A discrete-time robust extended Kalman filter

A discrete-time robust extended Kalman filter (REKF) formulation for uncertain systems expressed in terms of a set-valued state estimator is described in this paper. The robust filter and Riccati equations are derived as an approximate solution to a reverse-time optimal control problem defining this set-valued state estimator. As presented, the uncertainties are modeled by a sum quadratic constraint (SQC) that takes into account both modeling uncertainties as well as uncertainties introduced from exogenous noise sources.