ARTICLE Velasco_IEEE_2015/IDIAP TDOA Matrices: Algebraic Properties and their Application to Robust Denoising with Missing Data Velasco, Jose Pizarro, Daniel Macias-Guarasa, Javier Asaei, Afsaneh Matrix completion missing data skew- symmetric matrices TDOA denoising TDOA estimation EXTERNAL http://publications.idiap.ch/attachments/papers/2016/Velasco_IEEE_2015.pdf PUBLIC IEEE Transactions on Signal Processing 64 20 5242-5254 1053-587X 2016 http://ieeexplore.ieee.org/document/7518595/ URL 10.1109/TSP.2016.2593690 doi 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 rank-two 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-based localization, both in terms of TDOA accuracy estimation and localization error.