The iterated extended set membership filter applied to relative localization between autonomous vehicles based on GNSS and UWB ranging

This paper presents a novel Iterated Extended Set Membership Filter (IESMF) with an application to relative localization. For safe operation of formations of automatic vehicles, consistent uncertainty estimates are of crucial importance. Here, a localization filter that provides ellipsoidal regions that are guaranteed to contain another vehicles position is presented. The proposed iterative update step can appreciably reduce the size of the a posteriori state ellipsoid. The idea of using SIVIA as a baseline to quantify conservativeness is introduced. Another novelty is that we take into account parametric uncertainty of the observation equation. The proposed filter is applied to a two unmanned aircraft systems (UAS) localization problem in simulation with observation noise obtained from real sensors. Simulation results illustrate the effective reduction of filter conservativeness by a small number of iterative updates.