| Summary: | In this paper, to address the problem of array sensors failure, we propose a covariance matrix reconstruction method for direction-of-arrival (DOA) estimation. Firstly, we devise a diagnosis method to detect and locate the positions of failure sensors. According to the robustness of the array, the sensor failure scenarios are classified into redundant sensors failure and non-redundant sensors failure. Then, the corresponding DOA estimation method is adopted for two failure scenarios. The former can be solved using the virtual sensors in the difference coarray. As for the latter, the difference coarray has some holes, resulting in the decrease of available continuous virtual sensors or degrees of freedom (DOFs). Based on the matrix completion theory, the covariance matrix is extended to a high-dimensional Toeplitz matrix with missing data, where some elements are zero. We employ the mapping matrix, further use trace norm instead of the rank norm for convex relaxation to reconstruct the covariance matrix, thereby realizing the filling of the virtual sensor holes in difference coarray and restoring the DOFs. Compared with the sparsity-based methods, the proposed method can eliminate the effect of the discretization of the angle domain, and avoid regularization parameter selection. Finally, the root-MUSIC method is given for DOA estimation. Theoretical analysis and simulation results show that the proposed methods can alleviate the effect of array sensors failure and improve the estimation performance.
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