A second order minimum-energy filter on the special orthogonal group

Mohammad Zamani*, Jochen Trumpf, Robert Mahony

*Corresponding author for this work

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

    9 Citations (Scopus)

    Abstract

    This work documents a case study in the application of Mortensen's nonlinear filtering approach to invariant systems on general Lie groups. In this paper, we consider the special orthogonal group SO(3) of all rotation matrices. We identify the exact form of the kinematics of the minimum-energy (optimal) observer on SO(3) and note that it depends on the Hessian of the value function of the associated optimal control problem. We derive a second order approximation of the dynamics of the Hessian by neglecting third order terms in the expansion of the dynamics. This yields a Riccati equation that together with the optimal observer equation form a second order minimum-energy filter on SO(3). The proposed filter is compared to the multiplicative extended Kalman filter (MEKF), arguably the industry standard for attitude estimation, by means of simulations. Our studies indicate superior transient and asymptotic tracking performance of the proposed filter as compared to the MEKF.

    Original languageEnglish
    Title of host publication2012 American Control Conference, ACC 2012
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages1895-1900
    Number of pages6
    ISBN (Print)9781457710957
    DOIs
    Publication statusPublished - 2012
    Event2012 American Control Conference, ACC 2012 - Montreal, QC, Canada
    Duration: 27 Jun 201229 Jun 2012

    Publication series

    NameProceedings of the American Control Conference
    ISSN (Print)0743-1619

    Conference

    Conference2012 American Control Conference, ACC 2012
    Country/TerritoryCanada
    CityMontreal, QC
    Period27/06/1229/06/12

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