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Journal of Applied Mathematics
Volume 2012, Article ID 717504, 19 pages
Research Article

On Kalman Smoothing for Wireless Sensor Networks Systems with Multiplicative Noises

1Key Laboratory for Robot & Intelligent Technology of Shandong Province, Shandong University of Science and Technology, Qingdao 266510, China
2School of Control Science and Engineering, Shandong University, Jinan 250100, China

Received 12 March 2012; Revised 21 May 2012; Accepted 21 May 2012

Academic Editor: Baocang Ding

Copyright © 2012 Xiao Lu 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.


The paper deals with Kalman (or 𝐻2) smoothing problem for wireless sensor networks (WSNs) with multiplicative noises. Packet loss occurs in the observation equations, and multiplicative noises occur both in the system state equation and the observation equations. The Kalman smoothers which include Kalman fixed-interval smoother, Kalman fixedlag smoother, and Kalman fixed-point smoother are given by solving Riccati equations and Lyapunov equations based on the projection theorem and innovation analysis. An example is also presented to ensure the efficiency of the approach. Furthermore, the proposed three Kalman smoothers are compared.