Robust State Space Filtering under Incremental Model Perturbations Subject to a Relative Entropy Tolerance

TL;DR

This paper develops a robust filtering approach for Gaussian state-space models under incremental model perturbations constrained by relative entropy, resulting in a risk-sensitive filter with adaptive sensitivity parameters.

Contribution

It introduces a dynamic minimax game framework for robust filtering under relative entropy constraints, extending static estimation results to time-varying scenarios.

Findings

The proposed risk-sensitive filter outperforms the standard Kalman filter on least-favorable models.

The filter maintains near-nominal performance with only slight degradation.

Simulation results demonstrate significant robustness improvements.

Abstract

This paper considers robust filtering for a nominal Gaussian state-space model, when a relative entropy tolerance is applied to each time increment of a dynamical model. The problem is formulated as a dynamic minimax game where the maximizer adopts a myopic strategy. This game is shown to admit a saddle point whose structure is characterized by applying and extending results presented earlier in [1] for static least-squares estimation. The resulting minimax filter takes the form of a risk-sensitive filter with a time varying risk sensitivity parameter, which depends on the tolerance bound applied to the model dynamics and observations at the corresponding time index. The least-favorable model is constructed and used to evaluate the performance of alternative filters. Simulations comparing the proposed risk-sensitive filter to a standard Kalman filter show a significant performance advantage when applied to the least-favorable model, and only a small performance loss for the nominal model.