Decoupling of Filtering Equations

Abstract

The limiting (or steady-state) Kalman filter provides a very effi­cient method for estimating the state vector in a time-invariant linear system in real-time. However, if the state vector is of very high dimension n, and only a few components are of interest, this filter gives an abundance of useless information, an elimination of which should improve the efficiency of the filtering process. A decoupling method is introduced in this chapter for this purpose. It allows us to decompose an n-dimensional limiting Kalman filtering equation into n independent one-dimensional recursive for mulas so that we may drop the ones that are of little interest.