  We consider a robust state space filtering problem in the case that the
transition probability density is unknown and possibly degenerate. The
resulting robust filter has a Kalman-like structure and solves a minimax game:
the nature selects the least favorable model in a prescribed ambiguity set
which also contains non-Gaussian probability densities, while the other player
designs the optimum filter for the least favorable model. It turns out that the
resulting robust filter is characterized by a Riccati-like iteration evolving
on the cone of the positive semidefinite matrices. Moreover, we study the
convergence of such iteration in the case that the nominal model is with
constant parameters on the basis of the contraction analysis in the same spirit
of Bougerol. Finally, some numerical examples show that the proposed filter
outperforms the standard Kalman filter.
