Approaches for the robustification of Kalman filters (Q2772096)

This extensive work is a systematical and self-contained treatment of various robustification concepts for Kalman filtering. The requirement of robustness arises from practical applications where the filtering algorithm is corrupted by outliers. The robustification problem is complex due to different types of outliers: While the outliers in the observation noise produce a reduced impact of the observation in the prediction and correction steps, the outliers in the system noise give structural breaks which are to be recognized as fast as possible.NEWLINENEWLINENEWLINEThe first part of the work deals with the so-called rLS-, rIC-, and mIC-filters. These algorithms differ from the classical Kalman filter due to a robustified correction step. The author shows the asymptotic stationarity of these methods. A simulation study provides a comparison of the rLS- and rIC-filters with the posterior-mode estimators showing that the former perform better. The second part is devoted to statistical aspects of the EM-algorithm and its robustification. To get the local asymptotic approach, the \(L_2\)-differentiability is generalized giving the notions of the influence curve and of the linear estimator for a model with missings. Within this setting, a classical optimal one-step-algorithm and a robust one-step algorithm are presented.NEWLINENEWLINENEWLINEWe should emphasize the efforts to present the background needed for understanding the matter. The reader benefits permanently from the appendix, which provides a description of corresponding tools from probability theory, asymptotical statistics and other related fields.