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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 4860785, 7 pages
Research Article

System Model Bias Processing Approach for Regional Coordinated States Information Involved Filtering

1School of Aeronautics & Astronautics, University of Electronic Science and Technology of China, Chengdu 611731, China
2Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China
3Key Laboratory of Earthquake Geodesy, Institute of Seismology, China Earthquake Administration, Wuhan 430071, China

Received 14 December 2015; Revised 8 January 2016; Accepted 23 February 2016

Academic Editor: Ben T. Nohara

Copyright © 2016 Zebo Zhou and Yunlong Wu. 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.


In the Kalman filtering applications, the conventional dynamic model which connects the states information of two consecutive epochs by state transition matrix is usually predefined and assumed to be invariant. Aiming to improve the adaptability and accuracy of dynamic model, we propose multiple historical states involved filtering algorithm. An autoregressive model is used as the dynamic model which is subsequently combined with observation model for deriving the optimal window-recursive filter formulae in the sense of minimum mean square error principle. The corresponding test statistics characteristics of system residuals are discussed in details. The test statistics of regional predicted residuals are then constructed in a time-window for model bias testing with two hypotheses, that is, the null and alternative hypotheses. Based on the innovations test statistics, we develop a model bias processing procedure including bias detection, location identification, and state correction. Finally, the minimum detectable bias and bias-to-noise ratio are both computed for evaluating the internal and external reliability of overall system, respectively.