Low-Complexity Steered Response Power Mapping based on Nyquist-Shannon Sampling

The steered response power (SRP) approach to acoustic source localization computes a map of the acoustic scene from the output power of a beamformer steered towards a set of candidate locations. Equivalently, SRP may be expressed in terms of generalized cross-correlations (GCCs) at lags equal to the candidate locations' time-differences of arrival (TDOAs). Due to the dense grid of candidate locations, however, conventional SRP exhibits a high computational complexity, limiting its practical feasibility. In this paper, we propose a low-complexity SRP approach based on Nyquist-Shannon sampling. Noting that on the one hand the range of possible TDOAs is physically bounded, while on the other hand the GCCs are bandlimited, we critically sample the GCCs around their TDOA interval and approximate the SRP map by interpolation. In usual setups, the total number of sample points can be several orders of magnitude less than the number of candidate locations, yielding a significant complexity reduction. Simulations comparing the proposed approximation with conventional SRP indicate low approximation errors and equal localization performance. A MATLAB implementation is available online.