A super fast attitude solution is obtained for consumer electronics accelerometer-magnetometer combination. The quaternion parameterizing the orientation is analytically derived from a least-square optimization that maintains very simple form. Like previously developed approaches, this algorithm does not require predetermined magnetometer reference vector. It has been proven in the paper that the proposed algorithm is equivalent to two recent representative methods. Computational complexity analysis shows that the proposed algorithm has the least floating-number operations. Comparisons with recent and classical methods indicate the definite superiority of the proposed algorithm on execution time in real embedded applications.
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Wu et al. (2018) studied this question.
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