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Mathematical Problems in Engineering
Volume 2009, Article ID 507370, 23 pages
Research Article

Highly Efficient Sigma Point Filter for Spacecraft Attitude and Rate Estimation

1Department of Precision Instruments and Mechanology, Tsinghua University, Beijing 100084, China
2State Key Laboratory of Precision Measurement Technology and Instruments, Tsinghua University, Beijing 100084, China

Received 9 July 2009; Accepted 30 September 2009

Academic Editor: Tadashi Yokoyama

Copyright © 2009 Chunshi Fan and Zheng You. 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.


Nonlinearities in spacecraft attitude determination problem has been studied intensively during the past decades. Traditionally, multiplicative extended Kalman filter_MEKF_algorithm has been a good solution for most nominal space missions. But in recent years, advances in space missions deserve a revisit of the issue. Though there exist a variety of advanced nonlinear filtering algorithms, most of them are prohibited for actual onboard implementation because of their overload computational complexity. In this paper, we address this difficulty by developing a new algorithm framework based on the marginal filtering principle, which requires only 4 sigma points to give a complete 6-state attitude and angular rate estimation. Moreover, a new strategy for sigma point construction is also developed to further increase the efficiency and numerical accuracy. Incorporating the presented framework and novel sigma points, we proposed a new, nonlinear attitude and rate estimator, namely, the Marginal Geometric Sigma Point Filter. The new algorithm is of the same precision as traditional unscented Kalman filters, while keeping a significantly lower computational complexity, even when compared to the reduced sigma point algorithms. In fact, it has truly rivaled the efficiency of MEKF, even when simple closed-form solutions are involved in the latter.