Identification of errors in variables linear state space models using iterative principal component analysis

Development of dynamic process models from input-output data, also known as system identification, is a well-studied problem. The classical approach to system identification assumes that the input variables are measured without error. However, in practice all data collected from evolving processes (inputs and outputs) will contain errors. System identification using noisy inputs and outputs is known as Errors-in-Variables (EIV) identification. Existing methods for EIV model identification assume that the error variances are known and/or assume the system order to be known. We propose a novel approach combining subspace-based identification and a dynamic iterative principal components approach for identifying EIV MIMO models. The proposed method simultaneously estimates process order, delay, model coefficients, and error variances using a rigorous theoretical basis. A benchmark simulation example from literature is used to exhibit the effectiveness of the proposed approach.