A unified approach to multivariable discrete-time filtering based on the Wiener-theory

Abstract

Several theories of discrete-time optimal filtering are in current use but the relationships between these theories is not always appreciated. By using a slightly modified form of the Wiener theory, a unification of the various methods is obtainable. In the present paper this approach is used to discuss in the multivariable case, instantaneous filtering, one-step delayed filtering, fixed-lag filtering, and prediction. It is shown that the one-step delay filter has a natural feedback structure related to the Kalman filter. The relation of the theory with the Hagander -Wittenma rk filter is also discussed.