On Globalized Robust Kalman Filter Under Model Uncertainty

Abstract

This article proposes a novel state estimation strategy with globalized robustness for a class of systems under uncertainty. Departing from the classical minimax estimation, this article focuses on the globalized robust estimation (GRE), which minimizes the estimator's fragility to attain an acceptable loss compared with the nominal model. The GRE problem has an easily specified hyperparameter as compared to the maximal radius in the classical minimax estimation. Besides, it considers all possible densities for better adaptability to different uncertainties. First, the solution to the GRE problem subject to the Kullback–Leibler (K–L) divergence constraint is rigorously studied such that the explicit expressions of the least-squares estimator and the most-sensitive density are derived. Consequently, we formulate the robust filtering problem as a game to obtain the iterative equation of the globalized robust Kalman filter (GRKF). Moreover, the convergence of the proposed GRKF is established for systems with time-invariant nominal models. Finally, simulated examples show that the proposed GRKF outperforms the standard Kalman filter and the classical robust Kalman filter.