Journal of Applied Mathematics
Volume 2012 (2012), Article ID 324296, 16 pages
Research Article

Measurement Feedback Self-Tuning Weighted Measurement Fusion Kalman Filter for Systems with Correlated Noises

Department of Automation, Heilongjiang University, Harbin 150080, China

Received 26 February 2012; Accepted 19 March 2012

Academic Editor: Baocang Ding

Copyright © 2012 Xin Wang and Shu-Li Sun. 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.


For the linear discrete stochastic systems with multiple sensors and unknown noise statistics, an online estimators of the noise variances and cross-covariances are designed by using measurement feedback, full-rank decomposition, and weighted least squares theory. Further, a self-tuning weighted measurement fusion Kalman filter is presented. The Fadeeva formula is used to establish ARMA innovation model with unknown noise statistics. The sampling correlated function of the stationary and reversible ARMA innovation model is used to identify the noise statistics. It is proved that the presented self-tuning weighted measurement fusion Kalman filter converges to the optimal weighted measurement fusion Kalman filter, which means its asymptotic global optimality. The simulation result of radar-tracking system shows the effectiveness of the presented algorithm.