This paper revisits the stationary alignment problem of attitude and heading reference systems (AHRSs). The investigation is initiated from the three-axis attitude determination (TRIAD)–based method, purposely chosen to use nonunitary/nonorthogonal observations of the local gravity and Earth’s magnetic flux density vectors. For the simplifying assumption of body and navigation frames aligned, a comprehensive error analysis is developed, providing additional insight into the problem. Closed-form formulas for the residual normality and orthogonality errors are used to devise innovative pseudo-bias estimation (PBE) algorithms for the $x$ - and $z$ -axis magnetometer biases, as well as for the $z$ -axis accelerometer bias. As a direct consequence of applying the latter, and also figuring as the main contribution of this paper, an improved (more accurate) AHRS stationary alignment approach is obtained, herein called TRIAD-PBE. The error analysis is extended to representative state-of-the-art attitude determination techniques, confirming the relevance of TRIAD-PBE, especially in the presence of hard-iron magnetism. Results from simulated and experimental tests confirm the adequacy of the outlined verifications.

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This work was supported by the Brazilian Coordination for the Improvement of Higher Education Personnel, under grant 88881.169927/2018-01; the Brazilian Agricultural Research Corporation, under grant 212-20/2018; the São Paulo Research Foundation, under grant 2018/14024-2; the Minas Gerais Research Foundation, under grant CAG-APQ-01449-17; and the Brazilian National Council for Scientific and Technological Development, under grants 313160/2019-8 and 307255/2018-2. The authors would like to thank Jay A. Farrell, from the University of California Riverside, for the valuable comments on the manuscript and suggestions of improvements.

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Received18 March 2020
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Three-Axis Attitude Determination with Pseudo-Bias Estimation from Gravity/Magnetic Vector Observations

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