Robust DOA estimation method based on generalized co-prime array

Abstract

The invention discloses a robust DOA estimation method based on a generalized co-prime array. According to the scheme, the front array element and the rear array element of the two uniform sub-arrays are corrected auxiliary array elements, the distance between the uniform sub-arrays 1 is compressed, and the two sub-arrays are nested to form the generalized co-prime array. Receiving data of the array is decomposed into two sub-array data, amplitude-phase error estimation is carried out on the two sub-arrays according to the amplitude-phase characteristics of all elements in the covariance matrix, and the amplitude-phase errors of the sub-arrays are sorted and recombined to obtain the amplitude-phase error of the generalized co-prime array. Then error compensation is carried out on a received data covariance matrix, continuous virtual array elements are selected after the covariance matrix is vectorized, a Toeplitz matrix is constructed, and finally DOA estimation is carried out. Compared with the traditional method, the method provided by the invention firstly corrects the array error, expands the freedom degree of the array, does not need to carry out interpolation optimization on the hole, reduces the calculation cost, and has important application value in a subsurface buoy or a mobile observation platform for ocean observation.

Description

Technical Field

[0001] The present invention relates to a target detection and processing method for a buoy and a mobile observation platform for ocean observation, and is a robust DOA estimation method based on a generalized coprime array. Specifically, the method realizes the error-corrected DOA estimation of an underwater coprime hydrophone array with amplitude and phase errors by compressing the array element spacing of a subarray in a coprime array, correcting amplitude and phase errors, and selecting a continuous part of a virtual array to construct a Toeplize matrix and a DOA algorithm. Background Art

[0002] In the past decade, coprime arrays have attracted widespread attention in the field of DOA estimation because they can be expanded into virtual uniform linear arrays with higher degrees of freedom and suffer less coupling effects between array elements. In the study of coprime arrays, many methods for DOA estimation have been proposed. However, most methods are only for signals under ideal conditions. Since the actual underwater acoustic environment is very complex, there are many non-ideal factors that cause different amplitude and phase errors in the array. When the array manifold cannot be accurately known, these DOA estimation methods cannot achieve accurate positioning. Therefore, array error estimation and correction are an important part of array signal processing. Without array error correction, any high-resolution spatial spectrum estimation method cannot be used in practice. In order to improve the target detection accuracy of coprime arrays and enable them to be effectively used in real life, the research on amplitude and phase error correction and target detection of coprime arrays is still a hot topic at present, and is closely related to the development and stability of society.

[0003] A coprime array is a classic partially augmentable array, that is, there are holes in the virtual equivalent array of the coprime array, which leads to a model mismatch problem when using spatial smoothing technology. One of the existing processing methods is to directly discard the non-continuous array elements on both sides and only intercept a continuous linear subarray in its equivalent virtual array for DOA estimation, which results in a reduction in the available degrees of freedom, a reduction in the virtual aperture, and a reduction in the DOA estimation performance. Another method is to use an array interpolation algorithm to fill the holes to expand the degrees of freedom of the array, and use an optimization method to fill the array element information at the holes, but it will greatly increase the complexity of the calculation. In order to increase the number of virtual subarray elements after interception and reduce the complexity of the calculation, the usual practice is to use an extended coprime array. Compared with the standard coprime array, the advantage of the extended coprime array is that more virtual uniform linear subarrays can be intercepted from the equivalent virtual array. The generalized coprime array is a classic improvement method for the extended coprime array. By introducing a compression factor, the array element spacing is changed, thereby greatly increasing the degrees of freedom of the array.

[0004] This patent proposes a robust DOA estimation method based on a generalized coprime array, which combines the continuous virtual domain expansion method with the amplitude and phase error correction method to realize the DOA estimation method under amplitude and phase errors, improve the array's degrees of freedom, and reduce computational complexity. It has important application value in practical engineering. Summary of the invention

[0005] The actual ocean acoustic environment is very complex, and there are many non-ideal factors that cause different amplitude and phase errors in the array, resulting in the inability to accurately know the manifold and the inability to accurately locate the incident target. In order to improve the target detection accuracy of the coprime array and solve the problem of amplitude and phase errors, the present invention proposes a robust DOA estimation method based on a generalized coprime array, which decomposes the generalized coprime array receiving data after the compression factor is introduced into two sub-array data, adds auxiliary correction array elements to estimate the amplitude and phase errors, and then compensates the error of the receiving data covariance matrix, and finally expands the compensated covariance matrix, constructs the Toeplitz matrix from the continuous part after orientation quantization, and finally combines the spatial spectrum estimation method to perform angle estimation.

[0006] The present invention provides a robust DOA estimation method based on a generalized mutually prime array. The method is applicable to a generalized mutually prime sensor array. The generalized mutually prime sensor array is constructed as follows: the number of sensors in a uniform subarray 1 is N, and the sensor spacing is Md; the number of sensors in a uniform subarray 2 is M, and the sensor spacing is Nd; wherein the first and last array elements of subarray 1 and subarray 2 are corrected auxiliary array elements, and a positive integer compression factor p is introduced to compress the array element spacing of subarray 1, and the array element spacing of subarray 1 is compressed to in The generalized coprime array is composed of compressed uniform subarray 1 and uniform subarray 2 nested together. The first auxiliary array elements of the two subarrays are placed overlappingly. The array element position is described with half wavelength as the basic unit. The first auxiliary array element is the reference array element, and its position is recorded as 0. The array position set of the generalized coprime array is expressed as The number of sensors is Z=M+N-1, including 3 auxiliary array elements; the characteristic is that the DOA estimation method comprises the following steps:

[0007] Step 1: The generalized coprime array receiving data can be expressed as X(t) = [x1(t), x2(t), …, x M+N-1 (t)] T , perform Hilbert transform on these data, and get the complex signal form of the array receiving signal:

[0008] Step 2: According to the formation and The corresponding relationship between the uniform sub-array 1 and the received data is constructed as follows: The received data of uniform subarray 2 is constructed as follows:

[0009] Step 3: Using the complex signal of generalized coprime array Find the covariance matrix “(·) H ” is the conjugate transpose, where T is the number of snapshots in practical applications;

[0010] Step 4: Use the complex signal of uniform subarray 1 Find the covariance matrix Using the complex signal of uniform subarray 2 Find the covariance matrix

[0011] Step 5: According to the covariance matrix Estimate the phase error of each element of uniform subarray 1, which can be expressed as Estimate the amplitude error of each element of uniform subarray 1, which can be expressed as According to the covariance matrix Estimate the phase error of each element of uniform subarray 2, which can be expressed as Estimate the amplitude error of each element of uniform subarray 2, which can be expressed as

[0012] Step 6: Calculate the correction vector of uniform subarray 1 Calculate the correction vector for uniform subarray 2 in

[0013] Step 7: According to the position of each array element in the new uniform sub-array 1 and the new uniform sub-array 2, and The corresponding elements in are sorted and reorganized according to the positions of the new coprime array elements, and the duplicate elements are removed to obtain the amplitude and phase error matrix of the generalized coprime sensor array.

[0014] Step 8. For the covariance matrix in step 3 Perform error compensation to obtain the data covariance matrix of the generalized coprime sensor array after amplitude and phase error correction

[0015] Step 9: The differential position set of the generalized mutually prime sensor array is 0≤n,n i ,n j ≤N; 0≤m,m i ,m j ≤M, The difference position set and The range is continuous, so The array degrees of freedom are

[0016] Step 10: vectorize the covariance matrix R in step 8 to obtain z = vec(R), sort the elements in vector z, take the average of repeated elements, and take the continuous part after rearrangement to obtain Using vector Constructing a Toeplitz matrix by spatial smoothing

[0017] Step 11: Toeplitz matrix Perform feature decomposition and obtain The eigenvalue η i and its corresponding eigenvector, Arrange them from largest to smallest: The K larger eigenvalues ​​correspond to the signal subspace U S , The smaller eigenvalue corresponds to the noise subspace U N , K is the number of far-field narrowband incident signals, according to the signal subspace U S Or the noise subspace U N To estimate the direction of the incident signal;

[0018] In step 5 above The estimation method is as follows:

[0019] A1. Get the covariance matrix Phase information

[0020] angle(·) is the phase information of the extraction matrix;

[0021] A2. The upper triangular part of the phase information matrix contains exactly the same information as the lower triangular part of the matrix. Extract the phase information matrix The upper triangle of has:

[0022]

[0023] A3. Sum the first diagonal elements to get Taking the mean value, we get

[0024] A4. Subtract φ1 from all elements on the first diagonal of matrix T1, and set α 1n , n=1,2,...,N-1, according to this formula Solve make get

[0025] A5. Transform the covariance matrix in step A1 into Repeat the above steps A1 to A4 to get

[0026] In step 5 above The estimation method is as follows:

[0027] B1. Get the covariance matrix The main diagonal elements of Use this

[0028] B2. Get the covariance matrix The main diagonal elements of Using this vector, we can calculate

[0029] The Toeplitz matrix described in step 10 above The construction method is: Perform spatial smoothing, the number of smoothing times is The length of each subarray is for Segment corresponds to virtual data z r The resulting covariance matrix.

[0030] The DOA estimation method in the above step 11 is: According to the formula The spatial spectrum is calculated and the peak is searched for. The angle corresponding to the extreme value is the estimated value of the incident signal angle.

[0031] The DOA estimation method in step 11 above is: find the first K large eigenvalues, according to the formula An estimate of the angle of the incident signal can be obtained.

[0032] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0033] (1) In the present invention, a compression factor is introduced into the coprime array to obtain an expanded generalized coprime array, thereby increasing the degree of freedom of the array and improving the accuracy of DOA estimation;

[0034] (2) The present invention adds three corrected auxiliary array elements to estimate the amplitude and phase errors of the generalized coprime array, and then performs error compensation on the received data covariance matrix, thereby effectively restoring the DOA estimation performance of the generalized coprime array under the amplitude and phase errors, and realizing error correction of the array containing amplitude and phase errors;

[0035] (3) The present invention is a method for expanding a continuous virtual array aperture, which does not require interpolation optimization of the holes and reduces the computational cost compared to other methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 This is a model diagram of the array signal processing method of this patent;

[0037] Figure 2 This is a comparison chart of the array degrees of freedom of the patented signal processing method;

[0038] Figure 3 This is a diagram showing the DOA estimation results of the signal processing method of this patent and the signal processing method when there are amplitude and phase errors;

[0039] Figure 4 is the relationship curve between the root mean square error and the signal-to-noise ratio of the signal processing method of this patent;

[0040] Figure 5 This is the relationship curve between the probability of successful resolution and the signal-to-noise ratio of the signal processing method of this patent;

[0041] Figure 6 is the relationship curve between the root mean square error and the number of snapshots of the patented signal processing method;

[0042] Figure 7 The relationship curve between the probability of successful resolution and the number of snapshots of the patented signal processing method is shown in FIG. DETAILED DESCRIPTION

[0043] The present invention will now be further described with reference to the embodiments and the accompanying drawings:

[0044] The first embodiment: Figure 1 The generalized coprime array model in the present invention is given. The degrees of freedom of the generalized coprime array and the traditional coprime array are studied respectively, and the effect diagram is as follows Figure 2 The application conditions of the algorithm in the present invention are as follows:

[0045] First, we construct a 12-element generalized coprime array. Uniform subarray 1 consists of 7 elements with an element spacing of 6d. Uniform subarray 2 consists of 6 elements with an element spacing of 7d, where d is half the signal wavelength, 0.5m. We set the compression factor p = 3 to compress the element spacing of subarray 1. The element spacing of subarray 1 is compressed to The generalized coprime array is composed of subarray 1 and subarray 2 nested together, and the two subarrays share the first array element. The generalized coprime array position set S = {0, 2, 4, 6, 7, 8, 10, 12, 14, 21, 28, 35}. A signal is incident on the coprime array from the direction of θ1 = 20°, the signal-to-noise ratio is 0dB, and the number of snapshots is T = 500. Using the above conditions for azimuth estimation, the specific implementation process is:

[0046] Step 1: The generalized coprime array receiving data can be expressed as X(t) = [x1(t), x2(t), …, x 12 (t)] T, perform Hilbert transform on these data, and get the complex signal form of the array receiving signal:

[0047] Step 2: According to the formation and The corresponding relationship between the uniform sub-array 1 and the received data is constructed as follows: The received data of uniform subarray 2 is constructed as follows:

[0048] Step 3: Using the complex signal of generalized coprime array Find the covariance matrix “(·) H ” is the conjugate transpose;

[0049] Step 4: Use the complex signal of uniform subarray 1 Find the covariance matrix Using the complex signal of uniform subarray 2 Find the covariance matrix

[0050] Step 5: According to the covariance matrix Estimate the phase error of each element of uniform subarray 1, which can be expressed as Estimate the amplitude error of each element of uniform subarray 1, which can be expressed as According to the covariance matrix Estimate the phase error of each element of uniform subarray 2, which can be expressed as Estimate the amplitude error of each element of uniform subarray 2, which can be expressed as

[0051] Step 6: Calculate the correction vector of uniform subarray 1 Calculate the correction vector for uniform subarray 2 in

[0052] Step 7: According to the position of each array element in the new uniform sub-array 1 and the new uniform sub-array 2, and The corresponding elements in are sorted and reorganized according to the positions of the new coprime array elements, and the duplicate elements are removed to obtain the amplitude and phase error matrix of the generalized coprime sensor array.

[0053] Step 8. For the covariance matrix in step 3 Perform error compensation to obtain the data covariance matrix of the generalized coprime sensor array after amplitude and phase error correction

[0054] Step 9: The differential position set of the generalized mutually prime sensor array is

[0055] The difference position set and is continuous in the range [-29,29], The array degrees of freedom are DOF = 59;

[0056] Step 10: vectorize the covariance matrix R in step 8 to obtain z = vec(R), sort the elements in vector z, take the average of repeated elements, and take the continuous part after rearrangement to obtain Using vector Constructing a Toeplitz matrix by spatial smoothing

[0057] Step 11: Toeplitz matrix Perform eigendecomposition and obtain 29 eigenvalues ​​η i and its corresponding eigenvectors, i = 1, 2, ... 29, arranged from large to small: η1>η2>...>η 29 > 0, where K larger eigenvalues ​​correspond to the signal subspace U S , The smaller eigenvalue corresponds to the noise subspace U N , K is the number of far-field narrowband incident signals, according to the signal subspace U S Or the noise subspace U N To estimate the direction of the incident signal;

[0058] In step 5 above The estimation method is as follows:

[0059] A1. Get the covariance matrix Phase information

[0060] angle(·) is the phase information of the extraction matrix;

[0061] A2. The upper triangular part of the phase information matrix contains exactly the same information as the lower triangular part of the matrix. Extract the phase information matrix The upper triangle of has:

[0062]

[0063] A3. Sum the first diagonal elements to get Taking the mean value, we get

[0064] A4. Subtract φ1 from all elements on the first diagonal of matrix T1, and set α 1n , n=1,2,...,6, according to this formula Solve make get

[0065] A5. Transform the covariance matrix in step A1 into Repeat the above steps A1 to A4 to get

[0066] In step 5 above The estimation method is as follows:

[0067] B1. Get the covariance matrix The main diagonal elements of Using this vector, we can calculate

[0068] B2. Get the covariance matrix The main diagonal elements of Using this vector, we can calculate

[0069] The Toeplitz matrix described in step 10 above The construction method is: Perform spatial smoothing processing, the number of smoothing is 30, and the length of each subarray is also 30; R zr The virtual data z corresponding to the segment [-30+r,r-1] r The resulting covariance matrix.

[0070] The preferred solution of the DOA estimation method in step 11 above is: according to the formula The spatial spectrum is calculated and the peak is searched for. The angle corresponding to the extreme value is the estimated value of the incident signal angle.

[0071] The preferred solution of the DOA estimation method in the above step 11 is: find the first large eigenvalue, according to the formula i=1 can obtain an estimated value of the incident signal angle.

[0072] analyze Figure 2 It can be seen that the difference position set sum of the generalized coprime array with M=6, N=7 is continuous in the range of [-29,29], and the array degree of freedom is 59, while the difference position set sum of the traditional coprime array is continuous in the range of [-12,12], and the array degree of freedom is 25, so the generalized coprime array effectively improves the array degree of freedom.

[0073] analyze Figure 3 From the simulation results, it can be seen that the angle estimated by the patented method is basically consistent with the true angle, and the angle cannot be correctly estimated without amplitude and phase error correction, so the patented method can effectively correct the amplitude and phase errors.

[0074] Second embodiment: The relationship between the root mean square error (RMSE) and the signal-to-noise ratio and the relationship between the probability of successful resolution and the signal-to-noise ratio of the signal processing method of the present patent are studied respectively, and the effect diagram is as follows: Figure 4 , Figure 5 The application conditions of the algorithm in the present invention are as follows:

[0075] We use a 12-element generalized coprime array. Uniform subarray 1 consists of 7 elements with an element spacing of 6d. Uniform subarray 2 consists of 6 elements with an element spacing of 7d, where d is half the signal wavelength, 0.5m. We set the compression factor p = 3 to compress the element spacing of subarray 1. The element spacing of subarray 1 is compressed to The generalized coprime array is composed of subarray 1 and subarray 2 nested together, and the two subarrays share the first array element. The generalized coprime array position set S = {0, 2, 4, 6, 7, 8, 10, 12, 14, 21, 28, 35}, the number of sensors is 12, and it contains 3 calibrated auxiliary array elements. A signal is incident on the coprime array from the direction of θ1 = 20°, the number of snapshots is T = 500, the signal-to-noise ratio starts from -5dB and increases to 20dB in steps of 5dB. 200 independent Monte Carlo experiments are performed and simulated by the MATLAB software system.

[0076] analyze Figure 4 It can be seen that when the snapshot number T = 300, as the signal-to-noise ratio increases, the root mean square error of the two methods decreases. When the signal-to-noise ratio is -5dB, the root mean square error of the traditional coprime array method is about 0.907, and the root mean square error of the patented method is about 0.750, which is about 0.157 higher than the traditional coprime array method. When the signal-to-noise ratio is 0dB, the root mean square error of the traditional coprime array method is about 0.341, and the root mean square error of the patented method is about 0.141, which is about 0.2 higher than the traditional coprime array method. When the signal-to-noise ratio is 10dB, the root mean square error of the traditional coprime array method is about 0.094, and the root mean square error of the patented method is about 0.055, which is about 0.039 higher than the traditional coprime array method. It can be seen that the performance of the patented method is better than the traditional coprime array method, which is more obvious at low signal-to-noise ratios.

[0077] analyze Figure 5 It can be seen that when the snapshot number T=300, as the signal-to-noise ratio increases, the success probability of resolution of the patented method and the traditional coprime array method increases. The patented method reaches 100% when the signal-to-noise ratio is 0dB, and the traditional coprime array method reaches 100% when the signal-to-noise ratio is 5dB.

[0078] The third embodiment: The relationship between the root mean square error (RMSE) and the number of snapshots and the relationship between the probability of successful resolution and the number of snapshots of the signal processing method of the present patent are studied respectively, and the effect diagram is as follows: Figure 6 , Figure 7The application conditions of the algorithm in the present invention are as follows:

[0079] We use a 12-element generalized coprime array. Uniform subarray 1 consists of 7 elements with an element spacing of 6d. Uniform subarray 2 consists of 6 elements with an element spacing of 7d, where d is half the signal wavelength, 0.5m. We set the compression factor p = 3 to compress the element spacing of subarray 1. The element spacing of subarray 1 is compressed to The generalized coprime array is composed of subarray 1 and subarray 2 nested together, and the two subarrays share the first array element. The generalized coprime array position set S = {0, 2, 4, 6, 7, 8, 10, 12, 14, 21, 28, 35}, the number of sensors is 12, and it contains 3 calibrated auxiliary array elements. A signal is incident on the coprime array from the direction of θ1 = 20°, the signal-to-noise ratio snr = 10dB, the number of snapshots is changed from 50, and the step size is increased from 50 to 400. 200 independent Monte Carlo experiments are performed and simulated by the MATLAB software system.

[0080] analyze Figure 6 It can be seen that when the signal-to-noise ratio snr=10, as the number of snapshots increases, the root mean square error of both methods decreases. When the number of snapshots is 50, the root mean square error of the traditional coprime array method is about 0.293, and the root mean square error of the patented method is about 0.142, which is about 0.158 higher than the traditional coprime array method. When the number of snapshots is 250, the root mean square error of the traditional coprime array method is about 0.133, and the root mean square error of the patented method is about 0.063, which is about 0.07 higher than the traditional coprime array method. It can be seen that the performance of the patented method is better than the traditional coprime array method, which is more obvious at low snapshot numbers.

[0081] analyze Figure 7 It can be seen that when the signal-to-noise ratio snr=10, as the number of snapshots increases, the success probability of resolution of the patented method and the traditional coprime array method increases. When the number of snapshots is 50, the success probability of resolution of the patented method is 100%, while the success probability of resolution of the traditional coprime array method is 95%.

[0082] The specific examples described herein are merely illustrative of the present invention. A person skilled in the art may make various modifications, supplements or substitute similar methods to the specific examples described, but this will not deviate from the present invention or exceed the scope defined by the appended claims.

Claims

1. A robust DOA estimation method based on generalized coprime array, which is applicable to generalized coprime sensor array. The generalized coprime sensor array is composed as follows: the number of sensors in uniform subarray 1 is N, and the sensor spacing is Md; the number of sensors in uniform subarray 2 is M, and the sensor spacing is Nd. The first and last array elements of subarray 1 and subarray 2 are corrected auxiliary array elements. A positive integer compression factor p is introduced to compress the array element spacing of subarray 1. The array element spacing of subarray 1 is compressed to in 2≤p≤M, the generalized coprime array is composed of compressed uniform subarray 1 and uniform subarray 2 nested, the first auxiliary array elements of the two subarrays are overlapped, and the array element position is described with half wavelength as the basic unit. The first auxiliary array element is the reference array element, and its position is recorded as 0. The array position set of the generalized coprime array is expressed as The number of sensors is Z = M + N - 1, including 3 auxiliary array elements, characterized by: The steps of DOA estimation method are as follows: Step 1: The generalized coprime array receiving data can be expressed as X(t) = [x1(t), x2(t), …, x M+N-1 (t)] T , perform Hilbert transform on these data, and get the complex signal form of the array receiving signal: Step 2: According to the formation and The corresponding relationship between the uniform sub-array 1 and the received data is constructed as follows: The received data of uniform subarray 2 is constructed as follows: Step 3: Using the complex signal of generalized coprime array Find the covariance matrix "(·) H ” is the conjugate transpose, where T is the number of snapshots in practical applications; Step 4: Use the complex signal of uniform subarray 1 Find the covariance matrix Using the complex signal of uniform subarray 2 Find the covariance matrix Step 5: According to the covariance matrix Estimate the phase error of each element of uniform subarray 1, which can be expressed as Estimate the amplitude error of each element of uniform subarray 1, which can be expressed as According to the covariance matrix Estimate the phase error of each element of uniform subarray 2, which can be expressed as Estimate the amplitude error of each element of uniform subarray 2, which can be expressed as Step 6: Calculate the correction vector of uniform subarray 1 Calculate the correction vector for uniform subarray 2 in Step 7: According to the position of each array element in the new uniform sub-array 1 and the new uniform sub-array 2, and The corresponding elements in are sorted and reorganized according to the positions of the new coprime array elements, and the duplicate elements are removed to obtain the amplitude and phase error matrix of the generalized coprime sensor array. Step 8. For the covariance matrix in step 3 Perform error compensation to obtain the data covariance matrix of the generalized coprime sensor array after amplitude and phase error correction Step 9: The differential position set of the generalized mutually prime sensor array is The difference position set and The range is continuous, so The array degrees of freedom are Step 10: vectorize the covariance matrix R in step 8 to obtain z = vec(R), sort the elements in vector z, take the average of repeated elements, and take the continuous part after rearrangement to obtain Using vector Constructing a Toeplitz matrix by spatial smoothing Step 11: Toeplitz matrix Perform feature decomposition and obtain The eigenvalue η i and its corresponding eigenvector, Arrange them from largest to smallest: The K larger eigenvalues ​​correspond to the signal subspace U S , The smaller eigenvalue corresponds to the noise subspace U N , K is the number of far-field narrowband incident signals, according to the signal subspace U S Or the noise subspace U N to estimate the direction of the incident signal.

2. A robust DOA estimation method based on generalized coprime arrays as claimed in claim 1, characterized in that: Step 5 The estimation method is as follows: A1. Get the covariance matrix Phase information angle(·) is the phase information of the extracted matrix, A2. The upper triangular part of the phase information matrix contains exactly the same information as the lower triangular part of the matrix. Extract the phase information matrix The upper triangle of has: A3. Sum the first diagonal elements to get Taking the mean value, we get A4. Subtract φ1 from all elements on the first diagonal of matrix T1, and set α 1n , n=1,2,...,N-1, according to this formula Solve make get A5. Transform the covariance matrix in step A1 into Repeat the above steps A1 to A4 to get 3. The robust DOA estimation method based on generalized coprime array according to claim 1, characterized in that: Step 5 The estimation method is as follows: B1. Get the covariance matrix The main diagonal elements of Using this vector, we can calculate B2. Get the covariance matrix The main diagonal elements of Using this vector, we can calculate 4. The robust DOA estimation method based on generalized coprime array according to claim 1, characterized in that: The Toeplitz matrix described in step 10 The construction method is: Perform spatial smoothing, the number of smoothing times is The length of each subarray is for Segment corresponds to virtual data z r The resulting covariance matrix.

5. The robust DOA estimation method based on generalized coprime array according to claim 1, characterized in that: The DOA estimation method in step 11 is: The spatial spectrum is calculated and the peak is searched for. The angle corresponding to the extreme value is the estimated value of the incident signal angle.

6. A robust DOA estimation method based on generalized coprime arrays as claimed in claim 1, characterized in that: The DOA estimation method in step 11 is: find the first K large eigenvalues, according to the formula An estimate of the incident signal angle can be obtained.

Images