Parameters and System Order Estimation Using Differential Filters and Resultant

This paper deals with a method of estimating the parameters and the order of a linear system using differential digital filters and the resultant. From the observed signals of the input and output of an objective system, we extract the differential signals from the zero order to an appropriate high order with the same phase characteristics, using several digital filters. On the assumption that the system order is known, we estimate the parameters of the transfer function and evaluate the estimation error bounds. We propose a criterion function generated by the product of the highest order coefficients and the resultant of the numerator and denominator of the estimated transfer function. Applying this criterion function, we can estimate the order of the objective system. The threshold corresponding to this criterion function is evaluated from the deviation in the frequency characteristics of the used differential filters and the error bound of the estimated parameters. In order to demonstrate the propriety of the proposed method, some numerical simulations are presented. key words: digital filter, differential filter, identification, parameter estimation, resultant, system order estimation