Non-Asymptotic Confidence Regions for Errors-In-Variables Systems

Abstract

This paper deals with constructing non-asymptotic confidence regions for Errors-In-Variables (EIV) systems when there is noise on both the input and the output signal. The Leave-out Sign-dominant Correlation Regions (LSCR) approach originally devised for systems with no noise on the input is extended to EIV systems. The correlation functions used in LSCR for EIV systems are computed using elements of an innovation vector which is obtained from a state space model of the system where also the input is regarded as an output. As with standard LSCR, the confidence regions are guaranteed to contain the true parameter with a user chosen probability for any finite number of data points. Moreover, the confidence region shrinks around the true parameter when the number of data points increases. The method and its properties are illustrated in a simulation example.