Slide Window Bounded-Error Time-Varying Systems Identification

This technical note presents a new identification method for discrete linear systems with time-varying parameters based on bounded-error approach. It is assumed a bounded additive error on measurements and a bound on parameter variation. Each time instant, the identification method uses a slide window along historical data and an explicit expression to provide an outer bound of the set of model parameters that is consistent with measurements, model structure and bounds on error and variations considered. Furthermore, the center estimation of the obtained outer solution set is a suitable nominal estimation of the parameters. This center is the optimal solution of a least squares problem that penalizes the prediction error of the model and the parameter variations. The explicit expression that provides the outer bound of the parameters and the optimal property of the center estimation are the main contributions of the technical note. In order to clarify the proposed method, an application example and a comparison with a previous recursive bounded-error method are included.