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CEAS EuroGNC 2024

A Simple Quaternion Estimator with Error Analysis
Caitong Peng Graduate Student, Ben-Gurion University of the Negev, Mechanical Engineering dept., 84105, Beer Sheva, Israel.
Daniel Choukroun Senior Lecturer, Ben-Gurion University of the Negev, Mechanical Engineering dept., 84105, Beer Sheva, Israel.
Abstract:
A simple single-frame quaternion estimator is introduced where two vector observations are deterministically processed. This estimator is amenable to analytical expressions for the bias and the covariance matrix of the estimation error under white noise assumptions in the body and reference vectors. The statistics are developed in four dimensions both for the additive and multiplicative quaternion errors, before being reduced to three dimensions. The exceedingly simple structure of the estimator is instrumental in reaching analytical expressions and a thorough treatment of its singularities. Moreover, the impact of normalization of the quaternion estimate is studied in generic terms clarifying a misconception about the singular nature of its covariance. The estimator's error analysis is tested for statistical consistency and its accuracy is illustrated via extensive Monte Carlo simulations. Results show that the proposed estimator performs as well or better than a state-of-the-art similar quaternion estimator with about half the computation burden.
Keywords: Attitude quaternion; vector measurement; bias and covariance analysis; quaternion normalization
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Caitong Peng, Daniel Choukroun: A Simple Quaternion Estimator with Error Analysis. Proceedings of the 2024 CEAS EuroGNC conference. Bristol, UK. June 2024. CEAS-GNC-2024-086.
BibTeX entry:

@Incollection{CEAS-GNC-2024-086,
    author = {Peng, Caitong and Choukroun, Daniel},
    title = {A Simple Quaternion Estimator with Error Analysis},
    booktitle = {Proceedings of the 2024 {CEAS EuroGNC} conference},
    address = {Bristol, UK},
    month = jun,
    year = {2024},
    note = {CEAS-GNC-2024-086}
}