Source localization and denoising: a perspective from the TDOA space
This addresses noise reduction in TDOA-based localization, which is incremental as it builds on known subspace properties.
The paper tackles the problem of denoising Time Differences of Arrival (TDOA) measurements for source localization by projecting noisy TDOAs onto a linear subspace in the TDOA space, showing analytically and via simulation that this improves localization accuracy.
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.