Low-Complexity Steered Response Power Mapping based on Nyquist-Shannon Sampling
This work provides a method for reducing the computational burden of acoustic source localization for applications requiring real-time processing or deployment on resource-constrained devices, representing an incremental improvement over existing SRP methods.
The paper addresses the high computational complexity of Steered Response Power (SRP) for acoustic source localization, which conventionally requires numerous inverse Fourier transform (IFT) evaluations due to a dense grid of candidate locations. By critically sampling bandlimited generalized cross-correlations (GCCs) around their time-difference of arrival (TDOA) interval and using interpolation, the authors significantly reduce IFT computations, achieving comparable localization performance with low approximation errors.
The steered response power (SRP) approach to acoustic source localization computes a map of the acoustic scene from the frequency-weighted output power of a beamformer steered towards a set of candidate locations. Equivalently, SRP may be expressed in terms of time-domain generalized cross-correlations (GCCs) at lags equal to the candidate locations' time-differences of arrival (TDOAs). Due to the dense grid of candidate locations, each of which requires inverse Fourier transform (IFT) evaluations, conventional SRP exhibits a high computational complexity. 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 number of sample points can be orders of magnitude less than the number of candidate locations and frequency bins, yielding a significant reduction of IFT computations at a limited interpolation cost. Simulations comparing the proposed approximation with conventional SRP indicate low approximation errors and equal localization performance. MATLAB and Python implementations are available online.