Comprehensive Errors-invariables-based Model Identification (Part 1)

Learning or developing dynamic models from experimental data is crucial in monitoring and control of processes. In general, measurements of both inputs and outputs of a processare subject to noise. Model development from such data is treated under the broad banner of errors-invariables (EIV) identification. In the preceding two years, we have developed a dynamic iterative principal components (DIPCA)-based approach to identify linear dynamic models for the EIV case, which has the ability to estimate the delay, order, error variances and model parameters based on a rigorous theoretical formulation and without requiring any prior knowledge. We have successfully demonstrated the use of our proposed approach to develop models for single-input single-output systems, for a variety of model structures (auto-regressive exogenous, output-error, Box-Jenkins, etc.). This project aims to extend the above approach for developing models for multi-input single output (MISO) systems and further to multi-input multi-output (MIMO) systems. We also propose to derive the theoretical properties of the estimates, in particular the consistency of the estimates, to provide a strong theoretical basis. Our ultimate goal is to develop a comprehensive EIV-based model identification approach that is envisaged to become a standard technique and be a part of MATLAB’s System Identification Toolbox.