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 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 problem. These least-squares problems, subject to the bounded system uncertainties using the robust least squares method proposed by A. Ben-Tal and A. Nemirovski. Simulation results show that the new algorithm leads to a better performance than the conventional algorithms under outliers as well as system uncertainties.