Robust State Space Filtering with an Incremental Relative Entropy Tolerance

This paper considers robust filtering for a nominal Gaussian state-space model, when an incremental relative entropy tolerance is applied to each dynamical model component. The problem is formulated as a dynamic minimax game which is shown to admit a saddle point. The structure of the saddle point 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 matching model component. 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. Index Terms commitment, dynamic minimax game, least-favorable model, relative entropy, risk-sensitive filtering, robust filtering.