An Augmented Model Approach for Identification of Nonlinear Errors-in-Variables Systems Using the EM Algorithm

This paper proposes an augmented model approach for identification of nonlinear errors-in-variables (EIVs) systems. An EIV model accounts for uncertainties in the observations of both inputs and outputs. As the direct identification of nonlinear functions is difficult, we propose to approximate the nonlinear EIV model using multiple ARX models. To estimate the noise-free input signal, we use a collection of particle filters which run in parallel corresponding to each of the multiple ARX models. The parameters of local models are estimated by applying expectation maximization algorithm, under a maximum likelihood framework, using the input-output data of the nonlinear EIV system. Simulated numerical examples and an experiment study on a multitank system are used to illustrate the efficacy of the proposed approach.