A Bayesian Approach to Informed Spatial Filtering With Robustness Against DOA Estimation Errors

A Bayesian approach to spatial filtering is presented, which is robust to uncertain or erroneous direction-of-arrival (DOA) information. The proposed framework aims to capture multiple sound sources at each time-frequency instant with an arbitrary direction-dependent gain, while attenuating diffuse sound and noise. For robustness, the DOA corresponding to each sound source is assumed to be a discrete random variable with a prior defined on a discrete set of candidate DOAs over the whole DOA space. With this assumption, the desired spatial filter is given as a weighted sum of spatial filters corresponding to a specific combination of probable DOA values, where the weights are given by the joint posterior probabilities of the combination of DOA values. Assuming the whole DOA space as the support for each random variable results in redundant computations and contributes to a high computational cost. To alleviate this problem, a narrowband DOA estimate-based posterior probability approximation method is proposed, which isolates regions in the DOA space with high probability of containing the actual source DOAs to compute time-adaptive supports for each random variable. Through experimental analysis, we demonstrate the robustness of the proposed framework against DOA estimation errors. Experimental evaluation with simulated and measured room impulse responses, in terms of objective performance measures, demonstrates the effectiveness of the framework to perform spatial filtering in noisy and reverberant acoustic environments.