The optimal refined instrumental variable (RIV) 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.
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