Filtering of Gaussian Systems

Abstract

The filter problem is to derive an expression for the conditional distribution of the state of a stochastic system conditioned on the past outputs of the considered system and a recursion of the parameters of that conditional distribution. In this chapter the filter problem for a Gaussian stochastic system is solved. The Kalman filter is derived, including the time-varying, the time-invariant Kalman filter, and the conditional Kalman filter. The relation of the Kalman filter with stochastic realization is discussed. The Kalman filter is used in a very large number of research areas including signal processing, information theory, communication theory, weather prediction, hydrology, etc.