A Data-Based Augmented Model Identification Method for Linear Errors-in-Variables Systems Based on EM Algorithm

With a large amount of industrial data available, it is of considerable interest to develop data-based models. The challenge lies in the significant noises that appear in all data collected from industry. The errors-invariables (EIV) model is a model that accounts for measurement noises in all observations (both input and output). In most of the traditional EIV identification methods, the input generation dynamics is not considered. In this paper, a dynamic model is applied to describe the input generation process, and then, the Kalman smoother is used to estimate its state using all available measurements. In order to utilize all of the observed variables in the EIV process, an augmented EIV model is derived to describe both input generation process and the EIV process dynamics itself. The parameters in the EIV model are then estimated by applying an expectation maximization algorithm. Simulated numerical example and an experiment performed on a hybrid tank system are used to demonstrate the improved identification performance of the proposed method.