Source localization and denoising: a perspective from the TDOA space

TL;DR

This paper presents a novel method for denoising TDOA measurements by projecting noisy data onto a linear subspace in TDOA space, improving source localization accuracy.

Contribution

It introduces a projection-based denoising technique for TDOA data, including incomplete sets, with analytical and simulation validation.

Findings

Projection improves localization accuracy

Method handles incomplete TDOA sets

Analytical and simulation validation confirms effectiveness

Abstract

In this manuscript, we formulate the problem of denoising Time Differences of Arrival (TDOAs) in the TDOA space, i.e. the Euclidean space spanned by TDOA measurements. The method consists of pre-processing the TDOAs with the purpose of reducing the measurement noise. The complete set of TDOAs (i.e., TDOAs computed at all microphone pairs) is known to form a redundant set, which lies on a linear subspace in the TDOA space. Noise, however, prevents TDOAs from lying exactly on this subspace. We therefore show that TDOA denoising can be seen as a projection operation that suppresses the component of the noise that is orthogonal to that linear subspace. We then generalize the projection operator also to the cases where the set of TDOAs is incomplete. We analytically show that this operator improves the localization accuracy, and we further confirm that via simulation.