Journal of Applied Mathematics
Volume 2013 (2013), Article ID 318786, 8 pages
Research Article

Recursive Identification for Dynamic Linear Systems from Noisy Input-Output Measurements

School of Software, Tsinghua University, Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, China

Received 7 March 2013; Accepted 13 April 2013

Academic Editor: Xiaojing Yang

Copyright © 2013 Dan Fan and Kueiming Lo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Errors-in-variables (EIV) model is a kind of model with not only noisy output but also noisy input measurements, which can be used for system modeling in many engineering applications. However, the identification for EIV model is much complicated due to the input noises. This paper focuses on the adaptive identification problem of real-time EIV models. Some derivation errors in an accuracy research of the popular Frisch scheme used for EIV identification have been pointed out in a recent study. To solve the same modeling problem, a new algorithm is proposed in this paper. A Moving Average (MA) process is used as a substitute for the joint impact of the mutually independent input and output noises, and then system parameters and the noise properties are estimated in the view of the time domain and frequency domain separately. A recursive form of the first step calculation is constructed to improve the calculation efficiency and online computation ability. Another advantage of the proposed algorithm is its applicableness to different input processes situations. Numerical simulations are given to demonstrate the efficiency and robustness of the new algorithm.