Minimum variance time of arrival estimation for positioning

Abstract

Positioning systems based on time of arrival (TOA) rely on an accurate estimation of the first signal arrival which is the only one bearing position information. In this context, first arrival path detectors based on the minimum variance (MV) and the normalized minimum variance (NMV) criteria are robust against multipath propagation and non-line-of-sight (NLOS) situations. The aim of the paper is twofold. On the one hand, efficient implementations of those criteria will be presented. On the other hand, two polynomial rooting procedures based on the MV criterion will be exposed. As it will be shown, they lead to better performance than the traditional MV versions based on a grid search. In general, these methods imply finding the roots of a polynomial with complex coefficients. In order to reduce their computational burden a conformal mapping is proposed herein.