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Unbiased parameter estimation of linear systems in the presence of input and output noise
Author(s) -
And WeiXing Zheng,
Feng ChunBo
Publication year - 1989
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.4480030303
Subject(s) - estimator , noise (video) , a priori and a posteriori , white noise , variance (accounting) , least squares function approximation , ordinary least squares , mathematics , noise measurement , algorithm , estimation theory , minimum variance unbiased estimator , statistics , control theory (sociology) , computer science , noise reduction , artificial intelligence , philosophy , accounting , control (management) , epistemology , business , image (mathematics)
Abstract It is well known that in practical situations the observed input‐output data of an identified plant are usually corrupted by measurement noise. In this case the ordinary least‐squares estimator of the system parameters is biased. In order to obtain a consistent estimator, a new type of modified least‐squares estimation method, which is called the bias‐eliminated least‐squares (BELS) method, is presented in this paper. It is shown that the estimation bias can be determined if the variance of the white measurement noise can be obtained accurately. A designed first‐order prefilter is connected in parallel to the input of the identified system. Based on asymptotic analysis, the noise variance can be estimated correctly by using the processed sampled data. Both a batch algorithm and a recursive algorithm are presented. It is shown that the presented BELS method gives a consistent estimate without a priori knowledge of the variance of the white input and output noise. Simulation results are presented to support the theoretical discussions.