Continuous-Discrete von Mises-Fisher Filtering on S2 for Reference Vector Tracking

Filip Tronarp, Roland Hostettler, Simo Särkkä

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

1 Citation (Scopus)
135 Downloads (Pure)


This paper is concerned with tracking of reference vectors in the continuous-discrete-time setting. For this end, an Itô stochastic differential equation, using the gyroscope as input, is formulated that explicitly accounts for the geometry of the problem. The filtering problem is solved by restricting the prediction and filtering distributions to the von Mises-Fisher class, resulting in ordinary differential equations for the parameters. A strategy for approximating Bayesian updates and marginal likelihoods is developed for the class of conditionally spherical measurement distributions' which is realistic for sensors such as accelerometers and magnetometers, and includes robust likelihoods. Furthermore, computationally efficient and numerically robust implementations are presented. The method is compared to other state-of-the-art filters in simulation experiments involving tracking of the local gravity vector. Additionally, the methodology is demonstrated in the calibration of a smartphone's accelerometer and magnetometer. Lastly, the method is compared to state-of-the-art in gravity vector tracking for smartphones in two use cases, where it is shown to be more robust to unmodeled accelerations.

Original languageEnglish
Title of host publicationProceedings of the 21st International Conference on Information Fusion, FUSION 2018
Number of pages8
ISBN (Print)9780996452762
Publication statusPublished - 5 Sep 2018
MoE publication typeA4 Article in a conference publication
EventInternational Conference on Information Fusion - Cambridge, United Kingdom
Duration: 10 Jul 201813 Jul 2018
Conference number: 21


ConferenceInternational Conference on Information Fusion
Abbreviated titleFUSION
CountryUnited Kingdom


  • Directional statistics
  • robust filtering
  • sensor calibration
  • von Mises-Fisher distribution

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