Off-grid DOA estimation in real spherical harmonics domain using sparse Bayesian inference

When true targets do not locate exactly on discretized sampling grids, sparse reconstruction methods cannot estimate direction-of-arrival (DOA) accurately due to angular differences. This DOA estimation problem can be solved by off-grid sparse Bayesian inference (OGSBI). However, this method brings high computational complexity when estimating 2-D off-grid DOAs with spherical arrays. In order to solve 2-D off-grid DOA estimation, we adopt two steps to reduce computations and meanwhile maintain good performance. First, a real-valued off-grid model is constructed in real spherical harmonics domain. It models angular differences by exploiting the multivariable Taylor expansion to construct a matching matrix. Second, a projection-based basis selection sparse Bayesian learning combining with least squares (PSBL-LS) algorithm is proposed to estimate 2-D off-grid DOAs. This method reduces computations in learning both posterior of sparse signals and angular differences. The PSBL-LS uses the potential basis functions selected from the matching matrix to learning the posterior distribution of sparse signals. At the same time, the angular differences are estimated by least squares method based on the selected basis functions. Simulations show our proposed method improves accuracy and reduces computational load.