  We consider a robust filtering problem where the nominal state space model is
not reachable and different from the actual one. We propose a robust Kalman
filter which solves a dynamic game: one player selects the least-favorable
model in a given ambiguity set, while the other player designs the optimum
filter for the least-favorable model. It turns out that the robust filter is
governed by a low-rank risk sensitive-like Riccati equation. Finally,
simulation results show the effectiveness of the proposed filter.
