extract φ. i The information is obtained by combining m matrices:

[0097]

[0098] With K i (φ i ) represents K i (φ i ,θ1,...,θ m If the data vectors of the n sub-receiver arrays are combined, then:

[0099]

[0100] in, The covariance matrix of the received signal represents the combination of received data vectors of the i-th sub-receiver array.

[0101]

[0102]

[0103] Among them, R b =E[b (l) b (l)H ], Let represent the noise covariance matrix of the i-th sub-receiver array.

[0104] According to the system of the second aspect of the present invention, in step S2, the covariance matrix of the received signal is divided into n matrices with the same number of columns:

[0105]

[0106] …

[0107]

[0108] H i Represented as:

[0109]

[0110] The above n matrices are tensors The mode-3 slice, and J = max(MN1,...,MN) n The tensor is represented by slices after multithreaded generalized singular value decomposition (GSVD) and zero-padding for undefined elements.

[0111]

[0112] Where k∈{1,...,n} is a tensor The k-th slice, P is the number of targets to be detected. It is a non-negative diagonal matrix; diagonal matrix C k The diagonal elements are stacked to form a row vector of matrix C, C k =diag(C(k,:)); then the optimization problem is obtained:

[0113]

[0114] Using the ALS algorithm, in C k With A fixed, B k Optimize in B k Under fixed conditions, for C k Optimize with A, iterate multiple times to find the required signal subspace B. k =A((MN) k-1 +1):MN k ,:).

[0115] According to the system of the second aspect of the present invention, in step S2, the variables in the ALS algorithm are initialized, and A is initialized to... The left singular matrices, C1,...,C k All initialized to I P By adding l1 norm constraints to the optimization problem expression, the following equation is solved to update B. k :

[0116]

[0117] The following was obtained through an iterative shrinkage threshold algorithm:

[0118] B k =soft λt (B k (old) +α k (H k H -AC k (B k(old) ) H ) H AC k )

[0119] Among them, soft λt (·) is the soft thresholding operation function, B k (old) Indicates B in the previous iteration k matrix, Indicates a fixed step value;

[0120] set up Fixed B k Update matrices A and C k The specific steps are as follows:

[0121] Use n Tensors are stacked as mode-3 slices. tensor The constrained CP decomposition of the front slice can be expressed as:

[0122]

[0123] tensor The mode-1 and mode-3 expansions satisfy:

[0124]

[0125]

[0126] Where the row vectors of C contain matrix C k The least-squares solution for the diagonal elements of matrices A and C is expressed as follows:

[0127]

[0128]

[0129] When the number of iterations exceeds the preset maximum number of iterations or the residual When the value falls below a predefined threshold, it indicates that the loop has entered a convergence state and stops. Let B be the residual from the previous iteration. k =A((MN) k-1 +1):MN k ,:) represents the signal subspace of the k-th sub-receiver array.

[0130] A third aspect of this invention discloses an electronic device. The electronic device includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements an ALS-based RGSVD distributed MIMO radar direction finding method according to the first aspect of this disclosure.

[0131] A fourth aspect of this invention discloses a computer-readable storage medium. The computer-readable storage medium stores a computer program, which, when executed by a processor, implements an ALS-based RGSVD distributed MIMO radar direction finding method according to the first aspect of this disclosure.

[0132] In summary, this application, from the perspective of improving the direction finding accuracy of the system under low signal-to-noise ratio conditions, designs a direction finding algorithm for distributed MIMO radar systems. It mainly utilizes the generalized singular value decomposition technique to jointly decompose the covariance matrix of the echo signals of multiple receiving arrays of the system, effectively applying the intrinsic correlation of the data to achieve better denoising performance. The more accurate signal subspace is then input into the ESPRIT algorithm to realize the system's joint high-precision direction finding of multiple targets' DOA and DOD. Attached Figure Description

[0133] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0134] Figure 1 This is a flowchart of the joint direction finding process for bistatic MIMO radar using TSVD in existing technologies.

[0135] Figure 2 This is a diagram illustrating the echo signal model of a distributed MIMO radar system according to an embodiment of the present invention.

[0136] Figure 3 This is a flowchart of the GSVD joint direction finding for distributed MIMO radar according to an embodiment of the present invention.

[0137] Figure 4 This is a schematic diagram showing the estimation results of θ1 and φ1 according to an embodiment of the present invention.

[0138] Figure 5 This is a schematic diagram showing the estimation results of θ2 and φ2 according to an embodiment of the present invention.

[0139] Figure 6 This is a schematic diagram of the matching results of φ1 and φ2 according to an embodiment of the present invention.

[0140] Figure 7 This diagram illustrates the total root mean square error of four algorithms under different signal-to-noise ratios according to an embodiment of the present invention.

[0141] Figure 8This is a schematic diagram of the root mean square error of φ1 according to an embodiment of the present invention.

[0142] Figure 9 This is a schematic diagram of the root mean square error of φ2 according to an embodiment of the present invention.

[0143] Figure 10 This is a schematic diagram of the root mean square error of θ1 according to an embodiment of the present invention.

[0144] Figure 11 This is a schematic diagram of the root mean square error of θ2 according to an embodiment of the present invention.

[0145] Figure 12 This is a schematic diagram of the total root mean square error of four algorithms under different snapshot numbers according to an embodiment of the present invention.

[0146] Figure 13 This is a structural diagram of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0147] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0148] Specific Example 1

[0149] Step 1: Establishing a Distributed MIMO Radar Echo Signal Model: First, the system echo signal model is obtained by performing matched filtering and vectorization processing on the echo signal of the distributed MIMO radar receiving array. Then, based on the echo signal model η... (l) The covariance matrix R of the echo signal is obtained. ηη ;

[0150] Step 2: Use generalized singular value decomposition (SVFD) to decompose the echo signal covariance matrix to obtain the signal subspaces U of each receiving array. S The process involves using the alternating least squares algorithm to iteratively update each submatrix to achieve joint matrix decomposition.

[0151] Step 3: Substitute the calculated signal subspace into the ESPRIT algorithm to perform joint estimation and matching of multiple DOAs and DODs for each target.

[0152] Constructing a signal model

[0153] First, establish a distributed MIMO echo signal model, such as Figure 2As shown: The distributed MIMO radar consists of m sub-transmitter arrays and n sub-receiver arrays, each sub-array being a uniform linear array. The number of elements in each sub-transmitter array is M1, M2…M… m The element spacing is d t The total number of transmitting array elements is M = M1 + M2 + ... + M m The number of array elements in each sub-receiver array is N1, N2…N. n The element spacing is d r The total number of receiving array elements is N = N1 + N2 + ... + N n The spacing between array elements satisfies d t (d r φ ≤ λ / 2, where λ represents the wavelength of the transmitted signal. All transmitted signals are reflected by P targets and then received by the sub-receiver array. The DOA of the p-th target with respect to the i-th receiving sub-array is denoted as φ. ip The DOD of the i-th emitter subarray is denoted as θ. ip The target reflectance coefficient is expressed as β. p Therefore, the vectors of DOD and DOA of P targets with respect to the i-th array are represented as θ. i =[θ i1 θ i2 …θ iP ] T and φ i =[φ i1 φ i2 …φ iP ] T .

[0154] The steering vector of the i-th sub-receiver array about the p-th target is:

[0155]

[0156] The manifold matrix of the i-th sub-receiver array is:

[0157] A ri (φ i )=[a ri (φ i1 ) a ri (φ i2 ...a ri (φ iP )]#(2)

[0158] The steering vector of the i-th sub-emission array about the p-th target is:

[0159]

[0160] The manifold matrix of the i-th sub-emission array is:

[0161] A ti (θ i )=[a ti (θ i1 ) a ti (θ i2 ...a ti (θ iP )]#(4)

[0162] use Describes the m-th sub-emission matrix of the i-th sub-emission matrix. i A pulse emitted by each array element has K code elements, thus forming a K×1 vector. The transmitted waveform of the i-th sub-array is an M-shaped waveform. i A matrix of size ×K, i.e.:

[0163]

[0164] The received signal matrix of the receiving subarray can be represented as:

[0165]

[0166] in: This represents the l-th snapshot signal received by n receiver arrays. Let P be the reflection coefficients of P targets, following a distribution. Z (l) This represents zero-mean complex Gaussian white noise, following the distribution CN~(0,σ). 2 I N ), transmit signal

[0167] After performing matched filtering and vectorization on the received signal, we obtain:

[0168]

[0169] in, ζ (l) Represents the noise vector. This represents the Kronecker product.

[0170] R ζζ =σ 2 I MN #(8)

[0171] Because of A i1 A i2 ,...,A im Each of these contains the DOA information of the i-th sub-receiver array, therefore, to extract φ i The information is used to combine these m matrices to obtain the matrix:

[0172]

[0173] K will be mentioned later. i (φ i ,θ1,...,θ m (abbreviated as K) i (φ i Similarly, the data vectors of the n sub-receiver arrays can be combined to divide the received signal in equation (7) into the following form:

[0174]

[0175] in Let represent the combination of received data vectors from the i-th sub-receiver array. Therefore, the covariance matrix of the received signal can be expressed as:

[0176]

[0177] Substituting equations (7) and (9) into equation (11), we derive:

[0178]

[0179] Where R b =E[b (l) b (l)H ], Let represent the noise covariance matrix of the i-th sub-receiver array.

[0180] The ALS-based R-GSVD algorithm (e.g.) Figure 3 (As shown)

[0181] The covariance matrix of the received signal is divided into n matrices with the same number of columns:

[0182]

[0183] From equation (12), we can see that H i It can be represented as:

[0184]

[0185] The above n matrices can be viewed as tensors The mode-3 slice, where J = max(MN1,...,MN n ), fill the undefined elements in equation (13) with zeros.

[0186] The tensor, after undergoing multithreaded generalized singular value decomposition, is represented by slices as follows:

[0187]

[0188] Where k∈{1,...,n} is a tensor The k-th slice, P is the number of targets to be detected. It is a non-negative diagonal matrix. Furthermore, let the matrix... diagonal matrix C k The diagonal elements are stacked to form a row vector of matrix C, i.e., C0 k =diag(C(k,:)).

[0189] To minimize the impact of noise and obtain a more accurate signal subspace, the optimization problem to be solved is formulated as follows:

[0190]

[0191] This optimization problem is highly consistent with the PARAFAC2 model; therefore, to solve this optimization problem, the ALS algorithm can be used in C. k With A fixed, B k Optimize, and then in B k Under fixed conditions, for C k Optimize along with A, iterate multiple times to finally solve the function optimization problem, and find the required signal subspace B. k =A((MN) k-1 +1):MN k ,:).

[0192] First, initialize the variables in the algorithm: initialize A to... The left singular matrices, C1,...,C k All initialized to I P Then, by adding the l1 norm constraint to equation (16), equation (17) is solved to update B. k .

[0193]

[0194] This optimization problem can be solved using an iterative shrinkage threshold algorithm:

[0195] B k =soft λt (B k (old) +α k (H k H -AC k (B k (old) ) H ) H AC k )#(18)

[0196] Among them, soft λt (·) is the soft threshold operation function. B k (old) Indicates B in the previous iteration k matrix, This indicates a fixed step value.

[0197] set up Fixed B k Update matrices A and C k The specific steps are as follows:

[0198] Use n Tensors are stacked as mode-3 slices. tensor The constrained CP decomposition of the front slice can be expressed as:

[0199]

[0200] Therefore, tensor The mode-1 and mode-3 expansions satisfy:

[0201]

[0202]

[0203] The row vectors of C contain the matrix C. k The diagonal elements of A and C. Therefore, the least squares solution of matrices A and C can be expressed as follows:

[0204]

[0205]

[0206] This process utilizes the direct fitting algorithm for solving the PARAFAC2 model. In the indirect fitting algorithm of PARAFAC2, derived data is used to fit the original matrix, which cannot yield matrix B. k The direct fitting algorithm described above uses actual data for fitting and can directly calculate matrix B. k Furthermore, the direct fitting algorithm is easier to tune when constraints are imposed on parameters (such as nonnegativity constraints) and when missing data is replaced with the optimal model estimate. It is also easier to generalize to higher-order datasets and is more efficient.

[0207] When the number of iterations exceeds the preset maximum number of iterations, or the residual If the value is less than a predefined threshold, it indicates that the algorithm has converged and the loop stops. This represents the residual from the previous iteration. The algorithm is used to obtain B. k =A((MN) k-1 +1):MN k ,:) represents the signal subspace of the k-th sub-receiver array. The main steps of the algorithm are summarized in Table 1 below:

[0208] Table 1. Detailed flowchart of the ALS-based R-GSVD algorithm

[0209]

[0210]

[0211]

[0212] Specific Example 2

[0213] A comparative analysis of algorithm performance is conducted using a dual-transmit, dual-receive MIMO radar as an example:

[0214] Consider a dual-transmit, dual-receive MIMO radar system, where both the transmitting and receiving arrays are uniform linear arrays, and the element spacing is set to half the wavelength of the transmitted signal, i.e., d. t =d r =λ0 / 2, where λ0 is the wavelength of the transmitted signal. The reflection coefficient β of P targets. p The target angle estimation function (p = 1, ..., P) is modeled as a zero-mean Gaussian random variable with unit variance using the randn function. The performance is verified through 500 Monte Carlo experiments, with different detection targets and snapshot numbers set for each experiment. In the simulation, the signal-to-noise ratio (SNR) is defined as the ratio of the total power of the echo signal received by the receiving array to the ambient noise power.

[0215] Joint estimation of DOA and DOD effects

[0216] The number of transmit and receive arrays is set to M1=6, M2=7 and N1=4, N2=5, respectively. The number of iterations is set to no more than 5000 and the residual predefined threshold is 1e. -3 As the stopping criterion for the algorithm, the number of snapshots is set to L=200, and a total of P=6 targets are set. The DOD and DOA of these six targets are set as follows:

[0217] θ1=[-60 ° -45 ° 30 ° 50 ° 35 ° 60 ° ] T

[0218] θ2=[-45° -25 ° 25 ° 65 ° 55 ° 15 ° ] T

[0219] φ1=[-40 ° -20 ° 30 ° ,40 ° 60 ° 70 ° ] T

[0220] φ2=[-55 ° -35 ° 35 ° 45 ° 65 ° 75 ° ] T

[0221] The estimated results of conducting 500 Monte Carlo experiments are as follows: Figures 4 to 6 As shown. From Figures 4 to 6 As can be seen, in a spatial white noise environment with a signal-to-noise ratio of 5dB, the target's DOD relative to the transmitting array and DOA relative to the receiving array can be accurately and effectively identified, and the four DODs and DOAs of the six targets can be accurately matched. Meanwhile, the total root mean square error of the four target angle estimates measured in the simulation experiment is approximately 0.5204°, demonstrating good angle estimation performance and accuracy in a 5dB white noise environment.

[0222] Specific Example 3

[0223] Algorithm performance comparison analysis

[0224] Performance comparison under different signal-to-noise ratios

[0225] Within the signal-to-noise ratio (SNR) range of [-10, -8, -6, -4, 0, 5, 10, 15, 20], the total root mean square error (RMSE) and the RMSE of each of the four angles were calculated using the R-GSVD algorithm, the cross-covariance matrix TSVD algorithm, and the improved TSVD algorithm, respectively. The performance was compared using the Cramer-Rao boundary as a reference. In this experiment, the number of snapshots was set to 200, and three detection targets were set:

[0226] θ1=[30 ° 20 ° ,40 ° ] T θ2=[55 ° 65° 50 ° ] T

[0227] φ1=[30 ° ,40 ° 50 ° ] T φ2=[65 ° 55 ° 75 ° ] T

[0228] The target's angle relative to both transmit array 1 and receive array 1 is no greater than 50 degrees, and its angle relative to both transmit array 2 and receive array 2 is no less than 50 degrees. The results of 500 Monte Carlo experiments under each signal-to-noise ratio condition are as follows: Figures 7 to 11 The dotted curve represents the R-GSVD algorithm, the lower triangular curve represents the cross-covariance matrix TSVD algorithm, the diamond curve represents the improved TSVD algorithm, and the left triangular curve represents the CRB of the system direction finding error under the experimental conditions.

[0229] from Figure 5 As can be seen, at higher signal-to-noise ratios (SNRs), the R-GSVD algorithm performs essentially the same as the improved TSVD algorithm, and is slightly better than the cross-covariance matrix TSVD algorithm. However, under low SNR conditions, the R-GSVD algorithm's error is slightly smaller than the improved TSVD algorithm, with an error reduction of approximately 0.5° at an SNR of -5dB.

[0230] Depend on Figures 5 to 9 It is known that the R-GSVD algorithm performs better in estimating φ1, with an error approximately 0.5° smaller than the TSVD-based algorithm. However, under low signal-to-noise ratio (SNR) conditions, the R-GSVD algorithm's estimation performance for φ2 is similar to or even slightly larger than that of the TSVD algorithm. As the SNR increases, the performance of the cross-covariance matrix TSVD algorithm rapidly declines, while the performance of the other two algorithms is similar. This is due to the error in signal subspace decomposition caused by the insufficient application of the correlation between the received data from the two receiving arrays in the cross-covariance matrix TSVD algorithm. The R-GSVD algorithm significantly outperforms the two TSVD-based algorithms in estimating DOD, with an estimation error approximately 0.6° smaller for θ1 and approximately 0.7° smaller for θ2 at -5dB conditions. With increasing SNR, the performance of the other two algorithms is slightly better than that of the cross-covariance matrix TSVD algorithm. Therefore, the R-GSVD algorithm designed in this patent fully utilizes the correlation between all received data, thus achieving superior estimation performance.

[0231] Performance comparison at different snapshot counts

[0232] With a signal-to-noise ratio of 0dB, the target design is the same as in Section 5.2.1. The RMSE of the three algorithms is calculated for each snapshot number L = [50, 100, 150, 200, 250, 300, 350, 400, 450, 500]. The results of 500 Monte Carlo experiments under different snapshot numbers are as follows: Figure 12 .

[0233] Depend on Figure 10 As can be seen, with the increase of the number of snapshots, the intrinsic correlation of the signal in the covariance matrix increases, the impact of noise on the direction-finding accuracy decreases, and the direction-finding error of all three algorithms decreases. The R-GSVD algorithm designed in this patent makes fuller use of the intrinsic correlation of the data in the covariance matrix, slightly outperforming the other two algorithms. Therefore, within a certain range, with the increase of the number of snapshots, the estimation error of the R-GSVD algorithm decreases faster than the other two algorithms.

[0234] Specific Example 4

[0235] Update B in the algorithm k Part of B can be updated by minimizing equation (24). k :

[0236]

[0237] When constraint B exists k ·B k H When = I, for B k By optimizing, minimizing equation (24) can be equivalent to maximizing equation (25):

[0238]

[0239] The solution process for this optimization problem is as follows: First, for Perform singular value decomposition to obtain its left singular matrix U k and the right singular matrix V k Then we can obtain B that maximizes equation (25). k , can be represented as:

[0240]

[0241] In the actual optimization process of equation (25), since the number of detected targets is P, therefore, in the optimization process of equation (25)... After performing singular value decomposition, the singular vectors corresponding to the top P largest singular values ​​are used to form U. k and V k And then find B k The optimization result is as follows:

[0242]

[0243] However, the algorithm used for updating using this method has higher complexity and longer computation time.

[0244] A second aspect of this invention proposes an ALS-based RGSVD distributed MIMO radar direction finding system. ALS stands for Alternating Least Squares Algorithm, RGSVD for Low-Complexity Generalized Singular Value Decomposition, and MIMO radar for Multiple-Input Multiple-Output radar. The system includes a processing unit configured to execute:

[0245] Step S1: By performing matched filtering and vectorization processing on the echo signal of the receiving array of the distributed MIMO radar, the echo signal model η of the distributed MIMO radar is constructed. (l) And according to the echo signal model η (l) Calculate the covariance matrix R of the echo signal. ηη ;

[0246] Step S2: Apply RGSVD to the covariance matrix R of the echo signal. ηη The signal subspace of the receiving array is obtained by decomposition. The joint matrix decomposition is achieved by iterative update using ALS. The signal subspace of the transmitting array is obtained by permutation matrix.

[0247] Step S3: Substitute the calculated receiver array signal subspace and transmitter array signal subspace into the ESPRIT algorithm to perform joint estimation and matching of multiple DOAs and DODs for each target;

[0248] Where DOA represents the angle of arrival and DOD represents the angle of departure.

[0249] A third aspect of this invention discloses an electronic device. The electronic device includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements an ALS-based RGSVD distributed MIMO radar direction finding method according to the first aspect of this disclosure.

[0250] Figure 13 This is a structural diagram of an electronic device according to an embodiment of the present invention, such as... Figure 13As shown, the electronic device includes a processor, memory, communication interface, display screen, and input device connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, Near Field Communication (NFC), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input device can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the device's casing, or an external keyboard, touchpad, or mouse.

[0251] Those skilled in the art will understand that Figure 13 The structure shown is merely a structural diagram of the part related to the technical solution of this disclosure and does not constitute a limitation on the electronic device to which the solution of this application is applied. The specific electronic device may include more or fewer components than shown in the figure, or combine certain components, or have different component arrangements.

[0252] A fourth aspect of this invention discloses a computer-readable storage medium. The computer-readable storage medium stores a computer program, which, when executed by a processor, implements an ALS-based RGSVD distributed MIMO radar direction finding method according to the first aspect of this disclosure.

[0253] In summary, this application, from the perspective of improving the direction finding accuracy of the system under low signal-to-noise ratio conditions, designs a direction finding algorithm for distributed MIMO radar systems. It mainly utilizes the generalized singular value decomposition technique to jointly decompose the covariance matrix of the echo signals of multiple receiving arrays of the system, effectively applying the intrinsic correlation of the data to achieve better denoising performance. The more accurate signal subspace is then input into the ESPRIT algorithm to realize the system's joint high-precision direction finding of multiple targets' DOA and DOD.

[0254] Please note that the technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments have been described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification. The above embodiments only illustrate several implementation methods of this application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A distributed MIMO radar direction finding method based on ALS using RGSVD, characterized in that: ALS stands for Alternating Least Squares, RGSVD stands for Low Complexity Generalized Singular Value Decomposition, and MIMO radar stands for Multiple Input Multiple Output radar. The method includes: Step S1: By performing matched filtering and vectorization processing on the echo signal of the receiving array of the distributed MIMO radar, the echo signal model η of the distributed MIMO radar is constructed. (l) And according to the echo signal model η (l) Calculate the covariance matrix R of the echo signal. ηη ; Step S2: Apply RGSVD to the covariance matrix R of the echo signal. ηη The signal subspace of the receiving array is obtained by decomposition. The joint matrix decomposition is achieved by iterative update using ALS. The signal subspace of the transmitting array is obtained by permutation matrix. Step S3: Substitute the calculated receiver array signal subspace and transmitter array signal subspace into the ESPRIT algorithm to perform joint estimation and matching of multiple DOAs and DODs for each target; Where DOA represents the angle of arrival and DOD represents the angle of departure.

2. The RGSVD distributed MIMO radar direction finding method based on ALS according to claim 1, characterized in that, In step S1, the distributed MIMO radar includes m sub-transmit arrays and n sub-receive arrays, each sub-array being arranged in a uniform linear array configuration; wherein: The number of elements in each of the sub-emission arrays are M1, M2…M m The spacing between the transmitting array elements is d t Then the total number of transmitting array elements is M = M1 + M2 + ... + M m The number of array elements in each of the sub-receiver arrays are N1, N2…N n The spacing between the receiving array elements is d r Then the total number of receiving array elements is N = N1 + N2 + ... + N n And the spacing between the transmitting array elements satisfies d. t ≤λ / 2, the spacing between receiving array elements satisfies d r ≤λ / 2, where λ represents the wavelength of the transmitted signal; All transmitted signals are reflected by P targets and then received by the sub-receiving array. The DOA of the p-th target with respect to the i-th receiving sub-array is denoted as φ. ip The DOD of the i-th emitter subarray is denoted as θ. ip The target reflectance coefficient is β p Then the vectors of DOD and DOA of P targets with respect to the i-th array are represented as θ. i =[θ i1 θ i2 …θ iP ] T and φ i =[φ i1 φ i2 …φ iP ] T ; The steering vector of the i-th sub-receiver array about the p-th target is: The manifold matrix of the i-th sub-receiver array is: A ri (f i )=[a ri (f i1 ) a ri (f i2 ) … a ri (f iP ) The steering vector of the i-th sub-emission array about the p-th target is: The manifold matrix of the i-th sub-emission array is: A ti (i i )=[a ti (i i1 ) a ti (i i2 ) … a ti (i iP )] by The m-th sub-emission matrix represents the i-th sub-emission matrix. i If each element of the array emits a pulse, and each pulse contains K symbols with a dimension of K×1, then the transmitted waveform of the i-th sub-array is an M-shaped waveform. i A matrix of size ×K, and: The received signal matrix formed by each of the sub-receiver arrays is represented as follows: in, This represents the l-th snapshot signal received by the n sub-receiver arrays. Let P be the reflection coefficients of P targets, following a distribution. Z (l) This represents zero-mean complex Gaussian white noise, following the distribution CN~(0,σ). 2 I N ), transmit signal and: After performing matched filtering and vectorization on the received signal, we obtain: in, ζ (l) Represents the noise vector. Represents the Kronecker product; R ζζ =s 2 I MN Because of A i1 A i2 ,...,A im Each contains the DOA information of the i-th sub-receiver array, which is used to extract φ. i The information is obtained by combining m matrices: With K i (φ i ) represents K i (φ i ,θ1,...,θ m If the data vectors of the n sub-receiver arrays are combined, then: in, Let represent the combination of received data vectors of the i-th sub-receiver array, and let the covariance matrix of the received signal be: Among them, R b =E[b (l) b (l)H ], Let represent the noise covariance matrix of the i-th sub-receiver array.

3. The RGSVD distributed MIMO radar direction finding method based on ALS according to claim 2, characterized in that, In step S2, the covariance matrix of the received signal is divided into n matrices with the same number of columns: H i Represented as: The above n matrices are tensors The mode-3 slice, and J = max(MN1,...,MN) n The tensor is represented by slices after multithreaded generalized singular value decomposition (GSVD) and zero-padding for undefined elements. Where k∈{1,...,n} is a tensor The k-th slice, P is the number of targets to be detected. It is a non-negative diagonal matrix; diagonal matrix C k The diagonal elements are stacked to form a row vector of matrix C, C k =diag(C(k,:)); then the optimization problem is obtained: Using the ALS algorithm, in C k With A fixed, B k Optimize in B k Under fixed conditions, for C k Optimize with A, iterate multiple times to find the required signal subspace B. k =A((MN) k-1 +1):MN k ,:).

4. The ALS-based RGSVD distributed MIMO radar direction finding method according to claim 3, characterized in that, In step S2, the variables in the ALS algorithm are initialized, and A is initialized to... The left singular matrices, C1,...,C k All initialized to I P By adding l1 norm constraints to the optimization problem expression, the following equation is solved to update B. k : The following was obtained through an iterative shrinkage threshold algorithm: B k =soft λt (B k (old) +α k (H k H -AC k (B k (old) ) H ) H AC k ) Among them, soft λt (·) is the soft thresholding operation function, B k (old) Indicates B in the previous iteration k matrix, Indicates a fixed step value; set up Fixed B k Update matrices A and C k The specific steps are as follows: Use n Tensors are stacked as mode-3 slices. tensor The constrained CP decomposition of the front slice can be expressed as: tensor The mode-1 and mode-3 expansions satisfy: Where the row vectors of C contain matrix C k The least-squares solution for the diagonal elements of matrices A and C is expressed as follows: When the number of iterations exceeds the preset maximum number of iterations or the residual When the value falls below a predefined threshold, it indicates that the loop has entered a convergence state and stops. Let B be the residual from the previous iteration. k =A((MN) k-1 +1):MN k ,:) represents the signal subspace of the k-th sub-receiver array.

5. An ALS-based RGSVD distributed MIMO radar direction finding system, characterized in that: ALS stands for Alternating Least Squares, RGSVD stands for Low Complexity Generalized Singular Value Decomposition, and MIMO radar stands for Multiple Input Multiple Output radar. The system includes a processing unit configured to perform: Step S1: By performing matched filtering and vectorization processing on the echo signal of the receiving array of the distributed MIMO radar, the echo signal model η of the distributed MIMO radar is constructed. (l) And according to the echo signal model η (l) Calculate the covariance matrix R of the echo signal. ηη ; Step S2: Apply RGSVD to the covariance matrix R of the echo signal. ηη The signal subspace of the receiving array is obtained by decomposition. The joint matrix decomposition is achieved by iterative update using ALS. The signal subspace of the transmitting array is obtained by permutation matrix. Step S3: Substitute the calculated receiver array signal subspace and transmitter array signal subspace into the ESPRIT algorithm to perform joint estimation and matching of multiple DOAs and DODs for each target; Where DOA represents the angle of arrival and DOD represents the angle of departure.

6. The ALS-based RGSVD distributed MIMO radar direction finding system according to claim 5, characterized in that, In step S1, the distributed MIMO radar includes m sub-transmit arrays and n sub-receive arrays, each sub-array being arranged in a uniform linear array configuration; wherein: The number of elements in each of the sub-emission arrays are M1, M2…M m The spacing between the transmitting array elements is d t Then the total number of transmitting array elements is M = M1 + M2 + ... + M m The number of array elements in each of the sub-receiver arrays are N1, N2…N n The spacing between the receiving array elements is d r Then the total number of receiving array elements is N = N1 + N2 + ... + N n And the spacing between the transmitting array elements satisfies d. t ≤λ / 2, the spacing between transmitting array elements satisfies d r ≤λ / 2, where λ represents the wavelength of the transmitted signal; All transmitted signals are reflected by P targets and then received by the sub-receiving array. The DOA of the p-th target with respect to the i-th receiving sub-array is denoted as φ. ip The DOD of the i-th emitter subarray is denoted as θ. ip The target reflectance coefficient is β p Then the vectors of DOD and DOA of P targets with respect to the i-th array are represented as θ. i =[θ i1 θ i2 …θ iP ] T and φ i =[φ i1 φ i2 …φ iP ] T ; The steering vector of the i-th sub-receiver array about the p-th target is: The manifold matrix of the i-th sub-receiver array is: A ri (f i )=[a ri (f i1 ) a ri (f i2 ) … a ri (f iP )] The steering vector of the i-th sub-emission array about the p-th target is: The manifold matrix of the i-th sub-emission array is: A ti (i i )=[a ti (i i1 ) a ti (i i2 ) … a ti (i iP )] by The m-th sub-emission matrix represents the i-th sub-emission matrix. i If each element of the array emits a pulse, and each pulse contains K symbols with a dimension of K×1, then the transmitted waveform of the i-th sub-array is an M-shaped waveform. i A matrix of size ×K, and: The received signal matrix formed by each of the sub-receiver arrays is represented as follows: in, This represents the l-th snapshot signal received by the n sub-receiver arrays. Let P be the reflection coefficients of P targets, following a distribution. Z (l) This represents zero-mean complex Gaussian white noise, following the distribution CN~(0,σ). 2 I N ), transmit signal and: After performing matched filtering and vectorization on the received signal, we obtain: in, ζ (l) Represents the noise vector. Represents the Kronecker product; R ζζ =s 2 I MN Because of A i1 A i2 ,...,A im Each contains the DOA information of the i-th sub-receiver array, which is used to extract φ. i The information is obtained by combining m matrices: With K i (φ i ) represents K i (φ i ,θ1,...,θ m If the data vectors of the n sub-receiver arrays are combined, then: in, Let represent the combination of received data vectors of the i-th sub-receiver array, and let the covariance matrix of the received signal be: Among them, R b =E[b (l) b (l)H ], Let represent the noise covariance matrix of the i-th sub-receiver array.

7. The ALS-based RGSVD distributed MIMO radar direction finding system according to claim 6, characterized in that, In step S2, the covariance matrix of the received signal is divided into n matrices with the same number of columns: H i Represented as: The above n matrices are tensors The mode-3 slice, and J = max(MN1,...,MN) n The tensor is represented by slices after multithreaded generalized singular value decomposition (GSVD) and zero-padding for undefined elements. Where k∈{1,...,n} is a tensor The k-th slice, P is the number of targets to be detected. It is a non-negative diagonal matrix; diagonal matrix C k The diagonal elements are stacked to form a row vector of matrix C, C k =diag(C(k,:)); then the optimization problem is obtained: Using the ALS algorithm, in C k With A fixed, B k Optimize in B k Under fixed conditions, for C k Optimize with A, iterate multiple times to find the required signal subspace B. k =A((MN) k-1 +1):MN k ,:).

8. The RGSVD distributed MIMO radar direction finding system based on ALS according to claim 7, characterized in that, In step S2, the variables in the ALS algorithm are initialized, and A is initialized to... The left singular matrices, C1,...,C k All initialized to I P By adding l1 norm constraints to the optimization problem expression, the following equation is solved to update B. k : The following was obtained through an iterative shrinkage threshold algorithm: B k =soft λt (B k (old) +α k (H k H -AC k (B k (old) ) H ) H AC k ) Among them, soft λt (·) is the soft thresholding operation function, B k (old) Indicates B in the previous iteration k matrix, Indicates a fixed step value; set up Fixed B k Update matrices A and C k The specific steps are as follows: Use n Tensors are stacked as mode-3 slices. tensor The constrained CP decomposition of the front slice can be expressed as: tensor The mode-1 and mode-3 expansions satisfy: Where, the row vectors of C contain matrix C k The least-squares solution for the diagonal elements of matrices A and C is expressed as follows: When the number of iterations exceeds the preset maximum number of iterations or the residual When the value falls below a predefined threshold, it indicates that the loop has entered a convergence state and stops. Let B be the residual from the previous iteration. k =A((MN) k-1 +1):MN k ,:) represents the signal subspace of the k-th sub-receiver array.

9. An electronic device, characterized in that, The electronic device includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it implements the RGSVD distributed MIMO radar direction finding method based on ALS as described in any one of claims 1-4.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, which, when executed by a processor, implements the ALS-based RGSVD distributed MIMO radar direction finding method as described in any one of claims 1-4.

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