Research On Array Signal Parameter Estimation Algorithm Based On Sparse Representation

As an important research branch of array signal processing,sound source localization is widely used in various fields and has become a hot spot for scholars.Among the traditional sound source localization methods,the most representative is the subspace method,but the subspace algorithm has the disadvantages of low resolution and weak anti-noise performance.In order to solve the problems of the subspace algorithm,and because the spatial signal itself is sparse,the sparse reconstruction algorithm is reasonably applied to the sound source localization.Based on the sparse reconstruction algorithm,this thesis has done the following four aspects:1.In order to verify the outstanding advantages of sparse reconstruction algorithms in far-field sound source DOA estimation,Capon algorithm,MUSIC algorithm,and l₁-SVD algorithm were selected to analyze and compare.These three algorithms first be introduced briefly in this thesis,and be compared with simulations at last.It verifies that the sparse reconstruction algorithm has the advantages of high resolution,high positioning accuracy,and little influence by the number of snapshots.2.In order to improve the estimation accuracy of Direction of Arrival(DOA)for far-field non-coherent narrowband signals under non-stationary noise,an improved DOA estimation algorithm for sparse representation under non-stationary noise is proposed.Firstly,the class differential covariance algorithm is used to construct the difference matrix to suppress the influence of non-stationary noise;then the sparse representation model and the weight function are constructed based on the basic principle of estimation of signal parameters via rotational invariance technique algorithm;finally,the DOA estimation is realized by solving the model with CVX convex optimization toolkit.The simulation results show that compared with the traditional covariance difference algorithm,noise covariance matrix estimation algorithm,rank trace minimization algorithm and sparse reconstruction algorithm,the proposed algorithm can not only suppress the influence of non-stationary noise effectively,but also has strong robustness and high estimation accuracy under low signal noise ratio(SNR)and low snapshot number.3.Four currently representative far-field and near-field mixed sound source localization algorithms are analyzed and compared.The four algorithms are divided into two categories for introduction,and be compared with simulations by category.Through the simulation results,it can be seen that the sparse reconstruction algorithm has advantages in the localization of mixed sound sources.At the same time,the common problems of these four algorithms are analyzed,and the deficiencies of these four algorithms are verified by simulation experiments.4.In order to prevent the far-field and near-field sound sources from interacting with each other to cause problems such as low accuracy and difficulty in distinguishing when locating near-field and far-field mixed sound sources,an improved far-field and near-field mixed sound source localization algorithm is proposed.In this thesis,firstly,in a symmetrical uniform array structure,the far-field sound source covariance matrix is a Toeplitz matrix,and the near-field sound source covariance matrix is not a Toeplitz matrix.Therefore,the covariance difference algorithm can be used to remove far-field sound source information.and the near-field sound source information is preserved;then the ESPRIT algorithm with the sparse reconstruction algorithm can be combined to obtain the near-field sound source DOA estimate;after obtaining the near-field sound source DOA estimate,the two-dimensional MUSIC algorithm is used to obtain the distance parameter of the near-field sound source,and the near-field sound source covariance matrix estimate can be obtained by the near-field sound source DOA estimate and distance parameter.Finally,the near-field sound source covariance matrix is subtracted to obtain the covariance matrix of the pure far-field sound source.In order to reduce the computational complexity,₁l-SVD algorithm is used to obtain the far-field sound source DOA estimate.The simulation results show that compared with the sparse reconstruction algorithm based on the fourth-order cumulant domain and the sparse reconstruction algorithm based on the second-order statistic domain,the improved algorithm can separate far and near field sound sources well,so the positioning accuracy is improved;at the same time,the improved algorithm can be applied in the case of Gaussian signals and unknown noise.