Robust State Space Filtering under Incremental Model Perturbations Subject to a Relative Entropy Tolerance
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.
Cite
@article{arxiv.1004.2519,
title = {Robust State Space Filtering under Incremental Model Perturbations Subject to a Relative Entropy Tolerance},
author = {Bernard C. Levy and Ramine Nikoukhah},
journal= {arXiv preprint arXiv:1004.2519},
year = {2011}
}