Synthesis and properties of a modified linear reduced-order filter

The properties are discussed of a modified linear lower-order filter of Ref. [1] for evaluation of the states and linear transformation of the state vector of a simpled-data linear system. The error of modified evaluation is proved to be orthogonal to the estimate and observation. This finding leads to essentially simpler equations for design of a modified filter and to a new notation of the filtering equation. A way to optimize the matrix of linear transformation of the state vector is proposed.