Topic
Triad method
About: Triad method is a research topic. Over the lifetime, 49 publications have been published within this topic receiving 1998 citations.
Papers
TL;DR: Two computationally efficient algorithms are presented for determining three-axis attitude from two or more vector observations that are useful to the mission analyst or spacecraft engineer for the evaluation of launch-window constraints or of attitude accuracies for different attitude sensor configurations.
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.
1,513 citations
TL;DR: In this article, a critical comparison of estimators minimizing Wahba's loss function is presented for the QUaternion ESTimator (QUEST) and Estimators of the Optimal Quaternion (ESOQ) to avoid the computational burden of sequential rotations in these algorithms.
Abstract: This paper contains a critical comparison of estimators minimizing Wahba’s loss function Some new results are presented for the QUaternion ESTimator (QUEST) and Estimators of the Optimal Quaternion (ESOQ and ESOQ2) to avoid the computational burden of sequential rotations in these algorithms None of these methods is as robust in principle as Davenport’s q method or the Singular Value Decomposition (SVD) method, which are significantly slower Robustness is only an issue for measurements with widely differing accuracies, so the fastest estimators, the modified ESOQ and ESOQ2, are well suited to sensors that track multiple stars with comparable accuracies More robust forms of ESOQ and ESOQ2 are developed that are intermediate in speed
359 citations
TL;DR: In this paper, the authors presented two new fast quaternion attitude estimation algorithms using two vector observations, one optimal and one suboptimal, at reduced computational cost, which is almost as accurate as the optimal estimate in representative test scenarios.
Abstract: Many spacecraft attitude determination methods use exactly two vector measurements. The two vectors are typically the unit vector to the Sun and the Earth's magnetic field vector for coarse "sun-mag" attitude determination or unit vectors to two stars tracked by two star trackers for fine attitude determination. Existing closed-form attitude estimates based on Wahba's optimality criterion for two arbitrarily weighted observations are somewhat slow to evaluate. This paper presents two new fast quaternion attitude estimation algorithms using two vector observations, one optimal and one suboptimal. The suboptimal method gives the same estimate as the TRIAD algorithm, at reduced computational cost. Simulations show that the TRIAD estimate is almost as accurate as the optimal estimate in representative test scenarios.
130 citations
29 Jul 1996
TL;DR: In this article, the authors present a new algorithm called Optimized TRIAD, which blends in a specified manner the two matrices generated by TRIAD when processing one vector first, and then when processing the other vector first.
Abstract: TRIAD is a well known simple algorithm that generates the attitude matrix between two coordinate systems when the components of two abstract vectors are given in the two systems. TRIAD however, is sensitive to the order in which the algorithm handles the vectors, such that the resulting attitude matrix is influenced more by the vector processed first. In this work we present a new algorithm, which we call Optimized TRIAD, that blends in a specified manner the two matrices generated by TRIAD when processing one vector first, and then when processing the other vector first. On the average, Optimized TRIAD yields a matrix which is better than either one of the two matrices in that is ti the closest to the correct matrix. This result is demonstrated through simulation.
55 citations
TL;DR: In this paper, the TRIAD algorithm is shown to be derived as a maximum likelihood estimator using the QUEST measurement model, and the attitude error covariance matrix is derived as the inverse of the Fisher information matrix.
Abstract: The TRIAD algorithm is shown to be derivable as a maximum-likelihood estimator. In particular, using the QUEST measurement model, the TRIAD attitude error covariance matrix can be derived as the inverse of the Fisher information matrix. The treatment here gives a microscopic analysis of the algorithm and its connection to the QUEST algorithm. It also sheds valuable light on the origin of discrete degeneracies in deterministic attitude estimation.
34 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2020 | 1 |
| 2019 | 1 |
| 2018 | 3 |
| 2017 | 1 |
| 2016 | 1 |