Output Error Identification in the Presence of Structural Disturbances

In empirical system identification, models that are identified using output-error method are better suited for long-term predictions. The non-stationary structural disturbances, such as trends and outliers in data can have adverse affects on the estimation of the system parameters. We propose a method that performs the estimation of model parameters and structural disturbances simultaneously. The output-error model is constructed by an orthonormal basis functions (OBF) such as Laguerre or Kautz filters. The identification problem is formulated as a least-squares problem with a sparsity constraint, which is approximately solved using $\ell_{1}$-regularization with iterative reweighting. The Hankel reduction method is used for model order determination and reduction. The presented method is tested on simulated linear examples. The effects of cases in which different initial chosen poles and different order of OBF expansions are evaluated. The suggested method shows better performance compared to the standard least squares method regarding poles and mean square error of the identified model.