Robust extended Kalman smoothing under model uncertainties

This paper proposes a robust extended Kalman smoothing approach in the case that there is a modeling mismatch between the given nominal nonlinear state-space model and the actual one. The resulting algorithm follows a linearization process and takes the form of a robust fixed-lag smoother. At each time step the computation of the smoothing gain of the linearized model is required. The latter is derived from a dynamic game: one player selects the least favorable model in a prescribed “ball’’ centered about the nominal linearized model in Kullback-Leibler (KL) divergence topology, and the other selects the optimal smoothing gain. Finally, some numerical experiments show the effectiveness of the proposed algorithm.