Pose estimation using linearized rotations and quaternion algebra |
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| Authors: | Timothy Barfoot James R Forbes Paul T Furgale |
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| Institution: | 1. Department of Computer Engineering, Wroc?aw University of Science and Technology, Wybrze?e Stanis?awa Wyspiańskiego 27, 50-370 Wroc?aw, Poland;2. Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland;3. Polish-Japanese Academy of Information Technology, Aleja Legionów 2, 41-902 Bytom, Poland;1. Robotics Institute, Beihang University, Beijing 100191, China;2. School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK |
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| Abstract: | In this paper we revisit the topic of how to formulate error terms for estimation problems that involve rotational state variables. We present a first-principles linearization approach that yields multiplicative error terms for unit-length quaternion representations of rotations, as well as for canonical rotation matrices. Quaternion algebra is employed throughout our derivations. We show the utility of our approach through two examples: (i) linearizing a sun sensor measurement error term, and (ii) weighted-least-squares point-cloud alignment. |
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