A New Robust Kalman Filter Algorithm under Outliers and System Uncertainties

This paper proposes a new robust Kalman filter algorithm under outliers and system uncertainties. The robust Kalman filter of Durovic and Kovacevic (1999) is extended to include unknown-but-bounded parameter uncertainties in the state or observation matrix. We first formulate the robust state estimation problem as an M-estimation problem, which leads to an unconstrained nonlinear optimization problem. This is then linearized and solved iteratively as a series of linear least-squares problems. These least-squares problems are subject to the bounded system uncertainties using the robust least squares method proposed by A. Ben-Tal and A. Nemirovski (2001). Simulation results show that the new algorithm leads to a better performance than the conventional algorithms under outliers as well as system uncertainties.