System Identification of Feedback and "Causality" Structure Using Canonical Variate Analysis

Abstract

This paper addresses the problem of identification of components of a system that may involve unknown feedback around such a component as well as the presence of unmeasured disturbances. Further, the problem of comparing various hypotheses concerning the feedback structure among various components of an unknown system is discussed. The basic tool developed is an expression for the joint likelihood function of a process in terms of individual components of a system where measurements of the inputs and outputs of each component are available. It is show that maximum likelihood estimation of the whole structure decomposes into the separate maximum likelihood estimation of each component. This provides the basis for likelihood ratio tests of hypotheses for different feedback structures of the system. Canonical variate analysis provides a computationally stable procedure for the identification of state space models of the various component systems. These can then be combined to find the best system structure describing feedback and Granger causality.