Low-rank Kalman filtering under model uncertainty

TL;DR

This paper introduces a robust Kalman filter designed to handle model uncertainty by framing it as a dynamic game, resulting in a low-rank Riccati equation and demonstrating effectiveness through simulations.

Contribution

It develops a novel robust Kalman filtering approach based on a game-theoretic formulation addressing model ambiguity, leading to a low-rank Riccati equation.

Findings

The proposed filter effectively handles model uncertainty.

Simulation results demonstrate improved robustness.

The filter is governed by a low-rank Riccati equation.

Abstract

We consider a robust filtering problem where the nominal state space model is not reachable and different from the actual one. We propose a robust Kalman filter which solves a dynamic game: one player selects the least-favorable model in a given ambiguity set, while the other player designs the optimum filter for the least-favorable model. It turns out that the robust filter is governed by a low-rank risk sensitive-like Riccati equation. Finally, simulation results show the effectiveness of the proposed filter.