Robust Kalman Filtering under Model Perturbations

TL;DR

This paper introduces a family of robust Kalman filters designed to handle model perturbations using divergence-based minimax approaches, with a time-varying risk sensitivity parameter for improved robustness.

Contribution

It develops a novel family of Kalman-like filters based on Tau-divergence, extending risk sensitive filtering to better manage model uncertainties.

Findings

Filters adapt to model perturbations using divergence bounds

Gain matrices are updated via a risk sensitive-like iteration

Extension of risk sensitive filters to Tau-divergence family

Abstract

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.