TDOA Matrices: Algebraic Properties and their Application to Robust Denoising with Missing Data

Abstract—Measuring the Time delay of Arrival (TDOA) between a set of sensors is the basic setup for many applications, such as localization or signal beamforming. This paper presents the set of TDOA matrices, which are built from noise-free TDOA measurements. We prove that TDOA matrices are ranktwo and have a special SVD decomposition that leads to a compact linear parametric representation. Properties of TDOA matrices are applied in this paper to perform denoising, by finding the TDOA matrix closest to the matrix composed with noisy measurements. The paper shows that this problem admits a closed-form solution for TDOA measurements contaminated with Gaussian noise which extends to the case of having missing data. The paper also proposes a novel robust denoising method resistant to outliers, missing data and inspired in recent advances in robust low-rank estimation. Experiments in synthetic and real datasets show significant improvements of the proposed denoising algorithms in TDOA-...

• Type: Journal
• Year: 2016
• Where: CORR
• Authors: José A. Velasco, Daniel Pizarro, Javier Macías Guarasa, Afsaneh Asaei
• Keywords: CORR 2016, Education