Identification of the errors-in-variables setting with the behavioral approach

Well-posedness plays an important role in system identification. The behavioral approach provides a strong framework for representing a linear time-invariant dynamic system, for the reason that the assumptions of input/output partition and controllability are not required, and meanwhile the data-driven model with nonparametric formulation can be obtained. Low-rank approximation performs well on data with noises and model uncertainty. For better handling the errors-in-variables setting, a new low-rank approximation method is proposed and the optimization problem is solved. The new low-rank approximation method takes account of both the row space and the column space structure information. ADMM-based algorithm is used to solve the resulting optimization problem. Experimental results show that the parameter estimates are more accurate than that of two mostly used approximation methods.