Time difference localization in the presence of outliers

In this work we examine new ways to solve a time-difference-of-arrival (TDOA) localization problem when the set of measurements is contaminated by outliers. The proposed method relies on the minimization of an Lp-norm based cost function with p∈(0,1]. This norm is known to provide robustness against outliers. Some known positioning method can eventually successfully locate an emitter in the presence of outlier measurements, but it is at the expense of huge computational costs due to multi-dimensional grid search. We propose in this paper a way to dramatically lighten the computational load by reducing the problem to a few linear searches. Even if 70% of the measurements are outliers, the proposed positioning method provides high accuracy location estimates, while keeping the computational load very low. Optionally, the location estimates can be used to identify and reject outliers from the data set, which can then serve as an input of any common TDOA positioning method to obtain refined location estimates. Numerical examples corroborate our results, both in terms of accuracy and of computational time.