Minimax Performance Limits for Multiple-Model Estimation

This article concerns the performance limits of strictly causal state estimation for linear systems with fixed, but uncertain, parameters belonging to a finite set. In particular, we provide upper and lower bounds on the smallest achievable gain from disturbances to the point-wise estimation error. The bounds rely on forward and backward Riccati recursions -- one forward recursion for each feasible model and one backward recursion for each pair of feasible models. We give simple examples where the lower and upper bounds are tight.