Non-asymptotic Confidence Regions for Errors-In-Variables Systems in an Extended Noise Environment

Abstract

In this paper we consider the problem of constructing non-asymptotic confidence regions for the parameters of Errors-In-Variables systems where both inputs and outputs are contaminated by noise terms. The proposed method is based upon extending the Sign-Perturbed Sums (SPS) method for EIV systems in (Moravej Khorasani and Weyer (2020a)) to the case where the noise terms and input are modeled as ARMA systems driven by i.i.d. Gaussian processes. It is shown that the constructed confidence region include the true parameter with a user chosen probability for any finite number of data points. The method is illustrated in a simulation example.