A DOA estimation method for coprime arrays based on pseudo-snapshot increments in the presence of impulse noise

Abstract

The present invention discloses a coprime array DOA estimation method based on pseudo-snapshot increments under impulse noise. After obtaining observation information by using augmented coprime array antenna receiving signals, multiple PFLOM covariance matrices of different orders are calculated according to the observation information; then the obtained multiple covariance matrices are vectorized, redundant rows are deleted and continuous array element parts are intercepted to obtain virtual array receiving signal information with multiple snapshots; then the virtual receiving signal information is MSSP decorrelated to obtain a reconstructed covariance matrix; finally, the reconstructed covariance matrix is ​​eigen-decomposed, and the peak values ​​are respectively found through MUSIC spectrum peak search to obtain an accurate estimation of DOA. The present invention combines the method of stacking PFLOMs of different orders with the MSSP and the DOA estimation problem of coprime array coherent sources under impulse noise environment, thereby improving the decorrelation performance. Moreover, when the impulse noise is in a low signal-to-noise ratio environment and the number of sources is higher than the number of array elements, the present invention can still obtain better DOA estimation performance.

Description

Technical Field

[0001] The present invention relates to the technical fields of DOA (direction of arrival) estimation and radar sonar positioning, and in particular to a coprime array DOA estimation method based on pseudo-snapshot increments under impulse noise. Background Art

[0002] Most of the traditional DOA estimation methods, such as MUSIC and ESPRIT, are developed using equally spaced array layouts, such as uniform linear array (ULA) and uniform circular array (UCA), and their optimal characteristics are constrained by limited physical array geometry. On the one hand, the degree of freedom is limited by the number of sensors. Given a ULA with N isotropic sensors, the number of resolvable sources cannot exceed N-1. On the other hand, in order to avoid the angle ambiguity problem, the distance between two adjacent sensors in a traditional array should usually be less than half the wavelength of the incident signal, that is, d < λ / 2. However, too small an array element spacing will bring about a strong mutual coupling effect, thereby reducing the estimation accuracy. Therefore, the optimal design and performance analysis of such arrays are generally not easy.

[0003] In addition, most studies on coprime arrays assume that the environmental noise is Gaussian noise, which has second-order statistics or high-order cumulants that can be removed after vectorization. However, in real environments, noise in radar, sonar and wireless communication systems often exhibits non-Gaussianity, such as electromagnetic interference, atmospheric noise and sea clutter, which have large data mutations more frequently than Gaussian noise. Therefore, this noise is not suitable for Gaussian distribution to describe, but requires a probability distribution with a longer tail than Gaussian distribution to describe it. Previously, there was a method of constructing the equivalent covariance matrix of the received signal using PFLOM (phased fractional lowerorder moments), and then the covariance matrix of the received signal based on PFLOM was applied to the concept of coprime arrays, but after the transformation of the PFLOM-based covariance matrix, the virtual signal vector was obtained by using vectorization operations, which is still a single-snapshot signal model. In addition, the virtual source matrices with different fractional lower orders are estimated from the same source, and they are still highly correlated, so additional decorrelation techniques are still needed to restore the rank and ensure its positive definiteness after vectorization. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a coprime array DOA estimation method based on pseudo-snapshot increments under impulse noise in view of the defects involved in the background technology, calculate multiple phase fractional low-order moment (PFLOM) estimation covariance matrices of different orders, vectorize the obtained multiple estimated covariance matrices, delete redundant rows and intercept continuous array element parts to obtain virtual array received signal information with multiple snapshots, finally, perform MSSP (modified spatial smoothing pre-processing) decorrelation on the virtual received signal information to obtain a reconstructed covariance matrix, perform eigendecomposition on the reconstructed covariance matrix, and then perform MUSIC spectrum peak search to obtain accurate DOA estimation.

[0005] The present invention adopts the following technical solutions to solve the above technical problems:

[0006] A method for estimating DOA of a coprime array based on pseudo snapshot increment under impulse noise comprises the following steps:

[0007] Step 1), using an array antenna with an augmented mutually prime array structure to receive a signal and obtain observation information y; the array antenna with an augmented mutually prime array structure comprises two uniform linear arrays with 2M and N array elements respectively, and the array element spacings are Nλ / 2 and Mλ / 2 respectively, wherein M and N are mutually prime numbers and M<N, and λ is the carrier wavelength; the two uniform linear arrays have only one array element overlapped at the origin, and the total number of array elements is 2M+N-1;

[0008] Step 2), calculate multiple PFLOM covariance matrices R of different orders based on the observation information y i ;

[0009] Step 3), for each covariance matrix R i Perform vectorization processing, sort the obtained vector according to the phase, remove the redundant rows, and intercept the middle 2MN+2M-1 rows of the vector as the continuous virtual array element receiving signal y i ;

[0010] Step 4), each virtual array receives signal information y i Stacking is performed to obtain virtual array received signal information Y with multiple snapshots, thereby obtaining an enhanced covariance matrix

[0011] Step 5), perform MSSP decorrelation processing on the virtual received signal information Y to obtain the reconstructed covariance matrix

[0012] Step 6), reconstruct the covariance matrix Perform eigendecomposition and find the peaks in a small range through MUSIC spectrum peak search to obtain an accurate estimate of DOA.

[0013] As a further optimization scheme of the coprime array DOA estimation method based on pseudo snapshot increment under impulse noise of the present invention, the specific steps of step 2) are as follows:

[0014] Due to R PFLOM The (i,j)th element of

[0015] in, represents the expected operation operator, r i <-κ> =(r i * ) <κ> =(r i <κ> ) * , κ represents r i and r j The order of

[0016] Then the equivalent covariance matrix R of the received signal using the PFLOM method is PFLOM The formula is as follows:

[0017] R PFLOM =AΓ PFLOM A H +ΥI 2M+N-1

[0018] In the formula, Γ PFLOM is the source covariance matrix based on PFLOM; Υ is the impulse noise vector; I 2M+N-1 It is a (2M+N-1)×(2M+N-1)-dimensional identity matrix;

[0019] Since the representation of the covariance matrix based on PFLOM is determined by the parameters of the impulse noise α, and the operation can be repeated multiple times in different orders, so that a signal vector with incremental snapshots and enhanced observation information can be generated, a set of order κ is defined q , q=1,2,...,N t , where N t is a pre-set threshold, 0<κ q <α / 2, and obtain multiple R of different orders PFLOM :

[0020] R i =AΓ i A H +Υ i I 2M+N-1

[0021] In the formula, R i is the i-th order PFLOM covariance matrix, Γ i is the i-th order PFLOM-based source covariance matrix; i is the i-th order impulse noise vector.

[0022] As a further optimization scheme of the coprime array DOA estimation method based on pseudo snapshot increment under impulse noise of the present invention, the reconstructed covariance matrix in step 5) is In the formula, is a matrix The autocovariance matrix of the ith subarray of , J is the inverse identity matrix, and L is The number of subarrays, [] * Represents the conjugation operation on a matrix or vector.

[0023] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0024] After the transformation of the covariance matrix based on PFLOM, a virtual signal vector is obtained by using vectorization operation, but it is still a single-snap signal model. However, the present invention can reconstruct more snapshot covariance matrices from the virtual joint array received signal by using a method of stacking PFLOMs of different orders. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is a schematic diagram of the augmented coprime array structure of the present invention;

[0026] Figure 2 It is a schematic diagram of the virtual array structure of the augmented coprime linear array of the present invention;

[0027] Figure 3 (a) Figure 3 (b) are schematic diagrams of the spectrum peak search for DOA estimation in a single Monte Carlo experiment of the method of the present invention under an impulse noise environment when the characteristic index α=1.2 and α=0.5;

[0028] Figure 4 (a) Figure 4 (b) are schematic diagrams of the spectrum peak search for DOA estimation in a single Monte Carlo experiment of the method of the present invention under an impulse noise environment when the characteristic index α=1.2 and α=0.5;

[0029] Figure 5 (a) Figure 5 (b) are schematic diagrams showing the RMSE comparison performance of the method of the present invention under different generalized signal-to-noise ratios in an impulse noise environment when the characteristic index α=1.2 and α=0.5;

[0030] Figure 6 (a) Figure 6 (b) are schematic diagrams showing the RMSE comparison performance of the method of the present invention under different input signal angle intervals in an impulse noise environment when the characteristic index α=1.2 and α=0.5;

[0031] Figure 7 It is a schematic diagram of decorrelation performance of the method of the present invention and other algorithms under different signal source number conditions. DETAILED DESCRIPTION

[0032] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings:

[0033] The present invention can be implemented in many different forms and should not be considered to be limited to the embodiments described herein. On the contrary, these embodiments are provided to make this disclosure thorough and complete, and will fully express the scope of the present invention to those skilled in the art. In the accompanying drawings, components are enlarged for clarity.

[0034] The present invention provides a coprime array DOA estimation method based on pseudo-snapshot increment under impulse noise. The array antenna used in the method is an augmented coprime array. The structure consists of two uniform linear arrays with 2M and N array elements respectively, and the array element spacing is Nλ / 2 and Mλ / 2 respectively, wherein M and N are coprime numbers and M<N, and λ is the carrier wavelength. Due to the coprime characteristics, when two subarrays are combined together, except for the first array element, the other array elements will not overlap. Then, the augmented coprime array of 2M+N-1 array elements can obtain 2M(N+1)-1 virtual linear array continuous degrees of freedom (DOF). The augmented coprime array structure greatly increases the number of detectable sources of the array. The array structure also breaks through the limitation of half-wavelength of the traditional antenna array element spacing, so that the antenna aperture is greatly expanded, and the angle estimation performance can be improved. At the same time, the spacing between the subarray units is Mλ / 2 and Nλ / 2, which is much larger than half a wavelength, effectively weakening the mutual coupling effect between the array elements.

[0035] 1. Augmented Mutually Prime Array Noise Model and Data Model

[0036] Noise model:

[0037] Most studies on DOA estimation assume that the environmental noise is Gaussian noise, which has second-order statistics or high-order cumulants that can be removed after vectorization. However, in real environments, the noise in radar, sonar and wireless communication systems often exhibits non-Gaussian properties, such as electromagnetic interference, atmospheric noise and sea clutter, which have large data mutations more frequently than Gaussian noise. Therefore, this noise is not suitable for description by Gaussian distribution, but requires a probability distribution with a longer tail than Gaussian distribution to describe it. Studies have shown that SαS can better fit impulse noise, and the SαS noise model is expressed by the characteristic function as:

[0038]

[0039]

[0040]

[0041] Then this random variable X obeys the α-stable distribution and is uniquely determined by the parameters α, β, μ, and γ. Among them, α is the characteristic exponent, 0<α≤2, and its size can affect the pulse degree of this distribution. When α=2, the distribution is Gaussian distribution, and when α=1, the distribution is Cauchy distribution; γ is the distribution coefficient, γ>0, similar to the variance in Gaussian distribution; β is the symmetry parameter, -1≤β≤1; δ is the location parameter. When β=δ=0, the distribution is symmetric α-stable (SαS) distribution. The smaller α is in the SαS distribution, the more obvious the pulse is; conversely, the larger α is, the closer the noise is to Gaussian noise. Unlike the Gaussian distribution, it does not have finite second-order statistics or high-order cumulants. Therefore, in the pulse noise environment, the virtual co-array cannot be established through the classical coprime technology. In the pulse noise environment, the method based on the Gaussian noise model has degraded performance or even failed in the DOA estimation of coprime arrays.

[0042] Data Model:

[0043] like Figure 1 An example of an augmented coprime linear array that can use the present invention is shown, where M=4 and N=5.

[0044] Assume that K are from θ k , k = 1, 2, ..., K narrowband signal is incident on Figure 1 On the augmented coprime linear array shown in Figure 2, the array receiving signal can be expressed as

[0045] r(t)=As(t)+n(t)

[0046] where s(t) = [s 1 (t),…s p (t),s p+1 (t),…s K (t)] T is the signal matrix, t=1,2...,T N , where T N is the number of snapshots, s p (t), is the t-th sampling result of the p-th signal, and n(t) is the impulse noise. 1 ),…,a(θ k ),…a(θ K )] is the direction matrix of the array, a(θ k ) is θ kDirection vector in direction;

[0047]

[0048] in, represents the array sensor position set, and sort(·) is an operation to sort the array spacing from small to large based on the first array element as the reference system.

[0049] 2. Angle Estimation Method

[0050] In this embodiment, the above noise model and data model are applied to the DOA estimation algorithm of the present invention, and then a method of stacking PFLOMs of different orders is constructed from the perspective of pseudo snapshot increments to solve the problem that the virtual array equivalent covariance matrix has only a single snapshot in the coprime array pulse noise environment. It specifically includes the following steps:

[0051] Step 1), using an array antenna with an augmented mutually prime array structure to receive a signal and obtain observation information y;

[0052] Step 2), calculate multiple PFLOM covariance matrices R of different orders based on the observation information y i ;

[0053] Calculate the PFLOM estimated covariance matrix R PFLOM :

[0054] The (i,j)th covariance matrix of the PFLOM estimate is expressed as:

[0055]

[0056]

[0057] in, represents the expected operation operator, r i <-κ> =(r i * ) <κ> =(r i <κ> ) * , κ represents r i and r j The order of

[0058]

[0059] That is, the equivalent covariance matrix R of the received signal using the PFLOM method is PFLOM Can be written as

[0060] R PFLOM =AΓPFLOM A H +ΥI 2M+N-1

[0061] In the formula, Γ PFLOM is the source covariance matrix based on PFLOM; Υ is the impulse noise vector; I 2M+N-1 It is a (2M+N-1)×(2M+N-1)-dimensional identity matrix.

[0062] Since the representation of the covariance matrix based on PFLOM is mainly determined by the parameters of the impulse noise α, and this operation can be repeated multiple times in different orders, so that a signal vector with incremental snapshots and enhanced observation information can be generated, a set of order κ is defined q , q=1,2,...,N t , where N t is a pre-set threshold, 0<κ q <α / 2, then multiple R of different orders can be obtained PFLOM , expressed as

[0063] R i =AΓ i A H +Υ i I 2M+N-1

[0064] In the formula, Γ i is the i-th order PFLOM-based source covariance matrix; i is the i-th order impulse noise vector.

[0065] Step 3), for each covariance matrix R i Perform vectorization processing, sort the obtained vector according to the phase, remove the redundant rows, and intercept the middle 2MN+2M-1 rows of the vector as the continuous virtual array element receiving signal y i ;

[0066] R i After vectorization, we get:

[0067]

[0068] in, It can be regarded as a direction matrix of a long virtual array, x i =[σ i1 ,…σ ip ,σ ip+1 ,…,σ iK ] T is a single snapshot signal vector and is non-full rank. ik is the signal power of the kth signal, Υ irepresents the stretched impulse noise vector, vec(·) represents the vectorization operation, represents the Kronecker product, [] * Represents the conjugation operation on a matrix or vector.

[0069] Since the virtual array of the coprime array consists of a continuous uniform linear array and some discontinuous array elements, it can be proved that the range of the uniform linear array is [-[M(N+1)-1]d, [M(N+1)-1]d], that is, the middle 2M(N+1)-1 array elements of the virtual array are continuously distributed. Figure 2 The following is a virtual array when M=4 and N=5. The repeated rows in the image are intercepted and the continuous array element parts are intercepted to obtain the signal received by the continuous virtual array.

[0070] Step 4), each virtual array receives signal information y i Stacking is performed to obtain virtual array received signal information Y with multiple snapshots, thereby obtaining an enhanced covariance matrix

[0071] Vector y i corresponds to a single snapshot signal vector within the coprime virtual array. Definition We can stack vectorized matrices in different orders:

[0072]

[0073] in,

[0074] Y and X are respectively from t snapshots, and X is the refined source matrix with multiple pseudo snapshots from the virtual array. Given a larger number of pseudo snapshots, the enhanced covariance matrix is ​​estimated as

[0075]

[0076] in, is the K×K order covariance matrix of the coprime virtual array, Σ is the (2MN+2M-1)×(2MN+2M-1) order noise covariance matrix of the coprime virtual array, and the (MN+M,MN+M)th element is equal to The remaining elements are zero.

[0077] Step 5), perform MSSP decorrelation processing on the virtual received signal information Y to obtain the reconstructed covariance matrix

[0078] According to the structure of the improved noise matrix, we can conclude that since only the (MN+M,MN+M)th element of the noise matrix Σ is non-zero, MSSP decorrelation is applied. The noise-free MSSP covariance matrix with restored rank consisting of L subarrays is It can be expressed as:

[0079]

[0080] in, is a matrix The autocovariance matrix of the ith subarray of ; express The first 2MN+2M-L rows of are independent of the parameter i; is the signal source covariance matrix of the coprime virtual array after the proposed MSSP; D = diag{exp{jπsinθ 1},...,exp{jπsinθ K}} represents a K×K diagonal matrix; J is the (2MN+2M-L)×(2MN+2M-L) inverse identity matrix.

[0081] Step 6), reconstruct the covariance matrix Perform eigendecomposition and find the peaks in a small range through MUSIC spectrum peak search to obtain an accurate estimate of DOA.

[0082] 3. Performance Analysis and Experimental Analysis

[0083] 1. Degree of freedom (DOF) analysis

[0084] From the above analysis, it can be seen that the DOA estimation method of PFLOM stacking of different orders and the DOA estimation method of single snapshot PFLOM proposed in the present invention only use the middle continuous virtual array elements of the augmented coprime array, and the spatial degree of freedom obtained is DOF EFLOM =DOF PFLOM =MN+M-1.

[0085] 2. Decorrelation performance analysis

[0086] Using the snapshots added by the proposed method of stacking PFLOMs of different orders, the effective correlation coefficient ρ between the m-th and n-th received signals can be calculated:

[0087]

[0088] Where Φ(m,n) represents the (m,n)th element of Φ; x mi and x ni is the vector x iThe m-th and n-th elements of (the i-th snapshot of the virtual source signal X). The proposed PFLOM stacking method with different orders of increasing snapshots reduces the correlation between the received signals. Figure 7 is a graph of the correlation coefficient of the first and second signals as a function of the number of signal sources. In order to better compare the performance of the method of the present invention with that of the prior art, we ran 200 Monte Carlo experiments. At this time, the number of array elements of the coprime linear array is M = 2, N = 3, and the number of snapshots is T N =100, α=1, DOA is within [-60°, 60°], PFLOM The step size is 0.01; 0<κ i <α / 2. It can be seen that the proposed PFLOM stacking method with different orders of incremental snapshots reduces the correlation between the received signals.

[0089] 3. Accuracy analysis

[0090] The theoretical estimation error of the MUSIC algorithm is:

[0091]

[0092] in, Q=[q(θ 1 ),…,q(θ K )], U s and U n yes The signal subspace and noise subspace of It is obtained by eigenvalue decomposition. Therefore, it can be seen that the theoretical estimation error of MUSIC depends on the number of snapshots, the correlation between the input signals, and the length of the subarray. The more snapshots there are, the smaller the theoretical estimation error is. Therefore, in the DOA estimation of coprime arrays, the theoretical performance of the proposed PFLOM stacking method with different orders of incremental snapshots is better than the method based on single snapshot PFLOM.

[0093] 4. Experimental analysis

[0094] In order to verify the effect of the above method, multiple simulation experiments were conducted in this embodiment, and the experimental performance was analyzed, as follows:

[0095] 1. Experimental performance evaluation indicators

[0096] In an impulse noise environment, the generalized signal-to-noise ratio is defined as:

[0097]

[0098] The performance estimation criterion is the joint root mean square error (RMSE) defined as:

[0099]

[0100] in, is the accurate estimate of DOA of the jth Monte Carlo process, K represents the number of sources, and J 0 represents the number of Monte Carlo trials.

[0101] 2. Experimental effect diagram

[0102] For the convenience of drawing and observation, in the figure, EFLOM represents the method of stacking PFLOMs of different orders proposed by the present invention, and PFLOM represents the single-shot PFLOM method.

[0103] Figure 3 (a) Figure 3 In (b), when the number of signal sources K = 9 is incident on the coprime array, the DOA is [-36, 36]°, and the step size is 9. . The spectrum peak search diagram obtained by the method of the present invention. The comparison method is the single-shot PFLOM method. At this time, the number of array elements of the coprime linear array is M = 4, N = 5, the number of signal sources (K = 9) is less than the number of sensor elements (2M + N-1 = 12), and the number of snapshots T N =200, GSNR=5dB. Figure 3 (a) is the spectrum peak search diagram obtained by the method of the present invention when the pulse noise characteristic index α=1.2. It can be seen that the method of stacking PFLOMs of different orders proposed in the present invention can detect all signals, while the single snapshot PFLOM method weakens the estimation performance. Figure 3 (b) is the spectrum peak search diagram obtained by the method of the present invention when the pulse noise characteristic index α = 0.5. The DOA estimation performance of the method of stacking PFLOMs of different orders proposed in the present invention is still better than that of the single-shot PFLOM method. Figure 3 Compared with (a), when α is small, the estimation performance of the single-shot PFLOM method is weakened or even fails.

[0104] Figure 4 (a) Figure 4 In (b), when the number of signal sources K = 17 is incident on the coprime array, the DOA is [-48, 48]°, and the step size is 6. . The spectrum peak search diagram obtained by the method of the present invention. The comparison method is the single-shot PFLOM method. At this time, the number of array elements of the coprime linear array is M = 4, N = 5, the number of signal sources (K = 17) is higher than the number of sensor elements (2M + N-1 = 12), and the number of snapshots T N =200, GSNR=5dB. Figure 3(a) is a spectrum peak search diagram obtained by using the method of the present invention when the pulse noise characteristic index α=1.2; Figure 3 (b) is the spectrum peak search diagram obtained by the method of the present invention when the pulse noise characteristic index α=0.5. It can be seen that some real DOAs of the single-shot PFLOM method are invalid at different α values. In comparison, the method of stacking PFLOMs of different orders proposed by the present invention is still robust in this case and has enhanced estimation results.

[0105] In order to better compare the performance of the method of the present invention with that of the prior art under different generalized signal-to-noise ratios, we ran 200 Monte Carlo experiments. At this time, the number of array elements of the coprime linear array is M=4, N=5, the azimuth angle of the signal source is {-10°, 0°, 10°}, and the number of snapshots is T. N =200. Figure 5 (a) is a comparison chart of RMSE under different GSNR input signal angle intervals when α=1.2. It can be seen that when GSNR<0dB, the RMSE of the present invention is significantly lower than that of the single-shot PFLOM method. Figure 5 (b) is a comparison chart of RMSE under different GSNRs when α=0.5. At this time, when GSNR<5dB, the RMSE of the present invention is significantly lower than that of the single-shot PFLOM method. In summary, the present invention has better DOA estimation performance in a high impulse noise environment, especially when the GSNR is low.

[0106] In order to better compare the performance of the method of the present invention with the prior art under different input signal angle intervals, we ran 200 Monte Carlo experiments. At this time, the number of array elements of the coprime linear array is M=4, N=5, and the azimuth angle θ of the signal source is 1 =0°,θ 2 =θ 1 +Δθ,Δθ∈[2. ,15. ], GSNR=0dB. Figure 6 (a) is the RMSE comparison chart under different input signal angle intervals when α=1.2. Figure 6 (b) is a comparison of RMSE at different input signal angle intervals when α = 0.5. It can be seen that at small angle separations, due to resolution reasons, the proposed method and the single-shot PFLOM method cannot detect input signals at different α. As the angle interval increases, the RMSE of the proposed method and the danci snapshot PFLOM method continues to decrease. The proposed method of stacking PFLOMs of different orders has more accurate estimation results at each angle interval than the single-shot PFLOM method.

[0107] In summary, from the analysis of the simulation effect diagram, it can be seen that the coprime array DOA estimation based on pseudo-snapshot increment under impulse noise conditions proposed in the present invention realizes the accurate DOA estimation of coherent sources in the augmented coprime array impulse noise environment.

[0108] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as those generally understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with the meanings in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless defined as herein.

[0109] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A coprime array DOA estimation method based on pseudo-snapshot increments under impulse noise. It is characterized in that The steps include: Step 1), using an array antenna with an augmented mutually prime array structure to receive a signal and obtain observation information y; the array antenna with an augmented mutually prime array structure comprises two uniform linear arrays with 2M and N array elements respectively, and the array element spacings are Nλ / 2 and Mλ / 2 respectively, wherein M and N are mutually prime numbers and M<N, and λ is the carrier wavelength; the two uniform linear arrays have only one array element overlapped at the origin, and the total number of array elements is 2M+N-1; Step 2), calculate multiple PFLOM covariance matrices R of different orders based on the observation information y i ; Due to R PFLOM The (i,j)th element of in, represents the expected operation operator, κ represents r i and r j The order of Then the equivalent covariance matrix R of the received signal using the PFLOM method is PFLOM The formula is as follows: R PFLOM =AΓ PFLOM A H +γI 2M+N-1 In the formula, Γ PFLOM is the source covariance matrix based on PFLOM; γ is the impulse noise vector; I 2M+N-1 It is a (2M+N-1)×(2M+N-1)-dimensional identity matrix; Since the representation of the covariance matrix based on PFLOM is determined by the parameters of the impulse noise α, and the operation can be repeated multiple times in different orders, so that a signal vector with incremental snapshots and enhanced observation information can be generated, a set of order κ is defined q , q=1,2,...,N t , where N t is a pre-set threshold, 0<κ q <α / 2, and obtain multiple R of different orders PFLOM : R i =AΓ i A H +γ i I 2M+N-1 In the formula, R i is the i-th order PFLOM covariance matrix, Γ i is the i-th order PFLOM-based source covariance matrix; γ i is the i-th order impulse noise vector; Step 3), for each covariance matrix R i Perform vectorization processing, sort the obtained vector according to the phase, remove the redundant rows, and intercept the middle 2MN+2M-1 rows of the vector as the virtual array element receiving signal y i ; Step 4), each virtual array element receives the signal y i Stacking is performed to obtain virtual array received signal information Y with multiple snapshots, thereby obtaining an enhanced covariance matrix Step 5), perform MSSP decorrelation processing on the virtual array received signal information Y to obtain the reconstructed covariance matrix Reconstructed covariance matrix In the formula, is a matrix The autocovariance matrix of the ith subarray of , J is the inverse identity matrix, and L is The number of subarrays, [ ] * Represents the conjugation operation of a matrix or vector; Step 6), reconstruct the covariance matrix Perform eigendecomposition and find the peaks in a small range through MUSIC spectrum peak search to obtain an accurate estimate of DOA.

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