Research On Robust Beamforming And Sparse Spatial Spectrum Estimation Techniques For Circular Acoustic Vector-Sensor Arrays

Acoustic vector sensors(AVSs),which can simultaneously sense the acoustic pressure and particle velocity information in the acoustic field,have the advantages of the uniform receiving directivity independent of the signal frequency and the strong ability to suppress the environment noise.The appearance of AVSs greatly improves the detection ability of the underwater weak targets for the passive sonar system.In sonar system,the circular arrays can provide 360° unambiguous direction information and the almost same detection performance over the azimuthal plane,which have wide application in the underwater engineering area.Therefore,it is of great significance to study the signal processing technology of the circular acoustic vector-sensor arrays(CAVSAs).Recently,the beamforming and spatial spectrum estimation technologies of the CAVSA have become a research hotspot at home and abroad,and have achieved rich research results,but there are still some problems needing to be solved.Firstly,the channel amplitude and phase errors and element position errors of the CAVSA will inevitably exist in the practical application.These errors will bring about the mismatch of the steering vector of the CAVSA,which will lead to the decrease of the robustness of the CBF and MVDR beamforming.Besides,the spatial spectrum estimation technology of the CAVSA also faces the increasing complex signal environment,such as insufficient snapshots and multitarget bearing proximity.The complex signal environment leads to the decrease of the directionfinding accuracy and spatial resolution of the existing spatial spectrum estimation algorithms of the CAVSA.The above problems are seriously affected the detection performance of the underwater target of the CAVSAs.This paper focuses on the above problems,and then studies the robust beamforming and sparse spectrum estimation technology of the CAVSA based on the combined processing of the acoustic pressure and particle velocity(CPAPPVC).The main research contents include:1.In this paper,the method of the CPAPPVC is improved,and then a new covariance construction method of the CAVSA is proposed.This method firstly uses the pressure and x、y particle velocity components to construct an augment cross-covariance matrix,and then use the left singular vector and singular values of the augment cross-covariance matrix to construct the array covariance matrix with the form of Hermitian.This combined processing method increases the azimuth information of vibration velocity channel compared to the traditional CPAPPVC,and solves the problem of difficult observation direction selection of the traditional CPAPPVC.Then,the MVDR beamforming algorithms of the CAVSA based on the CPAPPVC methods are studied,and the results show that the improved CPAPPVC method has stronger noise suppression ability and higher direction-finding performance than the acoustic pressure and particle velocity independent processing and the traditional CPAPPVC methods.Besides,focusing on the DOA estimation problem of the MVDR for the coherent signals,this paper combines the proposed construction method of the covariance matrix with the decoherent algorithms in the element domain of the centrosymmetric circular array and the phase-mode domain.Then,the forward and backward spatial average(FBSA)in the element domain,the forward and backward spatial smoothing(FBSS)and vector reconstruction(VR)technologies in the phase-mode domain are proposed.Simulation and experimental results show that the decoherent algorithm in the element domain only solves the direction-finding problem of two coherent signals,while the decoherent algorithms in the phase-mode domain can be applied in the DOA estimation of multiple coherent signals,and the VR method has better DOA estimation performance than the FBSS in the phase-mode domain.2.For solving the problem of the spatial processing gain decreasing of the MVDR beamforming and CBF in the case of the steering vector mismatch,this paper proposes the realvalued robust beamforming algorithms of the worst-case performance optimization in the element domain and the phase-mode domain and the deconvolution projection CBF algorithm based on the augmented cross-covariance matrix,respectively.The real-valued robust beamforming algorithms transform the steering vector of the CAVSA into the steering vector with centrosymmetric characteristics.Based on this,the augmented cross-covariance matrices are constructed by using the acoustic pressure and x、y particle velocity components,and then they are converted into the real-valued ones by using the real-valued processing of the unitary matrices.The left singular vectors and the singular values of the real-valued augmented crosscovariance matrix are used to construct the real-valued covariance matrix with the form of the Hermitian.Finally,the worst-case performance optimization idea is applied to improve the robustness of the MVDR beamforming.Simulation and experimental results verify the effectiveness of the real-valued robust algorithms.The deconvolution projection CBF method has fully combined the eigenspace beamforming and the principle of the deconvolution image restoration.Firstly,the augmented cross-covariance matrix is decomposed to obtain the signal subspaces corresponding to the acoustic pressure and particle velocity channel by using singular decomposition.Then,according to the idea of the eigenspace beamforming,the steering vectors of the acoustic pressure and particle velocity components are projected onto the associated signal subspaces to obtain the spatial spectrum of the projection CBF and the projection beampattern function of the acoustic pressure and particle velocity channels.Finally,according to the principle of the deconvolution image restoration,the spatial spectrum of the projected CBF is obtained by deconvoluting the spatial spectrum of the projected CBF,which is by using the Richardson Lucy iterative algorithm and the point scattering function formed by the product of the projection beampattern function of the acoustic pressure and particle velocity channel.Simulation and experimental results verify the effectiveness of the deconvolution projection CBF algorithm.3.To solve the problem of super-resolution direction-finding of the spatial spectrum estimation technology for the CAVSA in the case of the few snapshots and multi-target bearing proximity,the sparse representation DOA estimation algorithm of the augmented crosscovariance vector is proposed.The proposed algorithm expresses the augmented crosscovariance matrix as the sum of the cross-correlation matrices of the acoustic pressure and particle velocity associated with every signal and the cross-correlation matrix of the acoustic pressure and particle velocity corresponding to any two different signals.Then,the augmented cross-covariance matrix is vectorized,and the Khatri-Rao and the cross Kronecker product of the overcomplete basis composed of the steering vector associated with the acoustic pressure and particle velocity channel on the discrete angle set are used to construct the virtual over complete and extra bases of the CAVSA.Based on these,the augmented cross-covariance vector is expressed as the sparse reconstruction problem with the l1-norm constraint,and the constraint coefficient is obtained according to the statistical characteristics of the residual estimation of the augmented cross-covariance vector,furthermore,the second-order cone programming is used to solve the spatial spectrum of the target signal.Simulation and pool experiment results show that the performance of the proposed algorithm is better than the MVDR,MUSIC,and the existing sparse representation algorithms.To improve the directionfinding performance of the CAVSA in the case of coherent signals further,the sparse representation of the left singular vector of the augmented cross-covariance matrix is proposed.In theory,the left singular vectors associated with the maximum singular value of the augmented cross-covariance matrix are the linear combinations of the steering vectors corresponding to the particle velocity components of all coherent signals,and the linear combination coefficients are not equal to zero.According to this property,the left singular vector is sparsely represented,and the sparse spatial spectrum estimation algorithm of coherent signals is established.Simulation and pool experiment results show that the performance of the proposed algorithm is better than the MVDR and MUSIC methods based on the vector reconstruction and the existing sparse spatial spectrum estimation algorithms.4.We have carried out the experimental research of the CAVSAs on the target direction finding and tracking in Songhua Lake.The experimental results have been investigated the target bearing estimation and tracking performance of the MVDR beamforming,real value robust beamforming based on worst-case performance optimization,the deconvolution projection CBF,sparse representation of the left singular value vector,and the sparse representation of the augmented cross-covariance vector.The experimental research lays the foundation for the practical engineering application of the passive sonar system of the CAVSA.