Non-minimal state-space polynomial form of the Kalman filter for a general noise model

Abstract

The optimal refined instrumental variable method for the estimation of the Box–Jenkins (BJ) model is modified so that it functions as an optimal filter and state-estimation algorithm. In contrast to the previously developed minimal and non-minimal state-space (NMSS) forms for an Auto-Regressive Moving Average with eXogenous variables (ARMAX) model, the new algorithm requires the introduction of a novel extended NMSS form. This facilitates representation of the more general noise component of the BJ model. The approach can be used for adaptive filtering and state variable feedback control. Show more