A Method for Error Quantification in the FIR Model
Tetsuo TEZUKA, Hiroyasu SHIGEMORI, Yoshikazu NISHIKAWA
The paper presents a method for quantifying modelling error of an FIR model whose parameters are estimated by using the least squares method. This method is also applicable to a model whose transfer function is expressed by a linear polynomial of the parameters.
First, we introduce the method proposed by G.C. Goodwin et al. The method assumes that the unmodelled dynamics of the system is expressed by realizations of random variables which have independent distributions with exponentially decaying variance. But the formulation of the modelling error is modified in this paper as Goodwin's formulation is rather difficult to understand.
Second, we point out that Goodwin's approximation is of a rough and unpractical nature, and also that the modelling error obtained by the method is not frequency-dependent. Hence, we propose a revised method where an assumption in Goodwin's method is modified to a more reasonable one. We also propose a parameter estimation algorithm which needs much less computation time with little loss of accuracy of estimation.
Finally, we show, through several numerical simulations, that the mean-squared error estimated by the revised method is much closer to the real modelling error than that obtained by Goodwin's method.