A Mixed-Field Sources Localization Algorithm Based on High-order Cumulant Matrix Reconstruction for General Symmetric Array

Abstract Sparse arrays have obvious advantages in mixed-field localization applications because the better estimation accuracy can be obtained by using consective lags. However, existing algorithms can not fully utilize the information provided by sparse arrays. In this paper, an interpolation processing method based on atomic norm is proposed to solve the sparse array localization problem. The high-order cumulant matrix is reconstructed by the interpolation method to generate an augmented cumulant matrix without holes, which can make full use of all the lags. Then, the atomic norm minimization (ANM) method is used to recover the sparse matrix after interpolation in a gridless way. The matrix after recovery enables off-grid direction-of-arrival (DOA) estimation. After the interpolation reconstruction, more consecutive lags can be exploited, the degrees of freedom (DOFs) are further increased, and the DOA estimation accuracy is also improved. Numerical simulations verify the superiority of the proposed algorithm compared with the existing algorithms.