On attitude representations for optimization-based Bayesian smoothing

Michael Lorenz, Bertram Taetz, Manon Kok, Gabriele Bleser

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

5 Citations (Scopus)
78 Downloads (Pure)


This paper presents a study of the behavior of seven different attitude representations in a batchwise orientation smoothing problem. The representations include the well-known unit quaternions and rotation vectors(/axis-angle), as well as modified Rodrigues parameters (MRPs). We consider error states as well as direct orientation formulations for the orientation and propose two methods to handle the singularity of MRPs in the latter case. The Bayesian smoothing problem is posed as a maximum a posteriori estimate with Gaussian noise, which results in a non-linear weighted least squares problem. With this we estimate the trajectory for a single inertial measurement unit with only sparse magnetometer samples for two challenging scenarios. In the evaluation we mainly focus on the convergence but also consider the estimation errors. Monte Carlo simulations show that orientation error states, with rotation vectors or MRPs, in general converge faster than other representations. However, with an initialization of the optimization problem up to deviations of 90 degrees MRPs with one of the proposed singularity handlings performs similar, but with a much smaller memory consumption. The source code for this study is available online.
Original languageEnglish
Title of host publicationProceedings of the 22nd International Conference on Information Fusion
Place of PublicationPiscataway, NJ, USA
Number of pages8
ISBN (Print)978-0-9964527-8-6
Publication statusPublished - 2019
Event22nd International Conference on Information Fusion (FUSION 2019) - Shaw Centre, Ottawa, Canada
Duration: 2 Jul 20195 Jul 2019


Conference22nd International Conference on Information Fusion (FUSION 2019)
Abbreviated titleFUSION 2019

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Bayesian smoothing
  • optimization
  • orientation estimation
  • attitude representations
  • inertial sensors


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