Noncausal minimax linear state estimation for systems with uncertain second-order statistics

This note considers the problem of minimax state estimation of the states of a linear time-invariant system which is driven by and observed in the presence of noise processes with uncertain second-order statistics. When the process noise and observations are scalars, the problem is shown to be equivalent to a scalar minimax estimation problem. The existence of a minimax solution is thereby established, and the minimax filter is shown to be a linear transformation of the minimax filter for the scalar problem.