A Bayesian Sparse-Plus-Low-Rank Matrix Decomposition Method for Direction-of-Arrival Tracking

The sparse Bayesian learning algorithm for multiple measurement vectors (also known as the MSBL algorithm) is an automatic method to estimate the stationary directions-of-arrival (DOAs) of multiple signals using an array of sensors. If there are time-varying DOAs along with stationary DOAs, then the DOAs of the signals can be tracked by using the sparse Bayesian learning algorithm for a single measurement vector (also known as the SSBL algorithm) by formulating the DOA estimation problem as a snapshot-by-snapshot estimation problem. When both stationary and time-varying DOAs are present, a novel approach is proposed in which we can estimate the DOAs of multiple signals by considering all snapshots together rather than estimating the DOAs snapshot-by-snapshot. This method is motivated by the fact that if the signals are sparse in the spatial domain, the stationary DOAs form the low-rank component, and the time-varying DOAs form the sparse component when all snapshots are considered together. All the parameters in the formulation are automatically estimated by using the sparse Bayesian learning principle. Simulation study using a uniform-linear-array has been carried out to compare the performance of the Bayesian sparse-plus-low-rank (BSPLR) matrix decomposition method and the SSBL method in terms of the root-mean-squared-error of the DOA estimates. We show that the BSPLR method has the potential to outperform the SSBL algorithm, which estimates the DOAs snapshot-by-snapshot. The methods are also applied on passive sonar data from the SWellEx- $\mathbf {96}$ ocean acoustic experiment to demonstrate their robustness to the modeling assumptions made.