Robust Extended Kalman Filtering in Hybrid Positioning Applications

Abstract

The Kalman filter and its extensions has been widely studied and applied in positioning, in part because its low computational complexity is well suited to small mobile devices. While these filters are accurate for problems with small nonlinearities and nearly Gaussian noise statistics, they can perform very badly when these conditions do not prevail. In hybrid positioning, large nonlinearities can be caused by the geometry and large outliers (blunder measurements) can arise due to multipath and non line-of-sight signals. It is therefore of interest to find ways to make positioning algorithms based on Kalman-type filters more robust. In this paper two methods to robustify the Kalman filter are presented. In the first method the variances of the measurements are scaled according to weights that are calculated for each innovation, thus giving less influence to measurements that are regarded as blunder. The second method is a Bayesian filter that approximates the density of the innovation with a non-Gaussian density. Weighting functions and innovation densities are chosen using Hubers min-max approach for the epsilon contaminated normal neighborhood, the p-point family, and a heuristic approach. Six robust extended Kalman filters together with the classical extended Kalman filter (EKF) and the second order extended Kalman filter (EKF2) are tested in numerical simulations. The results show that the proposed methods outperform EKF and EKF2 in cases where there is blunder measurement or considerable linearization errors present.