Robust Kalman Filtering: Asymptotic Analysis of the Least Favorable Model

TL;DR

This paper analyzes the asymptotic behavior of robust Kalman filters designed using least favorable models within a bounded model uncertainty set, demonstrating convergence under small modeling errors.

Contribution

It provides a convergence analysis of the Riccati-like recursion for computing the least favorable model in robust filtering.

Findings

Recursion converges when model uncertainty is sufficiently small.

Provides theoretical foundation for robust filter design.

Clarifies conditions for stability of the robust filtering approach.

Abstract

We consider a robust filtering problem where the robust filter is designed according to the least favorable model belonging to a ball about the nominal model. In this approach, the ball radius specifies the modeling error tolerance and the least favorable model is computed by performing a Riccati-like backward recursion. We show that this recursion converges provided that the tolerance is sufficiently small.