A 2D-DOA estimation method and system for acoustic vector sensors with arbitrary array structure

Abstract

The present invention provides a method and system for estimating the 2D-DOA of an acoustic vector sensor with an arbitrary array structure, and relates to array sensor direction-finding technology. The present invention obtains a covariance matrix, performs eigendecomposition on the covariance matrix, solves the signal subspace, and then roughly estimates the two-dimensional DOA in the vector information based on the signal subspace using the ESPRIT algorithm. The rough estimation result is then used to perform phase compensation for spatial ambiguity, thereby achieving accurate 2D-DOA estimation for an acoustic vector sensor with an arbitrary array structure. The method utilizes vector sensors to achieve the spatial layout of an arbitrary array, freeing the sensor's element spacing from the half-wavelength limit. The method utilizes not only the vector portion but also the spatial phase information, significantly improving estimation accuracy. It eliminates the need for spectral peak search and additional two-dimensional angle pairing calculations on the covariance matrix of the received signal, significantly reducing computational complexity.

Description

Technical Field

[0001] The present invention relates to an array sensor direction finding technology, and in particular to a 2D-DOA estimation method and system for an acoustic vector sensor with an arbitrary array structure. Background Art

[0002] MIMO radar (Multiple Input Multiple Output) is a radar system that draws on MIMO technology from the communications field. First proposed by Bliss and Forsythe in 2003, the concept of MIMO radar marked a significant advancement in radar technology and sparked significant interest from numerous scholars and research institutions both domestically and internationally. Since then, radar technology has entered a new phase of development. Unlike traditional single-input single-output (SISO) radar or phased array radar, MIMO radar uses multiple active antennas to transmit mutually orthogonal waveforms, enabling the radar system to achieve both spatial and temporal diversity. This creates a virtual aperture, improving angular resolution and enabling the radar system to more accurately determine the target's location. By utilizing multiple independent signal paths, MIMO radar also significantly enhances its anti-interference capabilities. With its rapid development, MIMO radar has demonstrated unique advantages in areas such as air surveillance, ground surveillance, maritime surveillance, and missile guidance.

[0003] In the field of multiple-input, multiple-output (MIMO) radar, direction finding has long been a hot research topic. Many excellent angle estimation methods have emerged, including the Multiple Signal Classification (MUSIC) method, the Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT), the Propagator Method (PM), and tensor-based methods (PARAFAC). The MUSIC algorithm effectively handles high-resolution angle estimation under arbitrary array geometries, but requires a highly complex peak search and high computational cost. The ESPRIT algorithm exploits the invariance of MIMO radar angle estimation and eliminates the need for spectral peak search. However, it does require constructing the covariance matrix of the received signal and its eigenvalue decomposition. The PM algorithm, on the other hand, exploits the internal relationships within the received data to calculate the propagation matrix and then construct the signal or noise subspace, eliminating the need for eigenvalue decomposition. Therefore, the PM algorithm has lower computational complexity than the ESPRIT algorithm. However, the PM algorithm suffers from poor estimation accuracy and may even fail under low signal-to-noise ratio conditions. The PARAFAC algorithm is also used for multi-target positioning based on trilinear decomposition in MIMO radar systems. It can be applied to arrays of arbitrary geometric shapes, but iteration leads to high complexity and high computational cost.

[0004] Currently, direction finding (DF) for co-located MIMO radars is primarily focused on one-dimensional DF using transmit (Tx) and receive (Rx) arrays configured with scalar sensors. To achieve two-dimensional (2D) DF, nonlinear sensor arrays, such as L-shaped arrays, circular arrays, and uniform rectangular arrays (URAs), must be used. However, while traditional sensor arrays can estimate angles, their spatial layout is rigid, making such a fixed layout difficult to implement in certain scenarios. Furthermore, because the DF algorithm for co-located MIMO radars relies on the spatial phase characteristics of the scalar sensor array, the element spacing between sensors must be less than (or equal to) half a wavelength, otherwise angular ambiguity will result.

[0005] Existing technologies, such as vector sensor arrays, offer a promising solution to these challenges, enabling arbitrary array layouts while also ensuring that sensor element spacing is not limited to a half-wavelength. However, current research on vector sensor arrays primarily focuses on the vector components, ignoring the inherent spatial phase information. Furthermore, the vector components are likely to couple with each other, resulting in poorly accurate predictions. Summary of the Invention

[0006] The main purpose of the present invention is to provide a 2D-DOA estimation method and system for an acoustic vector sensor with an arbitrary array structure, so as to solve the technical problem that the prior art only focuses on the information of the vector component part and ignores the original spatial phase information, resulting in poor accuracy of the predicted estimation results.

[0007] To solve the above technical problems, the technical solution adopted by the present invention is: a 2D-DOA estimation method for an acoustic vector sensor of an arbitrary array structure, comprising the following steps:

[0008] S1: The receiving end obtains the covariance matrix and performs eigendecomposition on the covariance matrix to solve the signal subspace. The receiving end uses a vector sensor array, which includes multiple speed receiving sensors.

[0009] S2: Using the signal subspace and the ESPRIT algorithm, a rough estimate of the 2D-DOA is obtained;

[0010] S3: Define the spatial selectivity matrix and multiply it by the left side of the signal subspace matrix. After matrix transformation, solve the spatial ambiguity. Take the diagonal elements to construct the row vector and put it into the initial phase matrix. The initial phase matrix is ​​phased to obtain the ambiguous spatial phase difference matrix.

[0011] S4: Perform phase compensation on the ambiguous spatial phase difference matrix based on the rough estimation result of step 2 to obtain an accurate estimation of 2D-DOA;

[0012] Here, 2D-DOA represents two-dimensional angle of arrival.

[0013] In the preferred embodiment, the specific steps of step S1 are as follows:

[0014] S101: Based on the fact that the positions of the transmitting array element and the receiving array element are set arbitrarily, and the transmitting array element has M There are transmitting sensors and receiving elements N The speed receiving sensor takes the coordinates of the first row of the transmitting array and the receiving array as the reference array element, then relative to the first m The first sending sensor and the n The arrival time differences of the velocity receiving sensors are:

[0015] (1);

[0016] (2);

[0017] Where, For the m The location of the root transmitter sensor, For the n The root velocity receives the position of the sensor, Respectively k The azimuth and elevation of the 2D-DOD of the target, Respectively k The azimuth and elevation of the 2D-DOA of a target; where 2D-DOD represents the two-dimensional wave departure angle;

[0018] S102: Under the narrowband assumption, the spatial response vector of the transmitting sensor array and the receiving sensor array spatial response vector They are:

[0019] (3);

[0020] (4);

[0021] Where, For the m The arrival time difference of the transmitting sensor relative to the reference sensor array element, For the n The arrival time difference of each velocity receiving sensor relative to the reference sensor array element, is the wavelength of the transmitted signal;

[0022] S103: The output formula of the matching filter of the receiving end speed sensor is:

[0023] (5);

[0024] Or:

[0025] (6);

[0026] Where, is the transmit array spatial response matrix, is the receiving array spatial response matrix, , is the received Gaussian white noise matrix, represents the Khatri-Rao product, represents the Kroc inner product; is the polarization response matrix, and:

[0027] , ,

[0028] ;

[0029] S104: Define the matrix according to step S103 :

[0030] (7);

[0031] The obtained signal model is:

[0032] (8);

[0033] Calculate the covariance matrix of the received signal for:

[0034] (9);

[0035] In the formula, the superscript H is the conjugate transpose, L is the number of snaps;

[0036] S105: Solve the signal subspace and calculate the received signal covariance matrix in equation (9): Perform eigendecomposition to obtain the signal subspace. The eigendecomposition formula is:

[0037] (10);

[0038] Where, for A diagonal matrix whose diagonal elements contain K A larger eigenvalue, for K The matrix consists of the eigenvectors corresponding to the largest eigenvalues, for The conjugate transposed matrix of ; for A diagonal matrix whose diagonal elements contain 3 MN - K Smaller eigenvalues, is the matrix composed of the eigenvectors corresponding to the remaining smaller eigenvalues, for The conjugate transposed matrix of ; is regarded as the signal subspace, Considered as a noise subspace;

[0039] Signal subspace and the spatial response vector matrix A The spanned subspace is the same, that is:

[0040] (11);

[0041] In the formula, the matrix , is a non-singular full-rank matrix.

[0042] In the preferred embodiment, the specific steps of step S2 are as follows:

[0043] S201: Set the selectivity matrix, the formula is:

[0044] (12a);

[0045] (12b);

[0046] (12c);

[0047] Where, for The identity matrix, for The identity matrix, for The identity matrix of k OK;

[0048] S202: Multiply the selectivity matrix by the left side of the signal subspace matrix, and let ,Right now:

[0049] (13a);

[0050] (13b);

[0051] (13c);

[0052] Where, Represented as a matrix No. k rows, where:

[0053] ,

[0054] ,

[0055] ;

[0056] S203: According to formula (13), the following matrix can be constructed:

[0057] (14);

[0058] Where, ;

[0059] At the same time: ,but:

[0060] (15);

[0061] In formula (13c), Substituting into formula (15), we can get:

[0062] (16);

[0063] Where, ;

[0064] From formula (16), we can get: ,in represents the generalized inverse of a matrix, Indicates the inverse of the matrix;

[0065] S204: Perform eigendecomposition on the output matrix of step S203 to obtain a rough estimate of 2D-DOA. Specifically, Perform eigendecomposition to obtain eigenvalues and eigenvectors ,Right now:

[0066] (17);

[0067] (18);

[0068] Then the rough estimate of the azimuth and elevation angles of 2D-DOA can be expressed as:

[0069] (19);

[0070] (20);

[0071] Where, abs () indicates the amplitude, angle () indicates phase.

[0072] In the preferred solution, to resolve the spatial ambiguity, step S3 specifically includes:

[0073] S301: Define the following spatial selectivity matrix, which is expressed as:

[0074] (twenty one);

[0075] Where, for The identity matrix of n OK;

[0076] S302: Multiply the selectivity matrix by the left side of the signal subspace matrix, that is:

[0077] (22a);

[0078] (22b);

[0079] Where, , is the receiving array spatial response vector The first line, , is the receiving array spatial response vector The second line of

[0080] S303: And , substituting into formula (22) we get:

[0081] (twenty three);

[0082] at this time:

[0083] ,

[0084] Where, , , , diag () means converting the row matrix into a diagonal matrix, , , ,but:

[0085] (twenty four);

[0086] S304: From formula (23), we can get , then the formula (18) Substituting in:

[0087] , (25);

[0088] (26);

[0089] Similarly, using the selectivity matrix Multiplying both sides of equation (11) at the same time, we can get ,and ,Right now:

[0090] (27);

[0091] at this time , , , , similarly, replace T Substituting into formula (27) we get:

[0092] (28);

[0093] (29);

[0094] Same as above, using the selectivity matrix ,Will The simulation formulas (27) (28) (29) are obtained;

[0095] S305: Take The diagonal elements of the row vector are constructed , , and then this N -1 row vector to be put into the initial phase matrix You can get:

[0096] (30);

[0097] The initial phase matrix Take the phase and get the initial phase difference matrix :

[0098] ;

[0099] Right now: (31);

[0100] in:

[0101] ,

[0102] .

[0103] In the preferred embodiment, step S4 specifically includes:

[0104] S401: First, using the rough estimation results in formulas (19) and (20), that is, obtaining the rough estimation results of the azimuth and elevation angles of the 2D-DOA in step S3, construct the following unambiguous low-precision Poynting vector matrix , the expression is:

[0105] (32);

[0106] Where, and are the rough azimuth and elevation angles respectively;

[0107] S402: Use the unambiguous low-precision Poynting vector matrix By using formula (31), the unambiguous low-precision phase difference matrix is ​​obtained , through the unambiguous low-precision phase difference matrix , get the fuzziness Solve it, that is:

[0108] (33);

[0109] S403: Blur The phase difference matrix compensated to the periodic ambiguity is obtained by equation (34): In the above example, we obtain the unambiguous and high-precision phase difference matrix Right now:

[0110] (34);

[0111] S404: Using the least squares principle, estimate the unambiguous and high-precision Poynting vector matrix ,Right now:

[0112] (35);

[0113] Thus, the azimuth and elevation angles of 2D-DOA are obtained. That is, the azimuth and elevation angle estimation formulas of 2D-DOA are:

[0114] (36);

[0115] (37).

[0116] The preferred solution also includes: using the root mean square error for evaluation, and the calculation formula is:

[0117] (38);

[0118] Where, for Estimates, for Estimates.

[0119] A 2D-DOA estimation system for an acoustic vector sensor with an arbitrary array structure, applicable to the 2D-DOA estimation method for an acoustic vector sensor with an arbitrary array structure, comprising:

[0120] A signal subspace module is used to obtain a covariance matrix at the receiving end, perform eigendecomposition on the covariance matrix, and solve the signal subspace; wherein the receiving end adopts a vector sensor array, which includes multiple velocity receiving sensors;

[0121] A rough estimation module is used to obtain a rough estimate of 2D-DOA using the signal subspace and the ESPRIT algorithm;

[0122] The spatial ambiguity module is used to define the spatial selectivity matrix and multiply it to the left of the signal subspace matrix. After matrix transformation, the spatial ambiguity is solved. The diagonal elements are taken to construct row vectors and put into the initial phase matrix. The initial phase matrix is ​​phased to obtain the ambiguous spatial phase difference matrix.

[0123] The precise estimation module is used to perform phase compensation on the spatial phase difference matrix according to the rough estimation result of the rough estimation module to obtain a precise estimation of 2D-DOA;

[0124] Here, 2D-DOA represents two-dimensional angle of arrival.

[0125] The present invention provides a 2D-DOA estimation method and system for an acoustic vector sensor with an arbitrary array structure. The method obtains a covariance matrix, performs eigendecomposition on the covariance matrix, solves the signal subspace, and then roughly estimates the two-dimensional DOA in the vector information based on the signal subspace using the ESPRIT algorithm. The rough estimation result is then used to perform phase compensation for spatial ambiguity, thereby achieving accurate estimation of the 2D-DOA of an acoustic vector sensor with an arbitrary array structure. The vector sensor is used to realize the spatial layout of an arbitrary array, and the array element spacing of the sensor is no longer limited to half a wavelength. Not only the information of the vector part but also the information of the spatial phase is used, which significantly improves the estimation accuracy. There is no need to perform spectral peak search and additional two-dimensional angle pairing calculation on the covariance matrix of the received signal, which significantly reduces the computational complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0126] The present invention will be further described below with reference to the accompanying drawings and examples:

[0127] Figure 1 is a flow chart of the estimation method of the present invention;

[0128] Figure 2 Schematic diagram of a single-base MIMO radar system applicable to the present invention;

[0129] Figure 3 It is a Monte Carlo test simulation scatter plot of the present invention;

[0130] Figure 4 The present invention and Figure 3 Comparative scatter plot of the ESPRIT algorithm simulation;

[0131] Figure 5 The present invention compares different signal-to-noise ratios SNR picture;

[0132] Figure 6 The present invention compares different numbers of sampling samples picture;

[0133] Figure 7 The present invention compares different numbers of array elements picture. DETAILED DESCRIPTION

[0134] Example 1

[0135] This embodiment considers a single-base MIMO radar system consisting of multiple transmitting sensors and multiple velocity receiving sensors. Assume that the array positions of the transmitting array elements and the receiving array elements are arbitrary, and the transmitting array elements have M There are transmitting sensors and receiving elements N The speed receiving sensor, the transmitting element m The location of the transmitting sensor is ( ), receiving element n The position of the speed receiving sensor is ( ).like Figure 1 As shown, assuming that the MIMO radar far field has K Target, k The two-dimensional departure direction angle 2D-DOD of a target relative to the transmitting array is ( ), the two-dimensional receiving direction angle 2D-DOA relative to the receiving array is ( ).

[0136] The transmitting antenna used in this embodiment transmits orthogonal waveform signals with the same bandwidth and center frequency, and the wavelength is ,These signals are reflected by the target and received by the speed sensor.

[0137] like Figure 1-7 As shown, a 2D-DOA estimation method for an acoustic vector sensor with an arbitrary array structure includes the following steps:

[0138] S1: The receiving end obtains the covariance matrix and performs eigendecomposition on the covariance matrix to solve the signal subspace. The receiving end uses a vector sensor array, which includes multiple speed receiving sensors.

[0139] S2: Using the signal subspace and the ESPRIT algorithm, a rough estimate of the 2D-DOA is obtained.

[0140] S3: Simultaneously utilize the signal subspace and an algorithm similar to ESPRIT to solve the spatial ambiguity, that is, to obtain the ambiguous spatial phase difference matrix.

[0141] That is, the spatial selectivity matrix is ​​defined and multiplied by the left side of the signal subspace matrix. After matrix transformation, the spatial ambiguity is solved, the diagonal elements are taken to construct the row vectors and put into the initial phase matrix. The initial phase matrix is ​​phased to obtain the ambiguous spatial phase difference matrix.

[0142] S4: Perform phase compensation on the ambiguous spatial phase difference matrix based on the rough estimation result of step 2 to obtain an accurate estimation of 2D-DOA.

[0143] Here, 2D-DOA represents two-dimensional angle of arrival.

[0144] This embodiment obtains a covariance matrix and performs eigendecomposition on it to solve the signal subspace. Based on the signal subspace, the ESPRIT algorithm is then used to roughly estimate the two-dimensional DOA in the vector information. This rough estimate is then used to perform phase compensation for spatial ambiguity, thereby achieving accurate estimation of the 2D-DOA for acoustic vector sensors with arbitrary array structures. This embodiment not only utilizes vector sensors to achieve arbitrary array spatial layouts, but also frees the sensor element spacing from the half-wavelength limit. It utilizes both vector information and spatial phase information, significantly improving estimation accuracy. Furthermore, the algorithm eliminates the need for spectral peak searching and additional two-dimensional angle pairing calculations on the covariance matrix of the received signal, significantly reducing computational complexity, improving estimation accuracy, and enhancing the robustness and applicability of the system.

[0145] Since the array element spacing is greater than half a wavelength, the spatial phase difference matrix will have phase ambiguity. The spatial phase difference matrix is ​​the information in the spatial domain, which means that there is ambiguity in the spatial domain, that is, spatial ambiguity. This embodiment addresses this feature and therefore not only utilizes the information of the vector part to make a rough estimate, but also utilizes the information of the spatial domain to make a refined estimate, thereby improving the accuracy of the algorithm.

[0146] In the preferred embodiment, the specific steps of step S1 are as follows:

[0147] S101: Based on the fact that the positions of the transmitting array element and the receiving array element are set arbitrarily, and the transmitting array element has M There are transmitting sensors and receiving elements N The speed receiving sensor takes the coordinates of the first row of the transmitting array and the receiving array as the reference array element, then relative to the first m The first sending sensor and the n The arrival time differences of the velocity receiving sensors are:

[0148] (1);

[0149] (2);

[0150] Where, For the m The location of the root transmitter sensor, For the n The root velocity receives the position of the sensor, Respectively k The azimuth and elevation of the 2D-DOD of the target, Respectively k The azimuth and elevation of the 2D-DOA of a target; where 2D-DOD represents the two-dimensional beam departure angle.

[0151] S102: Under the narrowband assumption, the spatial response vector of the transmitting sensor array and the receiving sensor array spatial response vector They are:

[0152] (3);

[0153] (4);

[0154] Where, For the m The arrival time difference of the transmitting sensor relative to the reference sensor array element, For the n The arrival time difference of each velocity receiving sensor relative to the reference sensor array element, The wavelength of the transmitted signal.

[0155] S103: Assume that the distance between the target and the monostatic radar system is far enough, so the signal reflected by the target can be regarded as a plane wave. The output formula of the matched filter of the receiving end velocity receiving sensor is:

[0156] (5);

[0157] Or:

[0158] (6);

[0159] Where, is the transmit array spatial response matrix, is the receiving array spatial response matrix, , is the received Gaussian white noise matrix, represents the Khatri-Rao product, represents the Kroc inner product; is the polarization response matrix, and

[0160] , ,

[0161] .

[0162] S104: Define the matrix according to step S103 :

[0163] (7);

[0164] The obtained signal model is:

[0165] (8);

[0166] According to the above signal model, the covariance matrix of the received signal can be calculated for:

[0167] (9);

[0168] In the formula, the superscript H is the conjugate transpose, L Snap count.

[0169] S105: Solve the signal subspace and calculate the received signal covariance matrix in equation (9): Perform eigendecomposition to obtain the signal subspace. The eigendecomposition formula is:

[0170] (10);

[0171] Where, for A diagonal matrix whose diagonal elements contain K A larger eigenvalue, for K The matrix consists of the eigenvectors corresponding to the largest eigenvalues, for The conjugate transposed matrix of ; for A diagonal matrix whose diagonal elements contain 3 MN - K Smaller eigenvalues, is the matrix composed of the eigenvectors corresponding to the remaining smaller eigenvalues, for The conjugate transposed matrix of ; is regarded as the signal subspace, is regarded as the noise subspace.

[0172] Signal subspace and the spatial response vector matrix A The spanned subspace is the same, that is:

[0173] (11);

[0174] In the formula, the matrix , is a non-singular full-rank matrix.

[0175] In this embodiment, step S1 provides the necessary signal model and mathematical foundation for subsequent DOA estimation by calculating the time difference of arrival (TDOA), determining the spatial response vector, defining the receiver output formula, calculating the covariance matrix, and solving the signal subspace through eigendecomposition. After the signal subspace is determined, a rough estimate of the 2D-DOA can be performed.

[0176] In the preferred embodiment, the specific steps of step S2 are as follows:

[0177] S201: Set the selectivity matrix, the formula is:

[0178] (12a);

[0179] (12b);

[0180] (12c);

[0181] Where, for The identity matrix, for The identity matrix, for The identity matrix of k OK.

[0182] S202: Multiply the selectivity matrix by the left side of the signal subspace matrix, and let ,Right now:

[0183] (13a);

[0184] (13b);

[0185] (13c).

[0186] Where, Represented as a matrix No. k rows, where:

[0187] ,

[0188] ,

[0189] ;

[0190] S203: According to formula (13), the following matrix can be constructed:

[0191] (14);

[0192] Where, .

[0193] At the same time: ,but:

[0194] (15);

[0195] In formula (13c), Substituting into formula (15), we can get:

[0196] (16);

[0197] Where, ;.

[0198] From formula (16), we can get: ,in represents the generalized inverse of a matrix, It means to find the inverse of a matrix.

[0199] S204: Perform eigendecomposition on the output matrix of step S203 to obtain a rough estimate of 2D-DOA. Specifically, Perform eigendecomposition to obtain eigenvalues and eigenvectors ,Right now:

[0200] (17);

[0201] (18);

[0202] Then the rough estimate of the azimuth and elevation angles of 2D-DOA can be expressed as:

[0203] (19);

[0204] (20);

[0205] Where, abs () indicates the amplitude, angle () indicates phase.

[0206] In the above steps, a rough estimation of the 2D-DOA is achieved by constructing a selectivity matrix, applying the matrix to the signal subspace, constructing and processing a new matrix, and performing eigendecomposition.

[0207] In the preferred solution, to resolve the spatial ambiguity, step S3 specifically includes:

[0208] S301: Define the following spatial selectivity matrix, which is expressed as:

[0209] (twenty one);

[0210] Where, for The identity matrix of n OK.

[0211] S302: The spatial selectivity matrix is ​​multiplied by the left side of the signal subspace matrix, that is:

[0212] (22a);

[0213] (22b);

[0214] Where, , is the receiving array spatial response vector The first line, , is the receiving array spatial response vector The second line.

[0215] S303: And , substituting into formula (22) we get:

[0216] (twenty three).

[0217] at this time:

[0218] ,

[0219] Where, , , , diag () means converting the row matrix into a diagonal matrix, , , ,but:

[0220] (twenty four);

[0221] S304: From formula (23), we can get , then the formula (18) Substituting in:

[0222] , (25);

[0223] (26);

[0224] Similarly, using the selectivity matrix Multiplying both sides of equation (11) at the same time, we can get ,and ,Right now:

[0225] (27);

[0226] at this time , , , , similarly, replaceT Substituting into formula (27) we get:

[0227] (28);

[0228] (29);

[0229] Same as above, using the selectivity matrix ,Will The simulation formulas (27) (28) (29) are obtained;

[0230] S305: Take The diagonal elements of the row vector are constructed , , and then this N -1 row vector to be put into the initial phase matrix You can get:

[0231] (30);

[0232] The initial phase matrix Take the phase and get the initial phase difference matrix :

[0233] ;

[0234] Right now: (31);

[0235] in:

[0236] ,

[0237] .

[0238] At this time, when the phase is taken using the built-in angle function in matlab, the phase greater than The phase value is periodically mapped to So the phase difference matrix of adjacent sensors is received There will be phase ambiguity, which will cause errors in the DOA estimation results. Therefore, the following phase compensation process is required to obtain accurate estimation results.

[0239] In the preferred embodiment, step S4 specifically includes:

[0240] S401: First, using the rough estimation results in formulas (19) and (20), that is, obtaining the rough estimation results of the azimuth and elevation angles of the 2D-DOA in step S3, construct the following unambiguous low-precision Poynting vector matrix , the expression is:

[0241] (32);

[0242] Where, and are the rough azimuth and elevation angles, respectively.

[0243] S402: Use the unambiguous low-precision Poynting vector matrix By using formula (31), the unambiguous low-precision phase difference matrix is ​​obtained , through the unambiguous low-precision phase difference matrix , get the fuzziness Solve it, that is:

[0244] (33).

[0245] S403: Blur The phase difference matrix compensated to the periodic ambiguity is obtained by equation (34): In the above example, we obtain the unambiguous and high-precision phase difference matrix Right now:

[0246] (34);

[0247] S404: Using the least squares principle, estimate the unambiguous and high-precision Poynting vector matrix ,Right now:

[0248] (35).

[0249] Thus, the azimuth and elevation angles of 2D-DOA are obtained. That is, the azimuth and elevation angle estimation formulas of 2D-DOA are:

[0250] (36);

[0251] (37).

[0252] The following is a specific example to illustrate the usefulness of the solution of the present invention. In this single-base MIMO radar system, the number of transmitting sensors is set to M =10, the number of speed receiving sensors N =10, the wavelength of the antenna =1. Assume that K = 3 targets appear within the range of the monostatic MIMO radar system, and the 2D-DOA of the three targets is , . In the sampling sample number L =100, signal-to-noise ratio SNR=12dB, the angle estimation is performed using the method proposed in the present invention. The scatter plot results of 100 Monte Carlo simulations are shown in the attached figure. Figure 2 As shown in the figure, in order to highlight the reliability of the solution of the present invention, the angle estimation method of obtaining 2D-DOA by using a velocity receiving sensor through an ESPRIT-like algorithm is compared, as shown in the attached figure. Figure 3 As shown, it can be seen Figure 2 Shows more Figure 3 These findings indicate that the proposed scheme can effectively estimate the receiving direction angle 2D-DOA of the target signal relative to the velocity receiving sensor array, and the performance of the estimation algorithm is also significantly improved.

[0253] The preferred solution also includes: using the root mean square error (RMSE) for evaluation, and the calculation formula is:

[0254] (38);

[0255] Where, for Estimates, for Estimates.

[0256] like Figure 4 As shown in the figure, the algorithm proposed in this embodiment has the following characteristics: L =100, the number of transmitting sensors M =8, the number of speed receiving sensors N =8, comparing different signal-to-noise ratios SNR Next In order to highlight the reliability of the solution of the present invention, the ESPRIT_Like algorithm is used for comparison. At this time, it can be clearly seen that regardless of the signal-to-noise ratio SNR No matter how the signal-to-noise ratio (SNR) is increased, the accuracy of the ESPRIT_Like algorithm is not very high. However, the algorithm proposed in the present invention can achieve higher and higher estimation accuracy as the signal-to-noise ratio (SNR) increases, and is much higher than the ESPRIT_Like algorithm.

[0257] like Figure 5 As shown in the figure, the algorithm proposed by the present invention has the following characteristics: M =8, the number of speed receiving sensors N =8, signal-to-noise ratio SNR =5dB, compare different sampling numbers L Next At this point, it can be clearly seen that as the number of sampling samples increases LAs the value of increases, the speed at which the accuracy of the ESPRIT_Like algorithm increases becomes slower and slower. However, the accuracy of the algorithm proposed in the present invention becomes higher and higher, and is always higher than that of the ESPRIT_Like algorithm.

[0258] like Figure 6 As shown in the figure, the algorithm proposed by the present invention has the following characteristics: L =100, signal-to-noise ratio SNR =10dB, compare different numbers of array elements At this time, as before, the algorithm proposed by the present invention will have higher and higher estimation accuracy as the number of array elements increases, and will always be higher than the ESPRIT_Like algorithm.

[0259] This embodiment has the following beneficial effects:

[0260] 1. Unlike traditional angle estimation based on scalar sensor arrays, the use of vector sensor arrays can achieve arbitrary spatial layout of sensors, such as placing sensors on the surface of an aircraft to reduce the radar cross-section and enhance the aircraft's stealth and maneuverability. It also eliminates the half-wavelength limit on sensor element spacing, reducing sensor position errors and mutual coupling effects, and improving the accuracy of the radar system.

[0261] 2. Unlike the previous angle estimation based on electromagnetic vector sensor arrays, a velocity receiving sensor is used. The hardware cost of this sensor is low, and it only has three vector channels, and the computational complexity is also low. Its low cost and high speed advantages make it suitable for large-scale applications.

[0262] 3. The embodiment not only utilizes the information of the vector part, but also fully utilizes the spatial phase information of the sensor array, significantly improving the estimation accuracy; the proposed algorithm does not require spectral peak search and additional angle pairing calculations on the covariance matrix of the received signal, significantly reducing the computational complexity.

[0263] Example 2

[0264] In combination with Example 1, a 2D-DOA estimation system for an acoustic vector sensor with an arbitrary array structure is proposed, which is applicable to the 2D-DOA estimation method for an acoustic vector sensor with an arbitrary array structure in Example 1, including:

[0265] The signal subspace module is used to obtain the covariance matrix at the receiving end, perform eigendecomposition on the covariance matrix, and solve the signal subspace; wherein the receiving end adopts a vector sensor array, which includes multiple speed receiving sensors.

[0266] The rough estimation module is used to obtain a rough estimate of 2D-DOA by using the signal subspace and the ESPRIT algorithm.

[0267] The spatial ambiguity module is used to define the spatial selectivity matrix and multiply it on the left side of the signal subspace matrix. After matrix transformation, the spatial ambiguity is solved, the diagonal elements are taken to construct the row vector and put into the initial phase matrix. The initial phase matrix is ​​phased to obtain the ambiguous spatial phase difference matrix.

[0268] The precise estimation module is used to perform phase compensation on the ambiguous spatial phase difference matrix according to the rough estimation result of the rough estimation module to obtain a precise estimation of the 2D-DOA.

[0269] Here, 2D-DOA represents two-dimensional angle of arrival.

[0270] The above embodiments are merely preferred technical solutions of the present invention and should not be construed as limiting the present invention. The scope of protection of the present invention shall be the technical solutions set forth in the claims, including equivalent alternatives to the technical features of the technical solutions set forth in the claims. In other words, equivalent alternatives and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A 2D-DOA estimation method for an acoustic vector sensor of arbitrary array structure, characterized in that: The following steps are involved: S1: The receiving end obtains the covariance matrix and performs eigendecomposition on the covariance matrix to solve the signal subspace. The receiving end uses a vector sensor array, which includes multiple speed receiving sensors. S2: Using the signal subspace and the ESPRIT algorithm, a rough estimate of the 2D-DOA is obtained; S3: Define the spatial selectivity matrix and multiply it by the left side of the signal subspace matrix. After matrix transformation, solve the spatial ambiguity. Take the diagonal elements to construct the row vector and put it into the initial phase matrix. The initial phase matrix is ​​phased to obtain the ambiguous spatial phase difference matrix. S4: Perform phase compensation on the ambiguous spatial phase difference matrix based on the rough estimation result of step 2 to obtain an accurate estimation of 2D-DOA; Here, 2D-DOA represents two-dimensional angle of arrival.

2. The 2D-DOA estimation method for an acoustic vector sensor of an arbitrary array structure according to claim 1, characterized in that: The specific steps of step S1 are as follows: S101: Assuming that the array positions of the transmitting array element and the receiving array element are arbitrarily set, and the transmitting array element has M transmitting sensors and the receiving array element has N velocity receiving sensors, and the coordinates of the first row of the transmitting array and the receiving array are used as reference array elements, the arrival time differences relative to the mth transmitting sensor and the nth velocity receiving sensor are respectively: d t,m,k =x tm cos(φ tk )sin(θ tk )+y tm sin(φ tk )sin(θ tk )+z tm cos(θ tk ) (1); d r,n,k =x rn cos(φ rk )sin(θ rk )+y rn sin(φ rk )sin(θ rk )+z rn cos(θ rk ) (2); In the formula, (x tm ,y tm ,z tm ) is the position of the mth transmitting sensor, (x rn ,y rn ,z rn ) is the position of the nth velocity receiving sensor, θ tk ,φ tk are the azimuth and elevation angles of the 2D-DOD of the kth target, θ rk ,φ rk are the azimuth and elevation of the 2D-DOA of the kth target, respectively; where 2D-DOD represents the two-dimensional wave departure angle; S102: Under the narrowband assumption, the transmitting sensor array spatial response vector a t (θ tk ,φ tk ) and the receiving sensor array spatial response vector a r (θ rk ,φ rk ) are: Where, d t,m,k is the arrival time difference of the mth transmitting sensor relative to the reference sensor array element, d r,n,k is the arrival time difference of the nth velocity receiving sensor relative to the reference sensor array element, and λ is the wavelength of the transmitted signal; S103: The output formula of the matching filter of the receiving end speed sensor is: Or: Y(t)=[A t ☉A r ☉B r ]s(t)+n(t) (6); Where A t =[a t (θ t1 ,φ t1 ),a t (θ t2 ,φ t2 ),...,a t (θ tK ,φ tK )]∈C M×K is the transmit array spatial response matrix, A r =[a r (θ r1 ,φ r1 ),a r (θ r2 ,φ r2 ),...,a r (θ rK ,φ rK )]∈C N×K is the spatial response matrix of the receiving array, s(t)=[s1(t),s2(t),…,s K (t)] T ∈C K×L , is the received Gaussian white noise matrix, ⊙ represents the Khatri-Rao product, represents the Kroc inner product; B r =[b r1 ,b r2 ,b r3 ] T ∈C 3×K is the polarization response matrix, and b r1 =[sinθ r1 cosφ r1 ,sinθ r2 cosφ r2 ,...,sinθ rK cosφ rK ] T , b r2 =[sinθ r1 sinφ r1 ,sinθ r2 sinφ r2 ,...,sinθ rK sinφ rK ] T , b r3 =[cosθ r1 ,cosθ r2 ,...,cosθ rK ] T ; S104: Define matrix A according to step S103: A=A t ☉A r ☉B r (7) The obtained signal model is: Y=AS+N (8); Calculate the covariance matrix R of the received signal Y for: R Y =YY H / L (9); Where, superscript H is the conjugate transpose, L is the number of snapshots; S105: Solve the signal subspace, and calculate the received signal covariance matrix R in equation (9) Y Perform eigendecomposition to obtain the signal subspace. The eigendecomposition formula is: Where, is a K×K diagonal matrix whose diagonal elements contain K large eigenvalues, is a matrix composed of eigenvectors corresponding to K larger eigenvalues, for The conjugate transposed matrix of ; is a (3MN-K)×(3MN-K) diagonal matrix whose diagonal elements contain 3MN-K smaller eigenvalues. is the matrix composed of the eigenvectors corresponding to the remaining smaller eigenvalues, for The conjugate transposed matrix of ; is regarded as the signal subspace, Considered as a noise subspace; Signal subspace The same as the subspace spanned by the spatial response vector matrix A, that is: Where, the matrix T∈C K×K , is a non-singular full rank matrix.

3. The 2D-DOA estimation method of an acoustic vector sensor with an arbitrary array structure according to claim 2, characterized in that: The specific steps of step S2 are as follows: S201: Set the selectivity matrix, the formula is: J1=[I M ☉I N ☉I 3，1 ] (12a); J2=[I M ☉I N ☉I 3，2 ] (12b); J3=[I M ☉I N ☉I 3，3 ] (12c); Where, Ι M is the M×M identity matrix, Ι N is the N×N identity matrix, Ι 3,k is the kth row of the 3×3 identity matrix; S202: Multiply the selectivity matrix by the left side of the signal subspace matrix, and let A0 = A t ⊙A r ,Right now: Where B r,k Represented as matrix B r The kth row of , where: Φ x =diag(sinθ r1 cosφ r1 ,sinθ r2 cosφ r2 ,...,sinθ rK cosφ rK ), F y =diag(sinθ r1 sinφ r1 ,sinθ r2 sinφ r2 ,...,synth rK sinφ rK ), F z =diag(cosθ r1 ,cosθ r2 ,...,cosθ rK ); S203: According to formula (13), the following matrix can be constructed: Where, At the same time: let Φ xy =Φ z Φ xyz ,but: Substituting A0 in formula (13c) into formula (15), we can obtain: Where, From formula (16), we can get: in represents the generalized inverse of a matrix, [·] -1 Indicates the inverse of the matrix; S204: Perform eigendecomposition on the output matrix of step S203 to obtain a rough estimate of 2D-DOA. Specifically, Perform eigendecomposition to obtain eigenvalues and eigenvectors Right now: Then the rough estimate of the azimuth and elevation angles of 2D-DOA can be expressed as: In the formula, abs() means taking the amplitude, and angle() means taking the phase.

4. The 2D-DOA estimation method of an acoustic vector sensor with an arbitrary array structure according to claim 3, characterized in that: To solve the spatial ambiguity, step S3 specifically includes: S301: Define the following spatial selectivity matrix, which is expressed as: P n =[I M ☉I N，n ☉I3],n=1,...,N (21); Where, Ι N,n is the nth row of the N×N identity matrix; S302: Multiply the selectivity matrix by the left side of the signal subspace matrix, that is: Where, is the receiving array spatial response vector A r The first line, is the receiving array spatial response vector A r The second line of S303: and A r,2 =A r,1 Φ r1 , substituting into formula (22) we get: at this time: Where u rk =cosφ rk sinθ rk , v rk = sinφ rk sinθ rk , w rk =cosφ rk , diag() means converting the row matrix into a diagonal matrix, let x r1 -x r2 =m 12 ,y r1 -y r2 =n 12 , z r1 -z r2 =l 12 ,but: S304: From formula (23), we can get Then substitute T in formula (18) to obtain: Similarly, by multiplying both sides of equation (11) with the selectivity matrix P3, we can get And A r,3 =A r,2 Φ r2 ,Right now: at this time m 23 =x r2 -x r3 , n 23 =y r2 -y r3 , l 23 =z r2 -z r3 , similarly, substitute T in formula (18) into formula (27) to obtain: Same as above, using the selectivity matrix P 4,...,N ,Will The simulation formula (27)(28)(29) is obtained; S305: Take The diagonal elements of the row vector are constructed Then put these N-1 row vectors into the initial phase matrix GG∈C N-1×K You can get: Take the phase of the initial phase matrix GG to obtain the initial phase difference matrix GGp: That is: GGp=EP h (31); in:

5. The 2D-DOA estimation method of an acoustic vector sensor with an arbitrary array structure according to claim 4, characterized in that: Step S4 specifically includes: S401: First, using the rough estimation results in formulas (19) and (20), that is, obtaining the rough estimation results of the azimuth and elevation angles of the 2D-DOA in step S3, construct the following unambiguous low-precision Poynting vector matrix The expression is: Where, and are the rough azimuth and elevation angles respectively; S402: Use the unambiguous low-precision Poynting vector matrix By using formula (31), the unambiguous low-precision phase difference matrix is ​​obtained Through this unambiguous low-precision phase difference matrix Get blur Solve it, that is: S403: Blur By compensating the periodic ambiguity into the phase difference matrix GGp through equation (34), the unambiguous and high-precision phase difference matrix GGpt is obtained: S404: Using the least squares principle, estimate the unambiguous and high-precision Poynting vector matrix Right now: Thus, the azimuth and elevation angles of 2D-DOA are obtained. That is, the azimuth and elevation angle estimation formulas of 2D-DOA are:

6. The 2D-DOA estimation method of an acoustic vector sensor with an arbitrary array structure according to claim 2, characterized in that: Also includes: The root mean square error is used for evaluation and is calculated as: Where, is θ rk Estimates, is φ rk Estimates.

7. A 2D-DOA estimation system for acoustic vector sensors of arbitrary array structure, characterized in that: A 2D-DOA estimation method for an acoustic vector sensor of an arbitrary array structure applicable to claim 1, comprising: A signal subspace module is used to obtain a covariance matrix at the receiving end, perform eigendecomposition on the covariance matrix, and solve the signal subspace; wherein the receiving end adopts a vector sensor array, which includes multiple velocity receiving sensors; A rough estimation module is used to obtain a rough estimate of 2D-DOA using the signal subspace and the ESPRIT algorithm; The spatial ambiguity module is used to define the spatial selectivity matrix and multiply it to the left of the signal subspace matrix. After matrix transformation, the spatial ambiguity is solved. The diagonal elements are taken to construct row vectors and put into the initial phase matrix. The initial phase matrix is ​​phased to obtain the ambiguous spatial phase difference matrix. The precise estimation module is used to perform phase compensation on the spatial phase difference matrix according to the rough estimation result of the rough estimation module to obtain a precise estimation of 2D-DOA; Here, 2D-DOA represents two-dimensional angle of arrival.

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