Identification of EIV models with coloured input–output noise: combining PEM and covariance matching method

Abstract

In this paper, a novel identification method for discrete-time linear systems when input–output observations are contaminated by coloured noise (errors-in-variables models) is proposed. To develop the new approach, modified prediction error and covariance matching methods are utilised. It is proved that the proposed approach leads to a consistent estimation. System identification through the proposed approach entails the existence of a flat frequency interval in power spectra of input and ratio of noise-free input to input signals which is a somewhat mild assumption. Two Monte Carlo simulations are provided to explain the efficiency, numerical complexity and the application of the proposed method.