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

This paper 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.