Research On Sparse Recovery DOA Estimation Of Acoustic Vector Sensor Array In Impulse Noise

The accuracy of direction of arrival(DOA)estimation algorithm,based on acoustic vector sensor array in impulse noise,degrades seriously,when signal-to-noise ratio(SNR)and snapshots goes down.A one-dimensional sparse recovery-based DOA estimation algorithm and an off-grid algorithm for off-grid targets are proposed to solve the problem in this paper.Baced on the characteristics of acoustic vector sensor array,the one-dimensional sparse recovery-based DOA estimation is extended to two-dimensional sparse recovery-based DOA estimation.The two-dimensional sparse recovery-based DOA estimation algorithm and off-grid algorithm are proposed.The convergence of the algorithm is proved and the complexity of the algorithm is analyzed.Simulation results show that the proposed algorithm has good estimation accuracy and success rate under the conditions of low SNR and small snapshots.The acoustic vector sensor is a new type of sensor.Owing to its ability to simultaneously measure sound pressure and sound velocity vector information in three orthogonal directions,sound vector sensors have greater performance advantages than traditional scalar sound pressure sensors and have become a hot research object in the field of acoustic detection and signal processing.Because it is mainly used for underwater target detections,the azimuth estimation of underwater targets has become an important branch in this research field and has attracted much attention.The existing underwater direction of arrival(DOA)estimation algorithms for acoustic vector sensors often require a high signal-to-noise ratio(SNR)and multiple snapshots.However,actual military applications require locating and tracking fast-moving targets in a strong noise environment;therefore,it is necessary to explore algorithms that can achieve high-precision estimation under the conditions of low SNR and small snapshots.Although the DOA estimation problem under the condition of small snapshots can be effectively solved using sparse recovery algorithms,most scholars only pay attention to the robustness of the algorithm instead of noise suppression in the processing of noisy signals,which results in low estimation accuracy of the algorithm under the condition of low SNR.Moreover,when considering errors,sparse recovery algorithms mostly use Gaussian stable distribution as the noise assumption.However,because the underwater environment has relatively complicated noise conditions,including a lot of impulse noise,the Gaussian stable distribution is unable to accurately describe it.Many scholars use the alpha-stable distribution to express the impulse noise because the alpha-stable distribution is more representative and practical as a model hypothesis for underwater impulse noise.The existing sparse recovery DOA estimation algorithms,based on Gaussian noise assumption and integer-order statistics,have lost efficiency in underwater impulse noise environments.This study aims to investigate and explore a type of sparse recovery DOA estimation algorithm for acoustic vector sensor arrays that can achieve small snapshots and low SNR under the background of alpha noise.In addition,it aims to develop from one-dimensional DOA estimation algorithm research to two-dimensional DOA estimation algorithm research.The paper can be divided into four parts as follows.1.A sparse reconstruction model under the background of alpha noise is constructed,and the sparse recovery algorithm is used to achieve DOA estimation.First,the received data of the line array of the acoustic vector sensor are processed using the fractional lower-order moment(FLOM),and then vectorization is performed based on the FLOM matrix.Second,the spatial angle is meshed,and the steering vector matrix is extended to form a dictionary matrix,thus yielding a model similar to the sparse recovery mathematical model.The orthogonal matching pursuit algorithm is used for vector sparse recovery.The position of the non-zero elements of the recovered vector is the distribution of signal energy in the spatial angle,while the position of other zero elements indicates that there is no signal in the angle,thus allowing for sparse one-dimensional DOA estimation.The simulation results show that the proposed algorithm is effective under the background of alpha noise,and its estimation accuracy and success rate are better than those of the commonly used CS-MUSIC,MVDR,and SBL algorithms under the conditions of low SNR and small snapshots.2.To cope with the decrease in estimation accuracy caused by ablative targets,an ablative sparse reconstruction model under the background of alpha noise is constructed based on the sparse reconstruction DOA estimation model,and an alternating iterative ablative sparse recovery DOA estimation algorithm is proposed.The first-order Taylor expansion of the reconstruction model is used to construct an ablative sparse DOA estimation model.The matrix form of the two-matrix Kronecker product differential operation result is derived to simplify the calculation,and the alternating iterative method is used to realize the sparse DOA estimation of the ablative orthogonal matching pursuit algorithm.The simulation results show that the proposed algorithm is effective in DOA estimation of ablative targets under the background of alpha noise,and its estimation accuracy and success rate are better than those of the representative MMV-OMP,Lp-MUSIC,and FLOM-MUSIC algorithms under the conditions of low SNR and small snapshots.3.A two-dimensional DOA estimation model suitable for matching pursuit algorithms under the background of alpha noise and a two-dimensional sparse DOA estimation algorithm based on block matching pursuit are put forward.The fractional low-order moment is performed on the two-dimensional DOA estimation model of the acoustic vector sensor line array,and the azimuth and elevation angles in the steering vector are meshed.The steering vector matrix is expanded in two directions to form a cube.The diagonal plane of the cube is adopted as the sparse restoration target,with the abscissa of the diagonal matrix representing azimuth and the ordinate representing elevation.The position of non-zero elements in the matrix is the distribution of signal energy in azimuth and elevation.Finally,a block matching pursuit algorithm is proposed to realize sparse two-dimensional DOA estimation with automatic matching of azimuth and elevation.The simulation results show that the proposed algorithm can realize two-dimensional DOA estimation with automatic matching of azimuth and elevation under the background of alpha noise,and its estimation accuracy and success rate are better than those of the V-MUSIC,AVS-SS-ST,and KR-AVS algorithms under the conditions of low SNR and small snapshots.4.An ablative two-dimensional sparse DOA estimation model under the background of alpha noise is constructed,and a three-step iterative method is proposed to realize the ablative two-dimensional DOA estimation.The first-order Taylor expansion is used to construct a two-dimensional ablative sparse DOA estimation model.Subsequently,a three-step iterative method is proposed to obtain various variables separately to solve the multi-variable solution.Because there is a root operation in the calculated deviation value,it is necessary to determine the sign of the deviation value.In this study,the principle of maximum correlation between the support vector base and the observation vector is proposed to determine it.The simulation results show that the proposed algorithm can achieve ablative two-dimensional DOA estimation for ablative targets under the background of alpha noise,and its estimation accuracy and success rate are better than those of the VS-SS-ST,L1 SVD,and AVS-AIAA algorithms under the conditions of low SNR and small snapshots.