A method for identification of discrete parametric models with unknown orders and delays

A novel method is presented to identify a discrete parametric model of a noisy system under open-loop or closed-loop operation. The order and time delay of the dynamic model are assumed to be unknown a priori. A time-weighted digital filter is employed to convert the sampled data of input-output measurements over different sets of time horizons to a group of linear algebraic equations. The moving horizon least-squares algorithm is then developed to estimate the model parameters in a recursive fashion. A very effective technique is also proposed to infer the model order and time delay from the observed data. In contrast with the conventional least-squares approach, the proposed method is able to yield unbiased parameter estimates despite the nature of noise. Furthermore, it is robust with respect to model structure mismatch and the selection of sampling period.