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

  • Author(s): Levy, Bernard C.
  • Nikoukhah, Ramine
  • et al.

Published Web Location

https://arxiv.org/pdf/1004.2519.pdf
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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.

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