Wideband Sparse Bayesian Learning for DOA estimation from multiple snapshots

The directions of arrival (DOA) of plane waves are estimated from multi-frequency multi-snapshot sensor array data using Sparse Bayesian Learning (SBL). The prior for the source amplitudes is assumed to be independently zero-mean complex Gaussian distributed with hyperparameters being the unknown variances (i.e. the source powers). For a complex Gaussian likelihood with unknown noise variance hyperparameter, the corresponding Gaussian posterior distribution is derived. For a given number of DOAs, the hyperparameters are automatically selected by maximizing the evidence and promote sparse DOA estimates. The SBL scheme for DOA estimation is discussed and evaluated competitively against MUSIC.