Research Article Multiple Adaptive Fading Schmidt-Kalman Filter for Unknown Bias Tai-Shan Lou, Zhi-Hua Wang, Meng-Li Xiao, and Hui-Min Fu School of Aeronautical Science and Engineering, BeiHang University, Beijing 100191, China Correspondence should be addressed to Zhi-Hua Wang; wangzhihua@buaa.edu.cn Received 24 September 2014; Accepted 12 November 2014; Published 24 November 2014 Academic Editor: Zheng-Guang Wu Copyright © 2014 Tai-Shan Lou et al. his 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 efects to the state estimates when using a conventional Kalman ilter 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 ilter “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 ilter (MAFSKF) is designed by using the proposed multiple adaptive fading Kalman ilter to mitigate the negative efects of the unknown biases in dynamic or measurement model. he performance of the MAFSKF algorithm is veriied by simulation. 1. Introduction An underlying assumption of the Kalman ilter is that the dynamic and measurement equations can be accurately mod- eled without any colored noise or unknown biases. However, in practice, these dynamic and measurement models include some additional biases, which always bring greatly negative efects to the state estimate. here are many methodologies to deal with these unknown biases. Ignoring them and augmenting them to estimate are two common approaches. Based on the sen- sitivity to the unknown bias, some techniques have been proposed, such as Η ∞ iltering [1, 2], set-valued estimation [3], and Schmidt-Kalman ilter (SKF) [4]. Schmidt proposed a “consider” analysis, which is the cornerstone of the SKF, to account for errors in both the dynamic and measurement models due to the unknown biases when the biases are considered as constants and remain unchanged [4]. Based on a minimum variance approach, the key idea of the SKF is the “consider” analysis that the preestimated bias covariance is formulated to update the state and covariance estimates, but these biases themselves are not estimated directly. he “consider” approach is especially useful when the unknown biases are low observable or when the extra computational power to estimate them is not worth [5]. Ater Schmidt, the “consider” approach for parameters has received much attention in recent years. he SKF is also called the consider Kalman ilter (CKF) ater its developer. Jazwinski provides the detailed derivation of the CKF in his book [6]. Subsequently, Tapley et al. amply descript the CKF and derivate a diferent formulation [7]. Zanetti and Souza introduce the UDU formulation into the SKF and provide a numerically stability, recursive implementation of the UDU SKF [8]. Bierman analyzes the efects on iltering accuracy of the unestimated biases and incorrect a priori covariance statistics and proposes a sensitivity matrix to evaluate them [9]. Woodbury et al. give novelty insight into considering biases in the measurement model and verify the negative efect of the errors in the initial parameter and covariance estimates [5, 10]. Chee and Forbes propose a norm-constrained consider Kalman iltering by taking into account the constraint on the state estimate and apply it to a nonlinear attitude estimation problem [11]. However, how to mitigate these negative efects from the initial state and covariance values of the unknown biases in the SKF has not attracted much attention. In fact, when Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2014, Article ID 623930, 8 pages http://dx.doi.org/10.1155/2014/623930