Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 342705, 15 pages
http://dx.doi.org/10.1155/2012/342705
Research Article

Asymptotic Parameter Estimation for a Class of Linear Stochastic Systems Using Kalman-Bucy Filtering

Xiu Kan,1 Huisheng Shu,2 and Yan Che1

1School of Information Science and Technology, Donghua University, Shanghai 200051, China
2School of Science, Donghua University, Shanghai 200051, China

Received 21 June 2012; Accepted 21 July 2012

Academic Editor: Jun Hu

Copyright © 2012 Xiu Kan et al. 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.

Abstract

The asymptotic parameter estimation is investigated for a class of linear stochastic systems with unknown parameter θ:dXt=(θα(t)+β(t)Xt)dt+σ(t)dWt. Continuous-time Kalman-Bucy linear filtering theory is first used to estimate the unknown parameter θ based on Bayesian analysis. Then, some sufficient conditions on coefficients are given to analyze the asymptotic convergence of the estimator. Finally, the strong consistent property of the estimator is discussed by comparison theorem.