On robust Kalman filtering

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.