Kalman Filtering for Attitude Estimation with Quaternions and Concepts from Manifold Theory
Department of Information and Communication Engineering, University of Murcia, 30100 Murcia, Spain
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Sensors 2019, 19(1), 149; https://doi.org/10.3390/s19010149
Received: 5 December 2018
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Revised: 26 December 2018
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Accepted: 27 December 2018
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Published: 3 January 2019
(This article belongs to the Collection Multi-Sensor Information Fusion)
The problem of attitude estimation is broadly addressed using the Kalman filter formalism and unit quaternions to represent attitudes. This paper is also included in this framework, but introduces a new viewpoint from which the notions of “multiplicative update” and “covariance correction step” are conceived in a natural way. Concepts from manifold theory are used to define the moments of a distribution in a manifold. In particular, the mean and the covariance matrix of a distribution of unit quaternions are defined. Non-linear versions of the Kalman filter are developed applying these definitions. A simulation is designed to test the accuracy of the developed algorithms. The results of the simulation are analyzed and the best attitude estimator is selected according to the adopted performance metric.
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Keywords:
attitude; orientation; estimation; Kalman filter; quaternion; manifold
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MDPI and ACS Style
Bernal-Polo, P.; Martínez-Barberá, H. Kalman Filtering for Attitude Estimation with Quaternions and Concepts from Manifold Theory. Sensors 2019, 19, 149. https://doi.org/10.3390/s19010149
AMA Style
Bernal-Polo P, Martínez-Barberá H. Kalman Filtering for Attitude Estimation with Quaternions and Concepts from Manifold Theory. Sensors. 2019; 19(1):149. https://doi.org/10.3390/s19010149
Chicago/Turabian StyleBernal-Polo, Pablo, and Humberto Martínez-Barberá. 2019. "Kalman Filtering for Attitude Estimation with Quaternions and Concepts from Manifold Theory" Sensors 19, no. 1: 149. https://doi.org/10.3390/s19010149
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