Fast Linear Quaternion Attitude Estimator Using Vector Observations

International audienceAs a key problem for multi-sensor attitudedetermination, Wahba’s problem has been studied for almost50 years. Different from existing methods, this paper presentsa novel linear approach to solving this problem. We name theproposed method the Fast Linear Attitude Estimator (FLAE)because it is faster than known representative algorithms. Theoriginal Wahba’s problem is extracted to several 1-dimensionalequations based on quaternions. They are then investigatedwith pseudo-inverse matrices establishing a linear solution to ndimensional equations, which are equivalent to the conventionalWahba’s problem. To obtain the attitude quaternion in a robustmanner, an eigenvalue-based solution is proposed. Symbolicsolutions to the corresponding characteristic polynomial isderived showing higher computation speed. Simulations aredesigned and conducted using test cases evaluated by severalclassical methods e.g. M. D. Shuster’s QUaternion ESTimator(QUEST), F. L. Markley’s SVD method, D. Mortari’s SecondEstimator of the Optimal Quaternion (ESOQ2) and some recentrepresentative methods e.g. Y. Yang’s analytical method andRiemannian manifold method. The results show that FLAEgenerates attitude estimates as accurate as that of severalexisting methods but consumes much less computation time(about 50% of the known best algorithm). Also, to verifythe feasibility in embedded application, an experiment onthe accelerometer-magnetometer combination is carried outwhere the algorithms are compared via C++ programminglanguage. An extreme case is finally studied, revealing a minorimprovement shows more effectiveness in this case inspired byY. Cheng et al