Outlier-Robust Constrained State Estimation via l1and Huber Penalization

Abstract

A robust approach to constrained state estimation is proposed. Classical optimal estimation methods such as Kalman filtering/smoothing have served well for the past half century. Recently, with a growing number of data sources/sensors and the demanding nature of new applications, a revisit of some of the fundamental assumptions of the aforementioned classical methods is necessary. Models that deviate from the standard Gaussian noise distribution assumption are considered in this research. This allows for the accommodation of measurement outliers, as well as impulsive disturbances on system dynamics. The particular focus in this work is on robustness to measurement outliers. The problem is framed as a convex optimization problem which enjoys global optimality guarantees. This formulation also enables the addition of convex state constraints with ease, giving more modeling flexibility. Traditional l2 penalty methods yield poor estimation performance in the face of measurement outliers. In this work, l1 and Huber penalties are introduced to handle cases that are outside of the reach of l2 methods. Simulation studies are conducted on a classic road vehicle navigation problem to show the efficacy of the proposed approaches.