A constrained quaternion estimator for single-frame attitude determination

U. Tamir, D. Choukroun

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


This paper presents a novel algorithm for quaternion estimation from single-frame vector measurements, which is developed in the realm of deterministic constrained least-squares estimation. Hinging on the interpretation of quaternion measurements errors as angular errors in the four-dimensional Euclidean space, a novel cost function is developed and a minimization problem is formulated under the quaternion unitnorm constraint. This approach sheds a new light on the Wahba problem and on the qmethod. The optimal estimate can be interpreted as achieving the least angular distance among a collection of planes in ℝ4 that are constructed from the vector observations. The resulting batch algorithm is mathematically equivalent to the q-method. Yet, taking advantage of the gained geometric insight, a recursive algorithm is developed, where the update stage consists of a rotation in the four-dimensional Euclidean space. The rotation is performed in a plane that is generated by the a priori quaternion estimate and by a measurement-related quaternion. The rotation angle is empirically designed as a fading memory factor. The main highlights of this novel algorithm are that the quaternion update stage is multiplicative such as to preserve the estimated quaternion unit-norm, and that no iterative search for eigenvalues is required. Extensive Monte- Carlo simulations showed that the novel recursive algorithm asymptotically converges to the q-method solution. Beyond the framework of single-frame quaternion estimation, this approach appears as a promising tool to embed norm-preserving quaternion update stages in augmented state estimators. More generally, the proposed approach lends itself to norm-preserving estimation algorithms in higher dimensions.

Original languageEnglish
Title of host publicationAIAA Guidance, Navigation, and Control Conference 2012
PublisherAmerican Institute of Aeronautics and Astronautics Inc.
ISBN (Print)9781600869389
StatePublished - 1 Jan 2012
Externally publishedYes
EventAIAA Guidance, Navigation, and Control Conference 2012 - Minneapolis, MN, United States
Duration: 13 Aug 201216 Aug 2012

Publication series

NameAIAA Guidance, Navigation, and Control Conference 2012


ConferenceAIAA Guidance, Navigation, and Control Conference 2012
Country/TerritoryUnited States
CityMinneapolis, MN

ASJC Scopus subject areas

  • Aerospace Engineering
  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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