A simple solution to the singular linear minimum-variance estimation problem

A simple expression is obtained for the transfer function matrix of the minimum-variance estimator for the states of a linear stationary continuous-time right invertible system whose output is measured perfectly. Using the -domain approach, it is shown that the optimal estimator first finds the driving noise input that achieves, when applied on the minimum-phase image model of the system, an output spectrum which is identical to the measurement spectrum. This input is then applied on a state-space representation of the minimum-phase image to produce the optimal estimate.