Localization based on periodic signals with ambiguity

In this work we examine new ways to solve a localization problem when the observed signals are periodic and the period is too small to provide ambiguity free measurements. Along its trajectory, a mobile receiver collects periodic signals from a target and provides ambiguous time-of-arrival measurements. We propose a procedure based on convex optimization that resolves measurement ambiguities and achieves target localization with high positioning accuracy. This procedure is efficient and reaches the Cramer-Rao accuracy bound. It even outperforms the grid-search based implementation of the Maximum Likelihood estimator, in terms of accuracy and computational complexity. Numerical examples corroborate our results.