Parameter identification of linear time-invariant systems with large measurement noises

Abstract

The parameter identification theories and algorithms have been developed well. For example, using the least squares and time-domain data to estimate the parameters of ARX (AutoRegresive model with eXternal input) or ARMAX (AutoRegresive Moving-Average model with eXternal input) models have become standard methods for estimating the parameters of linear time-invariant (LTI) systems. However, if we use the time-domain method to identify the parameters of a LTI system which input/output signals are disturbed by large noises, the results may cause serious error, even the estimated parameters become useless. In term of designing controllers, the engineers can choose or design more appropriate controllers, if they can know clearer or more accurate characteristics of the plants in advance. In this paper, we apply the Nelder-Mead simplex method to estimate the parameters of systems with large measurement noises based on frequency-domain. The simulation results show that using the simplex method based on frequency-domain, we can obtain more accurate models even the estimated systems including large measurement noises.