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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 623930, 8 pages
Research Article

Multiple Adaptive Fading Schmidt-Kalman Filter for Unknown Bias

School of Aeronautical Science and Engineering, BeiHang University, Beijing 100191, China

Received 24 September 2014; Accepted 12 November 2014; Published 24 November 2014

Academic Editor: Zheng-Guang Wu

Copyright © 2014 Tai-Shan Lou 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.


Unknown biases in dynamic and measurement models of the dynamic systems can bring greatly negative effects to the state estimates when using a conventional Kalman filter algorithm. Schmidt introduces the “consider” analysis to account for errors in both the dynamic and measurement models due to the unknown biases. Although the Schmidt-Kalman filter “considers” the biases, the uncertain initial values and incorrect covariance matrices of the unknown biases still are not considered. To solve this problem, a multiple adaptive fading Schmidt-Kalman filter (MAFSKF) is designed by using the proposed multiple adaptive fading Kalman filter to mitigate the negative effects of the unknown biases in dynamic or measurement model. The performance of the MAFSKF algorithm is verified by simulation.