A novel constrained quaternion filter

Daniel Choukroun, Uri Tamir

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


This paper presents a novel quaternion filter from vector measurements that belongs to the realm of deterministic constrained least-squares estimation. Hinging on the interpretation of quaternion measurements errors as angular errors in a four-dimensional Euclidean space, a novel cost function is developed and a minimization problem is formulated under the quaternion unit-norm constraint. This approach sheds a new light on the Wahba problem and on the q-method. 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 angle is empirically designed as a fading memory factor. The quaternion update stage is multiplicative thus preserving the estimated quaternion unit-norm and no iterative search for eigenvalues is required as opposed to the q-method. Simulations illustrate the convergence and accuracy properties of the proposed algorithm.

Original languageEnglish
Title of host publication59th Israel Annual Conference on Aerospace Sciences, IACAS 2019
PublisherIsrael Annual Conference on Aerospace Sciences
Number of pages17
ISBN (Electronic)9781510882782
StatePublished - 1 Jan 2019
Event59th Israel Annual Conference on Aerospace Sciences, IACAS 2019 - Tel-Aviv and Haifa, Israel
Duration: 6 Mar 20197 Mar 2019

Publication series

Name59th Israel Annual Conference on Aerospace Sciences, IACAS 2019


Conference59th Israel Annual Conference on Aerospace Sciences, IACAS 2019
CityTel-Aviv and Haifa

ASJC Scopus subject areas

  • Aerospace Engineering


Dive into the research topics of 'A novel constrained quaternion filter'. Together they form a unique fingerprint.

Cite this