Choukroun, Daniel (Ben-Gurion University of the Negev), Tamir, Uri (Ben-Gurion University)

A Novel Multiplicative Quaternion Filter

Scheduled for presentation during the Regular Session "Estimation 1" (WeA3), Wednesday, April 3, 2019, 16:30−17:00, BL281.2

5th CEAS Conference on Guidance, Navigation and Control, April 3-5, 2019, Milano, Italy

This information is tentative and subject to change. Compiled on April 24, 2024

Abstract

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 measurement 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 $real^4$ that are constructed from the vector observations. The resulting batch algorithm is mathematically equivalent to the q-method. 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. The two algorithms are extended to the case of time varying attitude, under the assumptions that the inertial angular rates are measured. Extensive Monte-Carlo simulations showed that the proposed filter asymptotically converges to the q-method solution. The performances are numerically investigated for a range of typical values of the noise intensities in the rate gyroscopes and the attitude sensing.