Parameter identification of distributed parameter systems in the presence of measurement noise

Abstract

A new approach to recursive parameter identification of second-order distributed parameter systems in the presence of measurement noise under unknown initial and boundary conditions is proposed. A two-dimensional low-pass filter is introduced to pre-filter the observed data corrupted by measurement noise. The low-pass filter is designed in the continuous time-space domain and discretized by bilinear transformation. Thus a discrete estimation model of the system under study is easily constructed with filtered input-output data for recursive identification algorithms. The recursive least squares method is still efficient in the presence of low measurement noise if the filter parameters are designed so that the noise effects are reduced sufficiently. Using filtered input data as instrumental variables, a recursive instrumental variable method is also presented to obtain consistent estimates when the digital low-pass filters are not designed successfully or when the output data is corrupted by high measurement noise. Illustrative examples are given to demonstrate the applicability of the proposed methods.