Three-axis attitude determination from vector observations
Abstract
Two computationally efficient algorithms are presented for determining three-axis attitude from two or more vector observations. The first of these, the TRIAD algorithm, provides a deterministic (i.e., nonoptimal) solution for the attitude based on two vector observations. The second, the QUEST algorithm, is an optimal algorithm which determines the attitude that achieves the best weighted overlap of an arbitrary number of reference and observation vectors. Analytical expressions are given for the covariance matrices for the two algorithms using a fairly realistic model for the measurement errors. The mathematical relationship of the two algorithms and their relative merits are discussed and numerical examples are given. The advantage of computing the covariance matrix in the body frame rather than in the inertial frame (e.g., in terms of Euler angles) is emphasized. These results are valuable when a single-frame attitude must be computed frequently. They will also be useful to the mission analyst or spacecraft engineer for the evaluation of launch-window constraints or of attitude accuracies for different attitude sensor configurations.
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The QUEST algorithm solves Wahba's problem and gives a quaternion-based optimal solution via Davenport's q-method in an efficient way.
“The QUEST algorithm solves the Wabha's problem [Whaba, 1965], and its quaternionbased optimal solution given by Davensport's q-method [Shuster and Oh, 1981] in an efficient way.”
From <sup>3</sup>CAT-2: Attitude Determination and Control System for a GNSS-R Earth Observation 6U CubeSat Mission (2016) · cites this paper as Shuster and Oh, 1981
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Spacecraft Attitude Determination and Control
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- Authors
- SHUSTER, M. D., & OH, S. D.
- Affiliations
- Computer Sciences Corporation (United States) (US)
- ORCID
- SHUSTER, M. D.
- Venue
- Journal of Guidance and Control
- Published
- 1981-01
- Volume
- 4
- Issue
- 1
- Pages
- 70-77
- ISSN
- 0162-3192 (ISSN-L)
- OpenAlex
- W2006863675
- Cited by
- 1,399
- References
- 1
- Citations by year
- 2026: 29 · 2025: 41 · 2024: 42 · 2023: 57 · 2022: 66 · 2021: 69 · 2020: 74 · 2019: 63 · 2018: 86 · 2017: 72 · 2016: 69 · 2015: 54 · 2014: 77 · 2013: 65 · 2012: 77
- FWCI
- 13.00
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Guidance and Control (publishedVersion)
- Funders
- Goddard Space Flight Center
- U.S. Naval Research Laboratory
- Topics
- Physical Sciences › Engineering › Aerospace Engineering › Inertial Sensor and Navigation
- Physical Sciences › Engineering › Aerospace Engineering › Spacecraft Dynamics and Control
- Physical Sciences › Engineering › Aerospace Engineering › Guidance and Control Systems
- Keywords
- vector observations, TRIAD algorithm, QUEST algorithm, covariance matrix, measurement error, spacecraft attitude determination, Euler angles
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