Two-dimensional grid-less angle estimation based on three parallel nested arrays

Abstract An array geometry with three parallel nested arrays is designed and a corresponding two-dimensional (2D) grid-less angle estimation method is proposed. The array can use 4 M physical elements to achieve 4M2 virtual degrees of freedom (DOF) after the extended vectorization of two cross-covariance matrices (CCMs), which also transforms the 2D angle estimation problem into one-dimensional (1D) and one-snapshot sparse recovery. Thereafter, without any spatial smoothing, the Toeplitz covariance matrix of the virtual array can be recovered through a robust semi-definite programming (SDP) based on atomic norm minimization (ANM). Meanwhile, the denoising virtual output is obtained as a by-product. Finally, 1D angle is obtained from the Vandermonde decomposition of the Toeplitz matrix and the other 1D angle is obtained in succession from the denoising virtual output via total least squares (TLS). The proposed method is robust to grid mismatch problem, obtains automatically paired two-dimensional angle estimation and requires only one-level Toeplitz matrix recovery, which makes the maximum identifiable source number exceed the physical sensor number. Furthermore, the angle estimation performance of the proposed method outperforms other state-of-the-art methods using parallel arrays. Numerical simulations verify the effectiveness of our approach.