  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, not requiring knowledge of the sensor array geometry. 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 TDOA-based
localization, both in terms of TDOA accuracy estimation and localization error.
