Closed-Loop System Identification with Modifications of the Instrumental Variable Method

Article type: Research Article

Authors: Atanasov, Nasko | Ichtev, Alexander

Affiliations: Technical University of Varna, Studentska 1, 9010 Varna, Bulgaria, e-mail: nratanasov@yahoo.com | Technical University of Sofia, Kliment Ohridski 8, 1000 Sofia, Bulgaria, e-mail: ichtev@tu-sofia.bg

Abstract: Least-squares method is the most popular method for parameter estimation. It is easy applicable, but it has considerable drawback. Under well-known conditions in the presence of noise, the LS method produces asymptotically biased and inconsistent estimates. One way to overcome this drawback is the implementation of the instrumental variable method. In this paper several modifications of this method for closed-loop system identification are considered and investigated. The covariance matrix of the instrumental variable estimates is discussed. A simulation is carried out in order to illustrate the obtained results.

Keywords: closed-loop system identification, prediction error, instrumental variable method, parameter estimation, observations

Journal: Informatica, vol. 21, no. 2, pp. 159-174, 2010