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We consider a robust state space filtering problem in the case that thetransition probability density is unknown and possibly degenerate. Theresulting robust filter has a Kalman-like structure and solves a minimax game:the nature selects the least favorable model in a prescribed ambiguity setwhich also contains non-Gaussian probability densities, while the other playerdesigns the optimum filter for the least favorable model. It turns out that theresulting robust filter is characterized by a Riccati-like iteration evolvingon the cone of the positive semidefinite matrices. Moreover, we study theconvergence of such iteration in the case that the nominal model is withconstant parameters on the basis of the contraction analysis in the same spiritof Bougerol. Finally, some numerical examples show that the proposed filteroutperforms the standard Kalman filter.

Robust Kalman Filtering Under Model Uncertainty: the Case of Degenerate Densities