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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 369252, 11 pages
Research Article

Weighted Fusion Robust Steady-State Kalman Filters for Multisensor System with Uncertain Noise Variances

Department of Automation, Heilongjiang University, Harbin 150080, China

Received 18 November 2013; Accepted 7 March 2014; Published 30 April 2014

Academic Editor: Jong Hae Kim

Copyright © 2014 Wen-Juan Qi 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.


A direct approach of designing weighted fusion robust steady-state Kalman filters with uncertain noise variances is presented. Based on the steady-state Kalman filtering theory, using the minimax robust estimation principle and the unbiased linear minimum variance (ULMV) optimal estimation rule, the six robust weighted fusion steady-state Kalman filters are designed based on the worst-case conservative system with the conservative upper bounds of noise variances. The actual filtering error variances of each fuser are guaranteed to have a minimal upper bound for all admissible uncertainties of noise variances. A Lyapunov equation method for robustness analysis is proposed. Their robust accuracy relations are proved. A simulation example verifies their robustness and accuracy relations.