An efficient off-grid direction-of-arrival estimation method based on inverse-free sparse Bayesian learning

The direction-of-arrival (DOA) estimation problem can be formulated in a Bayesian framework and solved well through sparse Bayesian learning (SBL). However, SBL-based methods often suffer from high computational complexity due to the matrix inversion of a large matrix in the Bayesian inference procedure. To address this issue, we propose an efficient DOA estimation method based on inverse-free sparse Bayesian learning (IFSBL). A real-valued vectorized array covariance model and a hierarchical Bayesian model are established. Then, a relaxed lower bound on the likelihood, namely relaxed evidence lower bound (relaxed-ELBO), is obtained as the optimization objective of the Bayesian inference. By utilizing the variational expectation–maximization method for the Bayesian inference, the estimation of the statistics of interest can be achieved, which is free of matrix inversion as the matrix to be inverted is diagonal. Moreover, when we take the off-grid DOAs into account, an efficient grid refinement is developed to iteratively modify the DOA estimates derived from the estimated spatial spectrum. The off-grid error obtained by the root of a simple polynomial is used to compensate for the corresponding DOA estimate. Simulations show good accuracy and improved computational efficiency of the proposed method compared with other state-of-art methods. Further experimental results verify the advantage in the runtime for the proposed method.