Alternative Model Structure with Simplistic Noise Modelling for Linear Processes Subjected to Non-Stationary Distrubances

A simple system identification technique to identify the linear processes affected by non-stationary disturbances is proposed. This uses a time varying bias term, a representative of the additive non-stationary external disturbance entering the process, in addition to the output predictions in an ARMAX or OE model framework. Decoupled loss function and covariance update with different forgetting factors for linear time invariant input-output dynamics part and time varying part (bias term) of the model ensured the unbiased estimation of true process dynamics along with disturbance dynamics.

Practical issues such as time delay estimation, model order selection are discussed. Extensions for time varying processes and MIMO processes are also proposed. Efficacy of the proposed identification technique in both open loop and closed loop cases against OE, ARMAX and BJ identification techniques is performed using various simulation studies.