PARAMETER IDENTIFICATION USING THE NELDER-MEAD SIMPLEX ALGORITHM FOR LOW SIGNAL-TO-NOISE RATIO SYSTEMS IN A FREQUENCY DOMAIN

Abstract

Parameter identification algorithms are very fundamental techniques in system engineering practices. For example, estimating the parameters of the AutoRegresive model with an eXternal input or AutoRegresive Moving-Average model with an eXternal input by using the least squares (LS) method has become a standard approach. However, the estimated parameters may generate extremely erroneous results when the signal is disturbed by large noise, which cannot be effectively filtered. If a frequency response method that scatters the power of a broadband noise over different frequencies is adopted, the effect of noise on the estimated parameters would be relatively reduced. Moreover, estimating whether the plant is a high-order system or is perturbed by a large noise is difficult. The estimated accuracy decreases even after applying the generalized LS method or other modified approaches. To overcome this problem, this study proposed a new technique combining a simplex algorithm and frequency response method for improving the accuracy of the parameter estimation of a dynamic system with a large noise (i.e., an extremely low signal-to-noise ratio) of the system. The algorithm is simple and easy to implement. Moreover, the precision of parameter identification can be increased even when estimated systems suffer from large measurement noises.