On robust Kalman filtering

Abstract

The problem of making the Kalman filter robust is considered in the paper. Proceeding from the equivalence between the Kalman filter and the least squares regression problem, a statistical approach named M-estimation is suggested to resolve the regression problem robustly. Since the derived robust M -filters do not have an attractive recursive form, the possibility is proposed of designing real-time estimators based on the general formulation of the robust stochastic approximation algorithm and step-by-step optimization with respect to the weighting matrix combined with suitable approximations. Results of simulation demonstrating the robustness of the proposed estimators are also included.