Robust filtering for uncertain nonlinear systems satisfying a sum quadratic constraint

This paper develops a robust extended Kalman filter for nonlinear uncertain systems with a deterministic description of noise and uncertainty. The system state dynamics are formulated in reverse time and the uncertainties are modeled in terms of sum quadratic constraints. The robust filtering problem is formulated as a set-valued state estimation problem which is recast into an optimal control problem. The solution of the resulting Hamilton-Jacobi-Bellman equation is obtained by using a quadratic approximation. This leads to an approximate information state for the filtering problem which is computed recursively through a difference Riccati equation derived by linearizing the observation equation and using a quadratic approximation to the system dynamics. The reduction of the robust estimator to the standard Kalman filter in the uncertainty-free linear case is also discussed.