Design and properties of a modified linear filter of lower order (Q1061711)

The properties are considered of a modified linear filter of lower order that has been proposed by the author [Avtom. Telemekh. 1981, No.11, 66-73 (1981; Zbl 0492.93061)] for estimating the states and a linear transformation of the state vector of a discrete linear system. The error of modified estimation is proved to be orthogonal to the estimate and the observation. Thus it is possible to obtain much simpler equations for the design of a modified filter, and also a new notation for the filtering equation. An optimization procedure is suggested for the matrix of linear transformation of the state vector.