Memory-efficient approximate three-dimensional beamforming

Abstract

Localization of acoustic sources using a sensor array is typically performed by estimating direction-of-arrival (DOA) via beamforming of the signals recorded by all elements. Software-based conventional beamforming (CBF) forces a trade-off between memory usage and direction resolution, since time delays associated with a set of directions over which the beamformer is steered must be pre-computed and stored, limiting the number of look directions to available platform memory. This paper describes a DOA localization method that is memory-efficient for three-dimensional (3D) beamforming applications. Its key lies in reducing 3D look directions [described by azimuth/inclination angles (ϕ, θ) when considering the array as a whole] to a single variable (a conical angle, ζ) by treating the array as a collection of sensor pairs. This insight reduces the set of look directions from two dimensions to one, enabling computational and memory efficiency improvements and thus allowing direction resolution to be increased. This method is described and compared to CBF, with comparisons provided for accuracy, computational speedup, and memory usage. As this method involves the incoherent summation of sensor pair outputs, gain is limited, restricting its use to localization of strong sources—e.g., for real-time acoustic localization on embedded systems, where computation and/or memory are limited.