Robust Kalman Filtering Under Model Perturbations

• Published in: IEEE transactions on automatic control Vol. 62; no. 6; pp. 2902 - 2907
• Main Author: Zorzi, Mattia
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Budgeting; Covariance matrices; Divergence; Estimation; Iterative methods; Kalman filters; Mean square error methods; Mean square values; Minimax problem; Minimax technique; Parameter sensitivity; Risk; risk sensitive filtering; robust Kalman filtering; Robustness; Sensitivity; Tau-divergence family; Uncertainty
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2016.2601879

We consider a family of divergence-based minimax approaches to perform robust filtering. The mismodeling budget, or tolerance, is specified at each time increment of the model. More precisely, all possible model increments belong to a ball which is formed by placing a bound on the Tau-divergence family between the actual and the nominal model increment. Then, the robust filter is obtained by minimizing the mean square error according to the least favorable model in that ball. It turns out that the solution is a family of Kalman like filters. Their gain matrix is updated according to a risk sensitive like iteration where the risk sensitivity parameter is now time varying. As a consequence, we also extend the risk sensitive filter to a family of risk sensitive like filters according to the Tau-divergence family.