A finite-time linear filter for discrete-time systems in singular case

Abstract

A finite-time linear time-invariant filter for discrete-time stationary systems in singular mode is presented in which the non-singular and coloured measurement noise solutions occur as special oases. The filter provides an optimal state estimate at the end of a specified time interval, identical to that of the reduced-order time-varying Brammer filter. It is characterized by a transfer-function matrix and is almost as easy to implement, as the infinite-time Brammer filter.