On-line Modified Least-squares Parameter Estimation of Linear Systems with Input-output Data Polluted by Measurement Noises

Abstract

It is well known that in practical situations observed inputoutput data of an identified plant are usually polluted by measurement noises. In this case the ordinary least-squares estimates of the system parameters are biased. In order to obtain consistent estimates a new type of modified least-squares (MLS) estimation method is presented in this paper. It is shown that the estimation biases can be determined if the variances of the measurement noises can be obtained accurately. A designed first-order prefilter is connected parallelly to the input of the identified system. On the basis of asymptotic analysis, the noise variances can be estimated correctly by using the processed sampled data. Both batch algorithm and recursive algorithm are presented. It is shown that the presented MLS method gives consistent estimates without a priori knowledge of the input and output noises. The Monte-Carlo stochastic simulation results are presented to support the theoretical discussions.