On the covariance singularity of quaternion estimators

Avishy Carmi, Yaakov Oshman

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

7 Scopus citations

Abstract

The asymptotic behavior of the estimation error covariance of quaternion estimators is mathematically examined. It is proved that the condition number of the asymptotic covariance matrix is of the order of the inverse of its largest eigenvalue, so that this matrix becomes asymptotically ill-conditioned as its trace tends to zero. Nevertheless, it is proved that the aforementioned asymptotic behavior cannot be captured by low-order Taylor approximations of the covariance, such as the one computed by the extended Kalman filter. The analytical results are demonstrated via a simulation study using the recently introduced quaternion particle filter and the additive quaternion extended Kalman filter.

Original languageEnglish
Title of host publicationCollection of Technical Papers - AIAA Guidance, Navigation, and Control Conference 2007
PublisherAmerican Institute of Aeronautics and Astronautics Inc.
Pages4648-4665
Number of pages18
ISBN (Print)1563479044, 9781563479045
DOIs
StatePublished - 1 Jan 2007
Externally publishedYes
EventAIAA Guidance, Navigation, and Control Conference 2007 - Hilton Head, SC, United States
Duration: 20 Aug 200723 Aug 2007

Publication series

NameCollection of Technical Papers - AIAA Guidance, Navigation, and Control Conference 2007
Volume5

Conference

ConferenceAIAA Guidance, Navigation, and Control Conference 2007
Country/TerritoryUnited States
CityHilton Head, SC
Period20/08/0723/08/07

ASJC Scopus subject areas

  • Aerospace Engineering
  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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