Two-dimensional coherent signal DOA estimation method based on double parallel coprime array movement
By optimizing the mobility and sparse mesh of the dual parallel coprime array, the problem of insufficient two-dimensional angle estimation of coprime array under coherent signal conditions is solved, and more accurate two-dimensional angle estimation is achieved, which is suitable for complex multipath scenarios.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- XINJIANG UNIVERSITY
- Filing Date
- 2023-10-24
- Publication Date
- 2026-07-03
AI Technical Summary
Existing coprime array methods cannot effectively estimate the DOA of two-dimensional coherent signals, especially when the signal is coherent, as they cannot obtain the differential comatrix, resulting in insufficient angle estimation.
By utilizing the mobility of a dual parallel coprime array, the covariance matrix is reconstructed and vectorized. Combined with a sparse off-grid optimization function, a sparse vector is constructed to obtain a two-dimensional angle estimate of the signal.
It achieves accurate two-dimensional angle estimation under coherent signal conditions, applicable to complex multipath scenarios, and improves the accuracy and practicality of angle estimation.
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Figure CN117420495B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of coherent signal orientation estimation technology, and in particular to a two-dimensional coherent signal DOA estimation method based on the movement of a dual parallel coprime array. Background Technology
[0002] Direction of Arrival (DOA) estimation is a crucial problem in wireless communication, radar, and sound processing, aiming to determine the direction of a transmitter or target. Currently, using coprime arrays for DOA estimation has become a promising technique. Coprime arrays are a special array configuration; unlike traditional uniform arrays where element spacing is uniform, their element spacing is non-uniform. Therefore, with the same number of physical elements, they can achieve a larger array aperture and better angular resolution. For coprime arrays, vectorizing their covariance matrix yields the output of a differential comatrix. The differential comatrix has more elements than the coprime array, enabling underdetermined DOA estimation. However, obtaining the differential comatrix presupposes that the incident signal is incoherent. In reality, if the incident signal is a two-dimensional coherent signal, existing methods cannot obtain the corresponding differential comatrix, thus preventing DOA estimation for two-dimensional coherent signals. Therefore, how to overcome the influence of coherent signals so that when the incident signal is coherent, we can still obtain the difference comatrix of the coprime array and thus obtain a two-dimensional angle estimate of the coherent signal is an urgent problem to be solved. Summary of the Invention
[0003] This invention addresses existing technical problems by proposing a two-dimensional coherent signal DOA estimation method based on the movement of a dual-parallel coprime array. It provides a method for DOA estimation of two-dimensional coherent signals using the mobility of a dual-parallel coprime array, thus solving the angle estimation problem of two-dimensional coherent signals using coprime arrays. This invention utilizes the array's mobility and, combined with the characteristics of coprime arrays, reconstructs the array's output at different positions to obtain a new covariance matrix. This new covariance matrix is then vectorized to obtain the corresponding difference covariance matrix output. Finally, a sparse off-grid method is used to obtain the final angle estimate of the two-dimensional coherent signal.
[0004] This invention provides a two-dimensional coherent signal DOA estimation method based on the movement of a dual parallel coprime array, comprising:
[0005] The dual parallel array includes a first subarray and a second subarray. Phase compensation is performed on the output of the first subarray to obtain the compensated output of the first subarray, and phase compensation is performed on the output of the second subarray to obtain the compensated output of the second subarray.
[0006] A first vector is obtained based on the compensation output of the first subarray and the compensation output of the second subarray, and a second vector is obtained based on the compensation output of the first subarray.
[0007] Construct a sparse mesh optimization function;
[0008] The accurate angle estimate between the incident signal and the X-axis is obtained based on the sparse mesh optimization function.
[0009] The angle estimate between the incident signal and the Y-axis is obtained based on the first vector and the second vector;
[0010] An angle estimate of the two-dimensional coherent signal is obtained based on the accurate angle estimate of the incident signal with the X-axis and the angle estimate of the incident signal with the Y-axis.
[0011] Optionally, a phase correction factor is used to perform phase compensation on the outputs of the first subarray and the second subarray to obtain the compensated outputs of the first subarray and the second subarray. The calculation formulas for the compensated outputs of the first subarray and the second subarray are as follows:
[0012]
[0013]
[0014] In the formula, t q This represents the shift time of the dual parallel array. The first subarray moves in the double parallel array in time t. q The first subarray compensation output after that, The second subarray moves in the double parallel array in time t. q The second subarray compensation output, B h This represents the direction matrix after the array has been moved. The coefficient of coherence between the signals is represented by s(t), where s(t) represents the incident signal. This represents the phase correction factor. and Represents the noise vector. in, β k Let θ represent the angle between the incident signal and the Y-axis, d represent the spacing between subarrays, λ represent the wavelength of the incident signal, θ represent the frequency of the incident signal, k represent the k-th element in the total number of incident signals, and j represent the imaginary number. 2 =-1.
[0015] Optionally, the process of obtaining the first vector based on the compensation output of the first subarray and the compensation output of the second subarray includes:
[0016] Extract the corresponding row elements from the compensation output of the first subarray and the compensation output of the second subarray to construct a concatenation matrix;
[0017] Based on the splicing matrix, correlation vectors at different times are obtained;
[0018] The cross-covariance matrix is obtained based on the correlation vectors at different times;
[0019] The first vector is obtained by vectorizing the cross-covariance matrix.
[0020] Optionally, before constructing the sparse mesh optimization function, the method further includes dividing the space into several meshes at equal intervals by spatial angles, and constructing a dictionary matrix based on the angles of the several meshes;
[0021] The formula for the dictionary matrix is:
[0022]
[0023] In the formula, Θ represents the dictionary matrix. This represents the angle of the F-th grid. The guide vector representing the F-th grid angle. for The conjugate matrix, It represents the Kronecker product.
[0024] Optionally, the sparse mesh optimization function is constructed based on the dictionary matrix, wherein the calculation formula of the sparse mesh optimization function includes:
[0025]
[0026] In the formula, Let represent the second vector, u represent the grid spacing, ε represent the penalty function, f represent the first sparse vector, and ζ represent the second sparse vector. f T ζ represents the transpose of the first sparse vector. T f represents the transpose of the second sparse vector. f Let f represent the f-th element in f, and ζ represent the f-th element in f. f Let f represent the f-th element in ζ.
[0027] Optionally, the process of obtaining an accurate angle estimate between the incident signal and the X-axis based on the sparse mesh optimization function includes:
[0028] An initial estimate is obtained based on the peak value of the elements in the first sparse vector;
[0029] An angle compensation value is obtained by performing a dot division operation on the elements of the first sparse vector and the second sparse vector.
[0030] Based on the initial estimate and the angle compensation value, a precise angle estimate of the incident signal and the X-axis is obtained.
[0031] Optionally, the formula for calculating the angle compensation value is:
[0032] ξ k =(ζ k . / f k )
[0033] In the formula, ξ k f represents the angle compensation value of the incident k-th signal. k ζ represents the peak value of the first sparse vector. k This represents the peak value of the second sparse vector.
[0034] Optionally, the process of obtaining the angle estimate between the incident signal and the Y-axis based on the first vector and the second vector includes:
[0035] Based on the overall least squares method, the first vector and the second vector are calculated to obtain a first calculation result corresponding to the first vector and a second calculation result corresponding to the second vector;
[0036] A result vector is obtained based on the first calculation result and the second calculation result;
[0037] The phase of each element in the resulting vector is calculated to obtain an estimate of the angle between the incident signal and the Y-axis.
[0038] Optionally, the formula for calculating the result vector is:
[0039]
[0040] In the formula, ρ represents the result vector, and y v Denotes the first vector. Represents the second vector.
[0041] Optionally, the calculation formula for the angle estimate between the incident signal and the Y-axis obtained by operating on the elements of the result vector is as follows:
[0042]
[0043] In the formula, This represents the angle estimate between the incident signal k and the Y-axis.
[0044] The present invention has the following technical effects:
[0045] The method proposed in this invention can use a dual parallel coprime array to estimate the angle of a two-dimensional coherent signal, thus overcoming the shortcomings of coprime arrays in estimating the angle of coherent sources in practical applications and obtaining an accurate two-dimensional incident angle.
[0046] Compared to existing angle estimation algorithms, the method of this invention can utilize the mobility of the array and the characteristics of coprime arrays to obtain more accurate two-dimensional angle estimation of the signal. In addition, compared to existing methods based on coprime arrays, the method of this invention can be applied to complex scenes with multipath fields, thus having higher practical value. Attached Figure Description
[0047] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0048] Figure 1 This is a flowchart illustrating a two-dimensional coherent signal DOA estimation method based on the movement of a dual parallel coprime array, as described in an embodiment of the present invention.
[0049] Figure 2 This is a schematic diagram of the structure of the dual parallel coprime array in a two-dimensional coherent signal DOA estimation method based on the movement of a dual parallel coprime array in an embodiment of the present invention.
[0050] Figure 3 The graph shows the estimation performance of the two-dimensional coherent signal DOA estimation method based on the movement of a dual parallel coprime array in an embodiment of the present invention for the α angle under different signal-to-noise ratios (SNR).
[0051] Figure 4 The graph shows the estimation performance of the β angle of a two-dimensional coherent signal DOA estimation method based on the movement of a dual parallel coprime array in an embodiment of the present invention under different signal-to-noise ratios (SNR).
[0052] Figure 5 The graph shows the estimation performance of the two-dimensional coherent signal DOA estimation method based on the movement of a dual parallel coprime array in an embodiment of the present invention for the α angle under different snapshot numbers.
[0053] Figure 6 The graph shows the estimation performance of the β angle of a two-dimensional coherent signal DOA estimation method based on the movement of a dual parallel coprime array in an embodiment of the present invention under different snapshot numbers. Detailed Implementation
[0054] 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.
[0055] Example 1
[0056] like Figure 1 As shown, this embodiment provides a two-dimensional coherent signal DOA estimation method based on the movement of a dual parallel coprime array, specifically including the following steps:
[0057] The dual parallel array includes a first subarray and a second subarray. Phase compensation is performed on the output of the first subarray to obtain the compensated output of the first subarray, and phase compensation is performed on the output of the second subarray to obtain the compensated output of the second subarray. The specific implementation process includes step S1.
[0058] Step S1: Perform phase compensation on the outputs of the two subarrays of the moving dual parallel array to obtain the compensated array output. and
[0059] The first vector is obtained based on the compensation output of the first subarray and the compensation output of the second subarray, and the second vector is obtained based on the compensation output of the first subarray. The specific implementation process includes steps S2-S5.
[0060] Step S2: Construct the cross-covariance matrix R using the outputs of the two compensated subarrays. h ;
[0061] Step S3: Vectorize the cross-covariance matrix to obtain the vector y. v ;
[0062] Step S4: Construct the cross-covariance matrix using the output of the compensated subarray 1.
[0063] Step S5: Vectorize the covariance matrix to obtain the vector.
[0064] Step S6: Divide the spatial angle into F equal parts to construct the dictionary matrix Θ;
[0065] Step S7: Construct the sparse mesh optimization function;
[0066] The accurate angle estimate between the incident signal and the X-axis is obtained based on the sparse mesh optimization function. The specific implementation process includes steps S8-S10.
[0067] Step S8: The off-grid optimization function yields two vectors f and ζ. The peak value of f is searched to obtain the initial estimated angle.
[0068] Step S9: Divide the corresponding elements in vectors f and ζ to obtain the difference ξ between the initial angle estimate and the precise angle estimate. k ;
[0069] Step S10: Add the initial estimate to the difference to obtain the accurate angle estimate α. k ;
[0070] The angle estimate between the incident signal and the Y-axis is obtained based on the first vector and the second vector. The specific implementation process includes steps S11-S12.
[0071] Step S11: Obtain the vector ρ containing the angle β information using the overall square method.
[0072] Step S12: Calculate the phase of the elements in ρ to obtain the estimated angle value β. k ;
[0073] Furthermore, in step S1, for a dual-parallel coprime array, it consists of two parallel subarrays, namely the first subarray and the second subarray, with a spacing of d = λ / 2, where λ is the wavelength of the incident signal. For each subarray, the set of its element positions is...
[0074]
[0075] Where M and N are two coprime integers, For the array aperture. Additionally, Arrange the elements in order to obtain a vector. Where -h1 = 0,
[0076] Furthermore, assume that K far-field narrowband coherent signals are incident on the array, with the set of incident angles being α = [α1, α2, ..., α...]. K ], β=[β1,β2,...,β K ], where α k (k∈[1,2,...,K]) is the angle between the incident signal and the X-axis, β k (k∈[1,2,...,K]) is the angle between the incident signal and the Y-axis. Assuming the array moves at a speed of v along the X-axis, the outputs of the two subarrays at time t are:
[0077]
[0078]
[0079] Among them, Ah =[a h (α1),a h (α2),...,a h (α K [)] is the direction matrix. Let s(t) be the steering vector, s(t) be the incident signal, and K be the total number of signal sources; and These are abbreviated forms and have no specific physical meaning; their expressions are as follows: j is an imaginary number, i.e., j 2 =-1, n is a non-zero complex number, representing the coherence coefficient between signals, and n1(t) and n2(t) are noise vectors. For noise energy, Represents a size of The identity matrix.
[0080] Furthermore, let the time for the array to move be t. q , t q =h q / v(q is an integer with no specific physical meaning, and The outputs of the first subarray and the second subarray are respectively:
[0081]
[0082]
[0083] Multiply the output of the above subarray by the phase correction factor θ is the incident signal frequency. The phase-corrected array outputs are obtained, namely the first compensated output and the second compensated output:
[0084]
[0085]
[0086] in,
[0087] A first vector is obtained based on the first compensation output and the second compensation output, and a second vector is obtained based on the first compensation output, specifically including the following:
[0088] Furthermore, the corresponding row elements in the compensation outputs of the first and second subarrays are extracted to construct a concatenation matrix. Specifically, in step S2, the following elements are constructed:
[0089]
[0090] Where q' is an integer with no specific physical meaning, and k1 and k2 are integers with no specific physical meaning, and 1 ≤ k1, k2 ≤ K; E{·} represents the expectation operation. The correlation vectors at different times are obtained based on the spliced matrix. The specific implementation process includes: following the method in the above formula, when q′ changes sequentially from 1 to... Vector r can be obtained q =r(:,q); when q is from When the value is changed to 1, the correlation vectors at different times can be obtained. Based on the correlation vectors at different times, the cross-covariance matrix is obtained, specifically by combining all the vectors to obtain the cross-covariance matrix of the two submatrices:
[0091]
[0092] in, This refers to noise energy.
[0093] Furthermore, in step S3, the cross-covariance matrix is vectorized to obtain a first vector:
[0094]
[0095] Among them, B v =[b v (α1),b v (α2),...,b v (α K )], Indicates the Kronecker product; b v (α k The terms in ) are in the form of In other words, b v (α k The terms in ) can be viewed as terms in the steering vector of the virtual array, and the corresponding element positions of the virtual array are .
[0096] Furthermore, in step S4, the following elements are constructed:
[0097]
[0098] Following the method described above, as q′ changes sequentially from 1 to... Vectors can be obtained When q from When the value is changed to 1, the correlation vectors at different times can be obtained; combining all the vectors, the cross-covariance matrix of the two subarrays can be obtained:
[0099]
[0100] Furthermore, in step S5, the covariance matrix is vectorized to obtain the second vector:
[0101]
[0102] Furthermore, in step S6, the spatial angle is divided into F grids at equal intervals, with each grid having an angle of . The grid spacing is u, F >> K, and a dictionary matrix is constructed:
[0103]
[0104] Furthermore, in step S7, an off-mesh optimization function is constructed:
[0105]
[0106] in, f f Let f represent the f-th element in f, and ζ represent the f-th element in f. f Let f represent the f-th element in ζ, u be the grid spacing, ε be the penalty function, and f and ζ be two sparse vectors, ζ = Λf, Λ = diag(ξ); for each element ξ in ξ... f ,when At that time, ξ f =ξ k In other cases, the value is 0; For the closest incident angle α k The grid value,
[0107] The accurate angle estimate between the incident signal and the X-axis is obtained based on the sparse open mesh optimization function, specifically including the following:
[0108] Furthermore, in step S8, an initial estimate is obtained based on the peak value of the elements in the first sparse vector. The specific implementation process includes: searching for the peak value of the elements in vector f; the element corresponding to the peak value is... It is the angle α k The initial estimate.
[0109] Furthermore, in step S9, a dot division operation is performed on the elements of the first and second sparse vectors to obtain the angle compensation value. Specifically, this involves performing a dot division operation on the elements of the two sparse vectors f and ζ to obtain the difference between the initial angle estimate and the precise angle estimate, which is the compensation value ξ. k :
[0110] ξ k =(ζ k . / fk (16)
[0111] ζ k and f k These are the peak values of vectors ζ and f, respectively.
[0112] Furthermore, in step S10, a compensation value is added to the initial estimated angle to obtain an accurate angle estimate. Right now:
[0113]
[0114] The angle estimate between the incident signal and the Y-axis is obtained based on the first and second vectors, specifically including:
[0115] Furthermore, in step S11, the total least squares method is applied to equations (10) and (13) respectively, and the result is divided by the dot to obtain the vector ρ:
[0116]
[0117] in, . / represents the dot division operation.
[0118] Furthermore, in step S12, corresponding operations are performed on the elements of vector ρ to obtain an angle estimate.
[0119]
[0120] Angle estimates of the two-dimensional coherent signal are obtained based on accurate angle estimates of the incident signal relative to the X-axis and the incident signal relative to the Y-axis.
[0121] This invention utilizes the mobility of a dual parallel array to combine the outputs of two subarrays at different times, obtaining a new cross-covariance matrix. After vectorizing the cross-covariance matrix, the output of the corresponding difference comatrix is obtained. Using the same process, the outputs of subarray 1 at different times are combined to obtain a new covariance matrix, which is then vectorized to obtain the output of the corresponding difference comatrix. Next, a dictionary matrix is constructed, and a sparse off-grid optimization function is constructed to obtain sparse vectors. The initial angle value and its difference from the precise value are obtained by searching for peaks. The initial value and the difference are then added to obtain the precise angle estimate. Finally, using total least squares and point division, a vector containing information about the other incident angle is obtained. The phase of the elements in the vector is calculated to obtain the final angle estimate. Compared to existing angle estimation algorithms, this invention's method can utilize the mobility of the array and the characteristics of coprime arrays to obtain a more accurate two-dimensional angle estimate of the signal. Furthermore, compared to existing methods based on coprime arrays, this invention's method can be applied to complex multipath fields, thus having higher practical value.
[0122] Example 2
[0123] This embodiment provides a two-dimensional coherent signal DOA estimation method based on the movement of a dual parallel coprime array, specifically including the following steps:
[0124] Phase compensation is performed on the outputs of the two subarrays of the moving dual parallel array to obtain the compensated array output. and
[0125] Construct the cross-covariance matrix R using the outputs of the two compensated subarrays. h ;
[0126] Vectorizing the cross-covariance matrix yields the vector y. v ;
[0127] Construct the cross-covariance matrix using the output of the compensated subarray 1.
[0128] Vectorize the covariance matrix to obtain a vector
[0129] Divide the spatial angle into F equal parts to construct the dictionary matrix Θ;
[0130] Construct a sparse mesh optimization function;
[0131] The off-grid optimization function yields two vectors, f and ζ. The peak value of f is searched to obtain the initial estimated angle.
[0132] Dividing the corresponding elements in vectors f and ζ yields the difference ξ between the initial angle estimate and the precise angle estimate. k ;
[0133] Adding the initial estimate to the difference yields the accurate angle estimate α. k ;
[0134] The vector ρ containing the angle β information is obtained using the total square method.
[0135] Find the phase of the elements in ρ to obtain the angle estimate β. k ;
[0136] To more clearly describe the method in this embodiment, a specific example is provided for illustration, which includes:
[0137] like Figure 2 As shown, step 1: For a dual parallel coprime array, it consists of two parallel subarrays, namely the first subarray and the second subarray, with a spacing of d = λ / 2, where λ is the wavelength of the incident signal. For each subarray, the set of its element positions is as follows:
[0138]
[0139] Where M = 16, N = 17, and the aperture of the array is... In addition, Arrange the elements in order to obtain a vector.
[0140] Assume three far-field narrowband coherent signals are incident on the array, with incident angle sets α = [40.6°, 65.5°, 80.3°] and β = [50.8°, 75.5°, 85.4°], where α... k (k∈[1,2,3]) is the angle between the incident signal and the X-axis, β k (k∈[1,2,3]) is the angle between the incident signal and the Y-axis. Assuming the array moves at a speed of v along the X-axis, the outputs of the two subarrays at time t are as follows:
[0141]
[0142]
[0143] Among them, A h =[a h (α1),a h (α2),a h [α3] is the direction matrix. Let s(t) be the guide vector and s(t) be the incident signal. n is a non-zero complex number, representing the coherence coefficient between signals, and n1(t) and n2(t) are noise vectors. For noise energy, This represents an identity matrix of size 32×32.
[0144] Let the time for the array to move be t. q , t q =h q / v, the outputs of the first and second subarrays are as follows:
[0145]
[0146]
[0147] Phase compensation is applied to the output of the first subarray to obtain the compensated output of the first subarray, and phase compensation is applied to the output of the second subarray to obtain the compensated output of the second subarray. Specifically, this involves multiplying the outputs of the above subarrays by a phase correction factor. θ is the frequency of the incident signal, and the phase-corrected array output is obtained as follows:
[0148]
[0149]
[0150] in,
[0151] The first vector is obtained based on the compensation output of the first subarray and the compensation output of the second subarray, and the second vector is obtained based on the compensation output of the first subarray. The specific implementation process includes steps 2-5.
[0152] Step 2: Extract the corresponding row elements from the compensation outputs of the first and second subarrays to construct a concatenated matrix. This specifically includes: extracting x... m1 (t q ) and x m2 (t q For all elements in the corresponding row of the given array, construct r(q′,q):
[0153]
[0154] Where E{·} represents the expectation operation, The correlation vectors at different times are obtained based on the concatenated matrix. The specific implementation process includes: following the method in the above formula, as q′ changes sequentially from 1 to 32, the vector r can be obtained. q =r(:,q); When q changes from 32 to 1, the correlation vectors at different times can be obtained. Based on the correlation vectors at different times, the cross-covariance matrix is obtained, specifically by combining all vectors to obtain the cross-covariance matrix of two submatrices:
[0155]
[0156] in, This refers to noise energy.
[0157] Step 3: Perform a vectorization operation on the cross-covariance matrix to obtain the first vector:
[0158]
[0159] Among them, B v =[b v (α1),b v (α2),b v (α3)], Indicates the Kronecker product; b v (α k The terms in ) are in the form of In other words, b v (α kThe terms in ) can be viewed as terms in the steering vector of the virtual array, and the corresponding element positions of the virtual array are .
[0160] Step 4: Extract x m1 (t q For all elements in the corresponding row of the given array, construct r(q′,q) and perform the following operations to calculate...
[0161]
[0162] As q′ changes sequentially from 1 to Vectors can be obtained When q from When the value is changed to 1, the correlation vectors at different times can be obtained; combining all the vectors, the cross-covariance matrix of the two subarrays can be obtained:
[0163]
[0164] Step 5: Perform a vectorization operation on the covariance matrix to obtain the second vector:
[0165]
[0166] Step 6: Divide the space into 1800 equally spaced grids, with each grid having an angle of 1800. The grid spacing is 0.1°, and a dictionary matrix is constructed:
[0167]
[0168] Step 7: Construct the sparse mesh optimization function
[0169]
[0170] in, u is the grid spacing, ε = 0.001 is the penalty function, f represents the first sparse vector, ζ represents the second sparse vector, ζ = Λf, Λ = diag(ξ); for each element ξ in ξ f ,when At that time, ξ f =ξ k In other cases, the value is 0; For the closest incident angle α k The grid value,
[0171] The accurate angle estimate between the incident signal and the X-axis is obtained based on the sparse mesh optimization function. The specific implementation process includes steps 8-10.
[0172] Step 8: Obtain the initial estimate based on the peak value of the elements in the first sparse vector. The specific implementation process includes: searching for the peak value of the elements in vector f; the element corresponding to the peak value is... It is the angle α k The initial estimate.
[0173] Step 9: Perform a dot division operation on the elements of the first and second sparse vectors to obtain the angle compensation value. Specifically, this involves performing a dot division operation on the elements of the two sparse vectors f and ζ to obtain the difference matrix between the initial angle estimate and the precise angle estimate, which is the compensation value ξ. k :
[0174] ξ k =(ζ k . / f k (16)
[0175] ζ k and f k These are the peak values of vectors ζ and f, respectively.
[0176] Step 10: Obtain the accurate angle estimate between the incident signal and the X-axis based on the initial estimate and the angle compensation value. The specific implementation process includes: adding the compensation value to the initial estimated angle to obtain the accurate angle estimate. Right now:
[0177]
[0178] The angle estimate between the incident signal and the Y-axis is obtained based on the first vector and the second vector. The specific implementation process includes steps 11-12.
[0179] Step 11: Apply the total least squares method to equations (10) and (13) respectively to obtain the first calculation result corresponding to the first vector and the second calculation result corresponding to the second vector, and divide the first calculation result and the second calculation result by the dot matrix to obtain the result vector ρ:
[0180]
[0181] in, . / represents the dot division operation.
[0182] Step 12: Perform the corresponding operations on the elements in the result vector ρ to obtain the angle estimate.
[0183]
[0184] Angle estimates of the two-dimensional coherent signal are obtained based on accurate angle estimates of the incident signal relative to the X-axis and the incident signal relative to the Y-axis.
[0185] To verify the correctness and advancement of the method in this embodiment, a simulation experiment was conducted. The specific simulation results are as follows: Figures 3-6 As shown, specifically, Figure 3 and Figure 4 The root mean square error (RMSE) plots for angles α and β are shown for the implementation method as the signal-to-noise ratio (SNR) changes. It can be seen that for angle α, the method of the present invention can obtain the best angle estimation accuracy compared to existing methods. For angle β, the method of the present invention can obtain the best estimation performance when the SNR is greater than 7 dB. Figures 5-6 The root mean square error (RMSE) plots for angles α and β are shown for the implementation method as the number of snapshots changes. It can be seen that for angle α, compared with existing methods, the method of the present invention can always obtain the best angle estimation accuracy. For angle β, when the number of snapshots is greater than 100, the method of the present invention can obtain the most accurate angle estimation.
[0186] In summary, this invention proposes a two-dimensional coherent signal DOA estimation method based on the movement of a dual-parallel coprime array. This method utilizes the mobility of the dual-parallel coprime array to reconstruct a new covariance matrix. Vectorizing the covariance matrix yields the output of the corresponding difference matrix. Then, by constructing and solving a sparse off-grid optimization problem, two sparse vectors are obtained. By searching for the peak value of the sparse vectors, an accurate estimate of one angle can be obtained. Furthermore, by using total least squares and vector point division, the estimate of the other angle of the signal can be obtained. Compared to traditional coherent signal estimation methods and coherent signal DOA estimation methods based on area arrays, this invention can obtain more accurate angle estimates for two-dimensional coherent signals with the same number of array elements. This invention can effectively resolve signal coherence scenarios caused by signal reflection and other factors in real-world applications, thus exhibiting greater practicality and adaptability.
[0187] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.
Claims
1. A two-dimensional coherent signal DOA estimation method based on the movement of a dual parallel coprime array, characterized in that, include: The dual parallel array includes a first subarray and a second subarray. Phase compensation is performed on the output of the first subarray to obtain the compensated output of the first subarray, and phase compensation is performed on the output of the second subarray to obtain the compensated output of the second subarray. A first vector is obtained based on the compensation output of the first subarray and the compensation output of the second subarray, and a second vector is obtained based on the compensation output of the first subarray. Construct a sparse mesh optimization function; The accurate angle estimate between the incident signal and the X-axis is obtained based on the sparse mesh optimization function. The angle estimate between the incident signal and the Y-axis is obtained based on the first vector and the second vector; An angle estimate of the two-dimensional coherent signal is obtained based on the accurate angle estimate of the incident signal with the X-axis and the angle estimate of the incident signal with the Y-axis. Phase compensation is performed on the outputs of the first subarray and the second subarray using a phase correction factor to obtain the compensated outputs of the first and second subarrays. The calculation formulas for the compensated outputs of the first and second subarrays are as follows: In the formula, This represents the shift time of the dual parallel array. This indicates that the first subarray moves in the double parallel array in a time of [time value missing]. The first subarray compensation output after that, This indicates that the second subarray moves in the double parallel array in a time of [time value missing]. The second subarray compensation output, This represents the direction matrix after the array has been moved. Represents the coherence coefficient between signals. Indicates the incident signal. , , This represents the phase correction factor. and Represents the noise vector. ,in, , The angle between the incident signal and the Y-axis is represented by d, the spacing between subarrays is represented by λ, and the wavelength of the incident signal is represented by λ. Indicates the frequency of the incident signal. Represents the th in the total number of incident signals indivual, represents an imaginary number, ; The process of obtaining the first vector based on the compensation output of the first subarray and the compensation output of the second subarray includes: extracting the corresponding row elements from the compensation output of the first subarray and the compensation output of the second subarray to construct a concatenation matrix; obtaining the correlation vectors at different times based on the concatenation matrix; obtaining the cross-covariance matrix based on the correlation vectors at different times; and performing a vectorization operation on the cross-covariance matrix to obtain the first vector. Before constructing the sparse mesh optimization function, the process also includes dividing the space into several meshes at equal intervals by spatial angles, and constructing a dictionary matrix based on the angles of the several meshes. The formula for the dictionary matrix is: In the formula, Represents a dictionary matrix. This represents the angle of the F-th grid. Indicates the first Guide vector for each grid angle, for The conjugate matrix, Indicates the Kronecker product; The sparse mesh optimization function is constructed based on a dictionary matrix, wherein the calculation formula of the sparse mesh optimization function includes: In the formula, , Represents the second vector. Indicates grid spacing. Represents the penalty function. Describes the first sparse vector. Describes the second sparse vector. , This represents the transpose of the first sparse vector. This represents the transpose of the second sparse vector. express The first in One element, express The first in One element; The process of estimating the angle between the incident signal and the Y-axis based on the first vector and the second vector includes: Based on the overall least squares method, the first vector and the second vector are calculated to obtain a first calculation result corresponding to the first vector and a second calculation result corresponding to the second vector; A result vector is obtained based on the first calculation result and the second calculation result; The phase of each element in the resulting vector is calculated to obtain an estimate of the angle between the incident signal and the Y-axis.
2. The two-dimensional coherent signal DOA estimation method based on the movement of a dual parallel coprime array according to claim 1, characterized in that, The process of obtaining an accurate angle estimate between the incident signal and the X-axis based on the sparse mesh optimization function includes: An initial estimate is obtained based on the peak value of the elements in the first sparse vector; An angle compensation value is obtained by performing a dot division operation on the elements of the first sparse vector and the second sparse vector. Based on the initial estimate and the angle compensation value, a precise angle estimate of the incident signal and the X-axis is obtained.
3. The two-dimensional coherent signal DOA estimation method based on the movement of a dual parallel coprime array according to claim 2, characterized in that, The formula for calculating the angle compensation value is: In the formula, This represents the angle compensation value of the k-th incident signal. Represents the peak value of the first sparse vector. This represents the peak value of the second sparse vector.
4. The two-dimensional coherent signal DOA estimation method based on the movement of a dual parallel coprime array according to claim 1, characterized in that, The formula for calculating the result vector is: In the formula, Represents the result vector. Denotes the first vector. Represents the second vector. .
5. The two-dimensional coherent signal DOA estimation method based on the movement of a dual parallel coprime array according to claim 4, characterized in that, The formula for calculating the angle estimate between the incident signal and the Y-axis by operating on the elements of the result vector is as follows: In the formula, This represents the angle estimate between the incident signal k and the Y-axis.