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Open AccessArticle

Optimal, Recursive and Sub-Optimal Linear Solutions to Attitude Determination from Vector Observations for GNSS/Accelerometer/Magnetometer Orientation Measurement

by Zebo Zhou 1,*,†, Jin Wu 1,2,*,†, Jinling Wang 3 and Hassen Fourati 4
1
School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 610054, China
2
School of Automation, University of Electronic Science and Technology of China, Chengdu 610054, China
3
Surveying and Geospatial Engineering, School of Civil and Environmental Engineering, University of New South Wales, Sydney 2052, NSW, Australia
4
Institute of Engineering, University Grenoble Alpes, CNRS, Inria, Grenoble INP, GIPSALab, 38000 Grenoble, France
*
Authors to whom correspondence should be addressed.
Zebo Zhou and Jin Wu contributed equally on the theory and experiment of this paper.
Remote Sens. 2018, 10(3), 377; https://doi.org/10.3390/rs10030377
Received: 11 December 2017 / Revised: 17 February 2018 / Accepted: 22 February 2018 / Published: 1 March 2018
The integration of the Accelerometer and Magnetometer (AM) provides continuous, stable and accurate attitude information for land-vehicle navigation without magnetic distortion and external acceleration. However, magnetic disturbance and linear acceleration strongly degrade the overall system performance. As an important complement, the Global Navigation Satellite System (GNSS) produces the heading estimates, thus it can potentially benefit the AM system. Such a GNSS/AM system for attitude estimation is mathematically converted to a multi-observation vector pairs matching problem in this paper. The optimal and sub-optimal attitude determination and their time-varying recursive variants are all comprehensively investigated and discussed. The developed methods are named as the Optimal Linear Estimator of Quaternion (OLEQ), Suboptimal-OLEQ (SOLEQ) and Recursive-OLEQ (ROLEQ) for different application scenarios. The theory is established based on our previous contributions, and the multi-vector matrix multiplications are decomposed with the eigenvalue factorization. Some analytical results are proven and given, which provides the reader with a brand new viewpoint of the attitude determination and its evolution. With the derivations of the two-vector case, the n-vector case is then naturally formed. Simulations are carried out showing the advantages of the accuracy, robustness and time consumption of the proposed OLEQs, compared with representative methods. The algorithms are then implemented using the C++ programming language on the designed hardware with a GNSS module, three-axis accelerometer and three-axis magnetometer, giving an effective validation of them in real-world applications. The designed schemes have proven their fast speed and good accuracy in these verification scenarios. View Full-Text
Keywords: attitude determination; GNSS receiver; Wahba’s problem; vector observations; autonomous navigation attitude determination; GNSS receiver; Wahba’s problem; vector observations; autonomous navigation
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Zhou, Z.; Wu, J.; Wang, J.; Fourati, H. Optimal, Recursive and Sub-Optimal Linear Solutions to Attitude Determination from Vector Observations for GNSS/Accelerometer/Magnetometer Orientation Measurement. Remote Sens. 2018, 10, 377.

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