High-order off-grid doa estimation method and system based on extended orthogonal array

Abstract

The application discloses a high-order off-grid DOA estimation method and system based on an extended coprime array and belongs to the field of polar water sound detection. The method comprises the following steps: acquiring signals received by the extended coprime array to form a receiving data matrix; introducing a phase fraction low-order moment method to construct a phase fraction low-order moment matrix C, vectorizing C, removing redundancy and rearranging to obtain a single-snapshot continuous virtual uniform linear array signal vector z1; based on z1, using a division method of an overlapping subarray to construct a multiple measurement signal vector matrix Z; using a high-order Taylor expansion term to construct an off-grid model, using an extrapolation-based iterative sparse projection algorithm to jointly estimate a sparse signal matrix and a grid offset according to the matrix Z, and estimating the DOA of a target. The application provides a new solution to the problems of performance decline of a conventional DOA estimation method in a polar pulse noise environment and a limited number of detectable targets of a traditional uniform linear array.

Description

Technical Field

[0001] This invention relates to a high-order off-grid DOA estimation method and system based on an extended coprime array, belonging to the field of polar underwater acoustic detection. Background Technology

[0002] The Arctic region is covered by ice and snow year-round. Natural factors such as ice layer fracturing and compression, driven by ice and wind, often result in a large amount of randomly fluctuating impulse noise propagating underwater, severely impacting polar underwater exploration. Most common Direction of Arrival (DOA) estimation methods typically assume that the background noise follows a Gaussian distribution, making them unsuitable for polar environments and significantly degrading their detection performance. Furthermore, as the number of targets to be detected by the array increases, the number of array elements cannot be increased indefinitely. Therefore, using sparse arrays, such as extended coprime arrays, can detect a greater number of targets without increasing the number of elements, achieving overdetermined DOA estimation. Thus, there is an urgent need to develop DOA estimation methods suitable for polar impulse noise environments and extended coprime arrays to provide strong support for polar underwater exploration.

[0003] In polar impulse noise environments, some researchers have proposed combining fractional low-order phase moments (FLS) with Multiple Signal Classification (MUSIC) methods for DOA estimation in extended coprime arrays, achieving relatively accurate DOA estimation results. However, the accuracy of MUSIC-based DOA estimation methods differs from that of off-grid DOA estimation methods based on sparse reconstruction. Furthermore, MUSIC-based DOA estimation methods cannot address the mesh mismatch problem. This invention aims to solve the problem of overcoming mesh mismatch by applying sparse reconstruction methods and off-grid models. Summary of the Invention

[0004] The purpose of this invention is to provide a high-order off-grid DOA estimation method and system based on extended coprime arrays, which solves the problem of decreased detection performance of conventional DOA estimation methods in polar impulse noise environments and the problem of the limited number of targets that can be detected by traditional uniform linear arrays.

[0005] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0006] Firstly, a high-order off-grid DOA estimation method based on an extended coprime array includes the following steps:

[0007] Obtain the signal x(t) received by the extended coprime array to form the received data matrix X;

[0008] For the array received data matrix X, introduce the phase fractional lower-order moment method to construct the phase fractional lower-order moment matrix C, vectorize the phase fractional lower-order moment matrix C, perform redundancy removal and rearrangement on it, and obtain the single snapshot continuous virtual uniform linear array signal vector z1;

[0009] Based on the single snapshot continuous virtual uniform linear array signal vector z1, adopt the overlapping subarray division method, slide one element to the right each time until reaching the last element of the single snapshot continuous virtual uniform linear array signal vector z1, to maximize the overlap between subarrays, and construct the multiple measurement signal vector matrix Z;

[0010] Use high-order Taylor expansion terms to construct the off-grid model, and according to the multiple measurement signal vector matrix Z, use the extrapolation-based iterative sparse projection algorithm to jointly estimate the sparse signal matrix and the grid offset, and estimate the DOA of the target. The extrapolation-based iterative sparse projection algorithm introduces an extrapolation step to perform extrapolation processing on the sparse signal matrix based on the iterative sparse projection algorithm. The extrapolation step uses the difference between the sparse signal matrices obtained from two consecutive iterations to compensate the sparse signal matrix of the current iteration.

[0011] Furthermore, the array structure of the extended co-prime array includes two subarrays, which are composed of 2M and N array elements respectively. The element spacings between them are Nd and Md respectively, where M and N are relatively prime, M < N, and d represents the half-wavelength spacing of the signal. Taking the first array element as the reference array element, the physical array element positions are: S ={Nmd|0 ≤ m ≤ 2M - 1} ∪ {Mnd|0 ≤ n ≤ N - 1}.

[0012] Furthermore, the construction of the received data matrix X includes:

[0013] The t-th snapshot signal received by the array is expressed as:

[0014] x(t) = A(θ)s(t) + n(t), t = 1, …, T

[0015] where, represents the t-th snapshot signal received by the array; s(t) represents the vector composed of the envelope amplitudes of each signal at the t-th snapshot; T represents the maximum number of snapshots; is the background noise signal; A(θ) is the array steering vector matrix;

[0016] The order of the signal data matrix composed of T snapshots is

[0017] Furthermore, the high-order Taylor expansion off-grid model is as follows:

[0018]

[0019] Where, a(θ) q ) represents the steering vector of the target signal. The steering vector representing the grid point closest to the target signal. express about The first derivative, express about The second derivative, express about The nth derivative, β q This represents the grid offset parameter.

[0020] Furthermore, the extrapolation-based iterative sparse projection algorithm includes a sparse signal matrix solution stage and a grid offset solution stage, wherein in the sparse signal matrix solution stage, according to The sparse signal matrix S obtained in the i-th iteration (i) Perform extrapolation based on Perform sparsification processing, and then according to Projection continues until the specified iteration is satisfied, or the parameter ξ is less than or equal to the set threshold ξ. f Where w represents a weighting constant between 0 and 1, and the parameter ξ is a differentiable function H. ξ The parameter, ΔH ξ Representation function H ξ The derivative operation, μ ξ This is the sparsification step size.

[0021] Furthermore, the differentiable function H ξ It is a function with an approximate 0 norm:

[0022]

[0023] Where e is the base of the natural logarithm, and s is a complex number whose real and imaginary parts are denoted as si and si, respectively. r and s i .

[0024] Secondly, an off-grid DOA estimation system for polar impulse noise environments includes:

[0025] The data acquisition module acquires the signal x(t) received by the extended coprime array and forms the received data matrix X;

[0026] The single-shot virtual signal vector construction module introduces the phase fraction low-order moment method to construct the phase fraction low-order moment matrix C for the array received data matrix X. The phase fraction low-order moment matrix C is vectorized, and redundancy is removed and rearranged to obtain the single-shot continuous virtual uniform linear array signal vector z1.

[0027] The multi-measurement vector model construction module is based on the single-shot continuous virtual uniform linear array signal vector z1. It adopts the overlapping sub-array division method, sliding one element at a time until the last element of the single-shot continuous virtual uniform linear array signal vector z1 is reached, so as to maximize the overlap between the sub-arrays and construct the multi-measurement signal vector matrix Z.

[0028] The DOA estimation module uses a high-order Taylor expansion to construct an off-grid model. Based on the multiple measurement signal vector matrix Z, it uses an extrapolation-based iterative sparse projection algorithm to jointly estimate the sparse signal matrix and grid offset to estimate the target's DOA. The extrapolation-based iterative sparse projection algorithm introduces an extrapolation step to extrapolate the sparse signal matrix on the basis of the iterative sparse projection algorithm. The extrapolation step uses the difference between the sparse signal matrices obtained from two consecutive iterations to compensate for the sparse signal matrix of the current iteration.

[0029] Thirdly, the present invention also provides a computer device comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, wherein when the programs are executed by the processors, they implement the steps of the high-order off-grid DOA estimation method based on an extended coprime array as described in the first aspect of the present invention.

[0030] Fourthly, the present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the high-order off-grid DOA estimation method based on an extended coprime array as described in the first aspect of the present invention.

[0031] Beneficial Effects: This invention first employs an extended coprime array (ECA) to detect targets. Considering the presence of impulse noise in the polar environment, a fractional phase low-order moment (PFLOM) is introduced to construct an equivalent covariance matrix (PFLOM matrix). Then, the PFLOM matrix is ​​vectorized, redundancy is removed, and it is rearranged to obtain a single-shot signal vector of a continuous virtual uniform linear array (ULA). Subsequently, based on the ECA, a multiple measurement vector (MMV) model is proposed using this virtual single-shot signal vector. Compared to the single measurement vector (SMV) model, the MMV model enables the sparse reconstruction algorithm to achieve higher DOA estimation accuracy. Furthermore, this invention proposes an extrapolation-based iterative sparse projection algorithm for DOA estimation. This algorithm includes an extrapolation step, using the difference between two iterations to compensate for the sparse signal matrix in the current iteration, enabling rapid convergence and improving the overall performance of the method. Based on the high-order off-mesh model proposed in this invention, the extrapolation-based iterative sparse projection algorithm is finally used to jointly estimate the sparse signal matrix and mesh offset, thereby overcoming the mesh mismatch problem and achieving high-precision estimation of the target's azimuth. Attached Figure Description

[0032] Figure 1 This is a flowchart of a high-order off-grid DOA estimation method based on an extended coprime array under polar impulse noise;

[0033] Figure 2 It is the actual position of the sensor elements in the extended coprime array;

[0034] Figure 3 This is a diagram illustrating the principle of array element smoothing.

[0035] Figure 4 The root mean square error (RMSE) curves of DOA estimation under different weight parameters are obtained by the improved proximal splitting and successive nonconvex sparse approximation algorithm (which applies an extrapolation step).

[0036] Figure 5 The RMSE curves of the first-order off-network sparse Bayesian algorithm, the first-order off-network proximal splitting and successive non-convex sparse approximation algorithm, and the proposed high-order off-network proximal splitting and successive non-convex sparse approximation algorithm under different input signal-to-noise ratio values ​​are shown.

[0037] Figure 6 This is a time-domain waveform of impulse noise collected in the Arctic.

[0038] Figure 7 These are the root mean square error curves of various algorithms under different input generalized signal-to-noise ratios in Arctic environmental noise. Detailed Implementation

[0039] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to specific embodiments and accompanying drawings.

[0040] Referring to Figure 1 , a multi - order off - grid DOA estimation method based on an extended co - prime array under polar impulse noise provided by the present invention includes the following steps:

[0041] Step 1: Considering the far - field narrow - band signal model, in the polar impulse noise environment, use an extended co - prime array to receive the target signal.

[0042] Referring to Figure 2 , the array structure of the extended co - prime array includes two sub - arrays. Both sub - arrays are uniform linear arrays. Sub - array 1 and sub - array 2 are composed of 2M and N array elements respectively, and the element spacings between them are Nd and Md respectively, where M and N are relatively prime, and d represents the half - wavelength spacing of the signal. Here, it is assumed that M < N. If the first element in the two sub - arrays is regarded as the reference element, the physical element positions are:

[0043] S p ={Nmd|0≤m≤2M - 1}∪{Mnd|0≤n≤N - 1}.

[0044] Then the t - th snapshot signal received by the array is expressed as:

[0045] x(t)=A(θ)s(t)+n(t), t = 1,…,T

[0046] Wherein, represents the t - th snapshot signal received by the array; s(t) represents the vector composed of the envelope amplitudes of each signal at the t - th snapshot; T represents the maximum number of snapshots; is the background noise signal; A(θ) is the steering vector matrix of the array.

[0047] Construct the received data matrix X according to the received signal x(t). x(t) represents the signal vector of the t - th snapshot, and its order is Therefore, the order of the signal data matrix composed of T snapshots is That is, X is composed of T one - dimensional vectors (t = 1,…,T).

[0048] Step 2: Obtain the array received data matrix X obtained in Step 1, and introduce the phase - fractional lower - order moment method to construct the phase - fractional lower - order moment matrix C.

[0049] Based on the definition of the phase - fractional lower - order moment, the (i,j) - th element of the phase - fractional lower - order moment matrix C is defined as follows:

[0050]

[0051] Where the phase - fractional lower - order matrix (PFLOM matrix) (.) * This indicates the conjugate operation. 0 < α ≤ 2 represents the characteristic exponent of impulse noise. i (t), x j (t) represents the i-th and j-th elements of the t-th snapshot vector x(t). p represents the lower order of the phase fraction. For example, if α = 1.8, then the range of values ​​for the lower order of the phase fraction p is... This is how impulse noise is effectively suppressed.

[0052] According to C ij The formula is defined as follows: if we let p = 1 (where α = 2 represents Gaussian noise, and p = 1 is suitable for handling Gaussian noise), substituting into the formula yields... This is the definition formula for the covariance matrix. Because in the case of impulse noise, 0 < α < 2, and p⁻¹ ≠ 0, therefore we have... The formula's formal structure is similar to the definition of a covariance matrix, hence it is called an equivalent covariance matrix.

[0053] Step 3: Vectorize the low-order phase fraction matrix C obtained in Step 2, remove redundancy and rearrange it to obtain the single-shot continuous virtual uniform linear array signal vector z1.

[0054] Because removing redundant virtual elements results in some virtual elements having discontinuous phases, and most DOA estimation methods can only handle virtual uniform linear matrices with continuous phases, the rearrangement process aims to find a uniform linear matrix with the maximum number of virtual elements having continuous phases.

[0055] Step 4: Construct the multiple measurement signal vector matrix Z using the single-shot continuous virtual uniform linear array signal vector z1 obtained in Step 3, specifically as follows:

[0056] like Figure 3 As shown, based on the single-shot continuous virtual uniform linear array signal vector z1, the overlapping subarray division method is adopted, and one element is slid to the right at a time until the last element of the single-shot continuous virtual uniform linear array signal vector z1 is reached, so as to maximize the overlap between the subarrays.

[0057] The number of array elements G in the subarray and the number of snapshots P in the multiple measurement vector matrix are determined. It is assumed that the single-snapshot continuous virtual uniform linear array signal vector z1 contains... If there are n elements, then the mathematical relationship between them is: For example, suppose a single snapshot of a virtual uniform linear array contains 24 elements. In this case, the number of elements that can be selected is less than or equal to 24. If 20 elements are selected, combined with... Figure 3The constructable multi-measurement vector matrix consists of five virtual elements: 1 to 20, 2 to 21, 3 to 22, 4 to 23, and 5 to 24. The number of virtual elements chosen depends on the user's priorities; 24 corresponds to... 5 corresponds to the number of snapshots, P.

[0058] This invention constructs a multiple measurement vector (MMV) model based on a single-shot continuous virtual uniform linear array signal vector z1 using an overlapping subarray partitioning method. The MMV model is then implemented using the multiple measurement signal vector matrix. Characterization, hypothesis It is a single-shot continuous virtual uniform linear array signal vector. The p-th element is the p-th snapshot signal vector of the multiple measurement signal vector matrix Z. It can be represented as For example, combining with the previous example, the matrix composed of 5 snapshot vectors is the multiple measurement signal vector matrix Z.

[0059] Step 5: Construct the off-mesh model based on higher-order Taylor expansion terms:

[0060]

[0061] Where, a(θ) q ) represents the steering vector of the target signal. The steering vector representing the grid point closest to the target signal. express about The first derivative, express about The second derivative, express about The nth derivative, β q Representing the grid offset parameter, specifically, the true orientation of the signal is: Where the grid offset parameter β q These are the parameters to be estimated.

[0062] Since the first-order Taylor expansion off-grid model loses higher-order information, higher-order Taylor expansion off-grid models can achieve more accurate approximations and more precisely estimate the grid offset β. q The size of the DOAs is determined to obtain more accurate DOAs estimates.

[0063] Step 6: Use an extrapolation-based iterative sparse projection algorithm to jointly estimate the sparse signal matrix and grid offset.

[0064] Input multiple measurement signal vector matrix Z, and the array manifold dictionary set corresponding to the multiple measurement signal vector matrix Z. The derivative matrices of each order of the array manifold dictionary set (in Represents the dictionary set of array manifolds Find the nth derivative), the maximum number of iterations in the inner loop is H = 100, and the maximum number of iterations in the outer loop is H. max =5, number of signal sources Q, compression factor c = 0.9, weight constant w = 0.9, grid offset relative error τ1 = 10 -4 .

[0065] Initialize the sparse signal matrix as follows Initialize the parameter ξ The column vector representing the nth column of the matrix, initialized with the sparse step size μ. ξ =0.5, initialize the number of iterations p=1.

[0066] The iterative sparse projection algorithm described in this paper can also be called: proximal splitting and successive nonconvex sparse approximation algorithm; the iterative sparse projection algorithm based on extrapolation described in this paper can also be called: proximal splitting and successive nonconvex sparse approximation algorithm based on extrapolation. This invention introduces an extrapolation step into the proximal splitting and successive nonconvex sparse approximation algorithm to jointly estimate the sparse signal matrix S and the grid offset β. The specific execution steps are as follows:

[0067]

[0068]

[0069] Output sparse signal matrix S and grid offset β.

[0070] First, there exists a large outer loop, which iterates 5 times, i.e., H. max =5. Within the larger outer loop, there are two smaller loops. The first smaller loop (called loop 1) updates the sparse signal matrix S, which includes a sparsification step and a projection step. The termination condition for loop 1 is: ξ ≤ ξ f Or its iteration count is greater than H = 200. In loop 1, ξ f =5×10 -4 ξ is a parameter of the differentiable function in the sparsification step, which is a function approximately in the 0-norm:

[0071]

[0072] Where ΔH ξ Representation function H ξ The derivative operation is performed where s is a complex number, and its real and imaginary parts are represented as si and si, respectively.r and s i .

[0073] In the second sub-loop (referred to as loop 2), after loop 1, the sparse signal matrix S is obtained, allowing the location of the grid points containing the signal to be found. Loop 2 only needs to update the grid offset b corresponding to the location of the grid points containing the signal. β (This vector is a grid offset vector composed of the offsets β of each grid point). Loop 2 also contains two steps: a sparsification step and a projection step. These two steps are similar to the two steps in loop 1, where μ... β The step size is represented by Δ, which is the derivative sign. It is a polynomial function that constructs an off-grid model based on higher-order Taylor expansion terms. The function ΔH Q With ΔH ξ The definition is similar, for It has the following definition:

[0074]

[0075] in, Where β q d represents the grid offset of the q-th signal, and d represents the grid spacing. For example, if the grid spacing is set to 1 degree between 0 degrees and 180 degrees, then the angle of the grid points is divided into: 0 degrees, 1 degree, ..., 180 degrees.

[0076] This invention adds an extrapolation step to the proximal splitting and successive nonconvex sparse approximation algorithms, improving the sparse signal recovery performance of the original algorithms. The extrapolation step is as follows: Among them, S (i) Let w = 0.9 represent the sparse signal matrix obtained in the i-th iteration. This extrapolation step enhances the convergence behavior and accelerates the performance of the algorithm. By utilizing information from previous iterations, the extrapolation step allows for a more efficient exploration of the solution space, thereby improving convergence and potentially obtaining better recovery results.

[0077] Step 7: After obtaining the sparse signal matrix S and the grid offset β, according to formula P s =diag(SS) H This allows us to estimate the target's DOAs.

[0078] Simulation and experimental data verification:

[0079] The advantages of this invention will be further explained below in conjunction with the experimental data processing results. Obviously, the described experimental results are only some embodiments of this invention, not all embodiments, and are used only for illustration and explanation, and are not intended to limit the application of this invention. All other embodiments obtained by those skilled in the art based on the experimental data processing results of this invention without inventive effort should fall within the scope of protection of this invention.

[0080] Simulation and experimental studies of this invention:

[0081] Simulation conditions: In the simulation experiment, the symmetric α-stable distribution (SαS) model was used to simulate the generation of impulse noise in the polar environment; the number of array elements in the two subarrays of the extended coprime array were 6 and 4 respectively, and the total number of array elements in the extended coprime array was 6+4-1=9.

[0082] The generalized signal-to-noise ratio is defined as:

[0083]

[0084] Where T represents the maximum number of snapshots, and q1 represents the deviation of the impulse noise, similar to the variance in Gaussian noise.

[0085] Simulation Experiment 1 investigated the root mean square error (RMSE) curves of DOA estimation using the improved proximal splitting and successive nonconvex sparse approximation algorithm (applying an extrapolation step) under different weight parameters. Figure 4 It is evident from the results that the improved proximal splitting and successive nonconvex sparse approximation algorithm with c=0.9 exhibits the lowest RMSE curve. Specifically, when c=0, the improved proximal splitting and successive nonconvex sparse approximation algorithm is equivalent to the original algorithm. Therefore, based on simulation experiment 1, it is easy to conclude that selecting an appropriate weight constant c and using an extrapolation step can effectively improve the performance of the proximal splitting and successive nonconvex sparse approximation algorithm.

[0086] In simulation experiment 2, the RMSE curves of the first-order off-network sparse Bayesian algorithm (OGSBI), the first-order off-network near-end splitting and successive non-convex sparse approximation algorithm (OGISP), and the high-order off-network near-end splitting and successive non-convex sparse approximation algorithm (NOGISP) proposed in this invention under different input signal-to-noise ratio values ​​are as follows: Figure 5As shown. The purpose of this simulation is to verify the performance of the proposed high-order off-net model by comparing it with the first-order off-net model under the same conditions. It is worth noting that Simulation Experiment 1 has already demonstrated the superior performance of the improved proximal split and successive non-convex sparse approximation algorithm compared to the proximal split and successive non-convex sparse approximation algorithm. Therefore, in Simulation 5, we combine the high-order off-net model with the successive non-convex sparse approximation algorithm and compare it with the first-order off-net sparse Bayesian algorithm and the first-order off-net proximal split and successive non-convex sparse approximation algorithm. Figure 5 As shown, compared with the first-order off-net sparse Bayesian algorithm and the first-order off-net proximal split and successive non-convex sparse approximation algorithm, the proposed high-order off-net proximal split and successive non-convex sparse approximation algorithm exhibits the lowest RMSE performance. Furthermore, the high-order off-net model outperforms the first-order off-net model, especially under low SNR conditions.

[0087] Experimental conditions: Using collected Arctic ambient noise, the root mean square error of various algorithms under different input generalized signal-to-noise ratios was studied. The two subarrays of the extended coprime array had 6 and 4 elements respectively, and the total number of elements in the extended coprime array was 6 + 4 - 1 = 9; the snapshot length of the data was T = 500.

[0088] Figure 6 The collected Arctic noise data shows that at certain times, the noise amplitude increases sharply, exhibiting impulse noise characteristics. Therefore, the method of this invention is designed to address this actual situation.

[0089] Figure 7 The graphs show the root mean square error (RMSE) curves of various algorithms under different input generalized signal-to-noise ratios (SNRs) in Arctic environmental noise. It can be seen that the proposed algorithm has the lowest RMS error compared to other algorithms; therefore, the method proposed in this invention has better DOA estimation performance in polar impulse noise environments.

[0090] The experiments above demonstrate that this invention addresses the performance degradation issue of traditional DOA estimation algorithms in polar environments. By introducing fractional phase low-order moments (PFLOMs) to construct an equivalent covariance matrix (PFLOM matrix) to process polar impulse noise data, the proposed method becomes applicable to polar impulse noise conditions. Furthermore, by selecting an appropriate order for the fractional phase low-order moments (choosing order 2), this method is statistically optimal in handling Gaussian noise. In conclusion, this invention is applicable and performs well in both Gaussian noise and polar impulse noise environments.

[0091] Traditional uniform linear arrays can detect a maximum number of targets less than the number of array elements. However, in real underwater environments, the number of underwater targets to be detected is constantly increasing, while the number of array elements cannot be increased indefinitely. Therefore, how to use a fixed number of sensors to detect as many targets as possible (the number of targets greater than the number of sensors in the array) has become a real problem that needs to be solved. The method proposed in this invention, combined with an extended coprime array, enables the array to detect a number of targets far greater than the number of sensors in the array, thereby achieving overdetermined DOA estimation.

[0092] Traditional DOA estimation methods assume that the target falls exactly on a discrete grid. However, in reality, the target is highly unlikely to fall on the pre-divided discrete grid, leading to grid mismatch and decreased estimation accuracy. In contrast, this invention employs an improved proximal splitting and successive non-convex sparse approximation algorithm combined with a proposed high-order off-grid model to jointly estimate the sparse signal matrix and grid offset, thereby overcoming the grid mismatch problem and achieving high-precision target location estimation. Furthermore, compared to the first-order Taylor interpolation off-grid model, the proposed high-order Taylor expansion off-grid model achieves higher DOA estimation accuracy at low generalized signal-to-noise ratios (GSNR).

[0093] Based on the same technical concept as the method embodiments, the present invention also provides an off-grid DOA estimation system for polar impulse noise environments, comprising:

[0094] The data acquisition module acquires the signal x(t) received by the extended coprime array and forms the received data matrix X;

[0095] The single-shot virtual signal vector construction module introduces the phase fraction low-order moment method to construct the phase fraction low-order moment matrix C for the array received data matrix X. The phase fraction low-order moment matrix C is vectorized, and redundancy is removed and rearranged to obtain the single-shot continuous virtual uniform linear array signal vector z1.

[0096] The multi-measurement vector model construction module is based on the single-shot continuous virtual uniform linear array signal vector z1. It adopts the overlapping sub-array division method, sliding one element at a time until the last element of the single-shot continuous virtual uniform linear array signal vector z1 is reached, so as to maximize the overlap between the sub-arrays and construct the multi-measurement signal vector matrix Z.

[0097] The DOA estimation module uses a high-order Taylor expansion to construct an off-grid model. Based on the multiple measurement signal vector matrix Z, it uses an extrapolation-based iterative sparse projection algorithm to jointly estimate the sparse signal matrix and grid offset to estimate the target's DOA. The extrapolation-based iterative sparse projection algorithm introduces an extrapolation step to extrapolate the sparse signal matrix on the basis of the iterative sparse projection algorithm. The extrapolation step uses the difference between the sparse signal matrices obtained from two consecutive iterations to compensate for the sparse signal matrix of the current iteration.

[0098] It should be understood that the off-grid DOA estimation system in the polar impulse noise environment of the present invention can implement all the technical solutions in the above method embodiments. The functions of each functional module can be specifically implemented according to the methods in the above method embodiments. The specific implementation process can be referred to the relevant descriptions in the above embodiments, which will not be repeated here.

[0099] The present invention also provides a computer device comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, wherein the programs, when executed by the processors, implement the steps of the method described above.

[0100] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described above.

[0101] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, apparatus (systems), computer devices, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0102] This invention is described with reference to a flowchart of a method according to embodiments of the invention. It should be understood that each step in the flowchart and combinations thereof can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing device, generate instructions for implementing the process. Figure 1 A device for a function specified in one or more processes.

[0103] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 The function specified in one or more processes.

[0104] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 Steps of a specified function in one or more processes.

Claims

1. A high-order off-grid DOA estimation method based on an extended coprime array, characterized in that, Includes the following steps: Obtain the signal x(t) received by the extended coprime array to form the received data matrix X; For the array received data matrix X, the phase fractional low-order moment method is introduced to construct the phase fractional low-order moment matrix C. The phase fractional low-order moment matrix C is vectorized, and redundancy is removed and rearranged to obtain the single-shot continuous virtual uniform linear array signal vector z1. Based on the single-shot continuous virtual uniform linear array signal vector z1, the overlapping subarray partitioning method is adopted, and one element is slid to the right one at a time until the last element of the single-shot continuous virtual uniform linear array signal vector z1 is reached to maximize the overlap between subarrays and construct a multiple measurement signal vector matrix Z. A high-order Taylor expansion term is used to construct an off-grid model. Based on the multiple measurement signal vector matrix Z, an extrapolation-based iterative sparse projection algorithm is used to jointly estimate the sparse signal matrix and the grid offset to estimate the target's DOA. The extrapolation-based iterative sparse projection algorithm introduces an extrapolation step to extrapolate the sparse signal matrix on the basis of the iterative sparse projection algorithm. The extrapolation step uses the difference between the sparse signal matrices obtained from two consecutive iterations to compensate for the sparse signal matrix of the current iteration.

2. The method according to claim 1, characterized in that, The array structure of the extended co-prime array includes two sub-arrays, which are composed of 2M and N array elements respectively. The element spacings between them are Nd and Md respectively, where M and N are co-prime numbers, M < N, and d represents the half-wavelength spacing of the signal. Taking the first array element as the reference array element, the physical array element positions are: S p ={Nmd|0 ≤ m ≤ 2M - 1} ∪ {Mnd|0 ≤ n ≤ N - 1}.

3. The method according to claim 2, characterized in that, The construction of the received data matrix X includes: The t-th snapshot signal received by the array is represented as: x(t)=A(θ)s(t)+n(t),t=1,…,T in, s(t) represents the t-th snapshot signal received by the array; s(t) represents the vector composed of the envelope amplitudes of each signal at the t-th snapshot; T represents the maximum number of snapshots. It is the background noise signal; A(θ) is the array steering vector matrix; The order of the signal data matrix composed of T snapshots is 4. The method according to claim 1, characterized in that, The higher-order Taylor expansion off-network model is as follows: Where, a(θ) q ) represents the steering vector of the target signal. The steering vector representing the grid point closest to the target signal. express about The first derivative, express about The second derivative, express about The nth derivative, β q This represents the grid offset parameter.

5. The method according to claim 1, characterized in that, The extrapolation-based iterative sparse projection algorithm includes a sparse signal matrix solution stage and a grid offset solution stage. In the sparse signal matrix solution stage, according to... The sparse signal matrix S obtained in the i-th iteration (i) Perform extrapolation based on Perform sparsification processing, and then according to Projection continues until the specified iteration is satisfied, or the parameter ξ is less than or equal to the set threshold ξ. f Where w represents a weighting constant between 0 and 1, and the parameter ξ is a differentiable function H. ξ The parameter, ΔH ξ Representation function H ξ The derivative operation, μ ξ This is the sparsification step size.

6. The method according to claim 5, characterized in that, Differentiable function H ξ It is a function with an approximate 0 norm: Where e is the base of the natural logarithm, and s is a complex number whose real and imaginary parts are denoted as si and si, respectively. r and s i .

7. The method according to claim 1, characterized in that, Obtaining a sparse signal matrix After the grid offset β, according to the formula Estimate the target's DOA.

8. A high-order off-grid DOA estimation system based on an extended coprime array, characterized in that, include: The data acquisition module acquires the signal x(t) received by the extended coprime array and forms the received data matrix X; The single-shot virtual signal vector construction module introduces the phase fraction low-order moment method to construct the phase fraction low-order moment matrix C for the array received data matrix X. The phase fraction low-order moment matrix C is vectorized, and redundancy is removed and rearranged to obtain the single-shot continuous virtual uniform linear array signal vector z1. The multi-measurement vector model construction module is based on the single-shot continuous virtual uniform linear array signal vector z1. It adopts the overlapping sub-array division method, sliding one element at a time until the last element of the single-shot continuous virtual uniform linear array signal vector z1 is reached, so as to maximize the overlap between the sub-arrays and construct the multi-measurement signal vector matrix Z. The DOA estimation module uses a high-order Taylor expansion to construct an off-grid model. Based on the multiple measurement signal vector matrix Z, it uses an extrapolation-based iterative sparse projection algorithm to jointly estimate the sparse signal matrix and grid offset to estimate the target's DOA. The extrapolation-based iterative sparse projection algorithm introduces an extrapolation step to extrapolate the sparse signal matrix on the basis of the iterative sparse projection algorithm. The extrapolation step uses the difference between the sparse signal matrices obtained from two consecutive iterations to compensate for the sparse signal matrix of the current iteration.

9. A computer device, characterized in that, include: One or more processors; Memory; as well as One or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, wherein when the programs are executed by the processors, they implement the steps of the high-order off-grid DOA estimation method based on an extended coprime array as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the high-order off-grid DOA estimation method based on an extended coprime array as described in any one of claims 1-7.

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