UNBIASED WIENER FILTERING - NONSTATIONARY PROCESSES

This paper gives an analytic solution to the unbiased filtering problem of the system X(t) = S(t) + N(t), where {S(t)} has known second-order properties, {N(t)} is an ARMA process with time-dependent coefficients, and {X(t)} is observed for T = 0, 1,..., T, T finite. The approach is based on solving a Wiener-Hopf type equation using properties of one-sided Green's matrices of a corresponding system. The paper also gives a method for extending the covariance matrix of S(t) when this is known only up to time lag T. The covariance extension will have a maximum entropy property.