Minimum-energy filtering on the unit circle

Mohammad Zamani*, Jochen Trumpf, Robert Mahony

*Corresponding author for this work

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

    6 Citations (Scopus)

    Abstract

    We apply Mortensen's deterministic filtering approach to derive a third order minimum-energy filter for a system defined on the unit circle. This yields the exact form of a minimum-energy filter (namely an observer plus a Riccati equation that updates the observer gain). The proposed Riccati equation is perturbed by a term depending on the third order derivative of the value function of the associated optimal control problem. The proposed filter is third order in the sense that it approximates the dynamics of the third order derivate of the value function by neglecting the fourth order derivative of the value function. Additionally, we show that the near-optimal filter proposed by Coote et al. in prior work can indeed be derived from a second order application of Mortensen's approach to minimum-energy filtering on the unit circle.

    Original languageEnglish
    Title of host publicationProceedings of the 2011 Australian Control Conference, AUCC 2011
    Pages236-241
    Number of pages6
    Publication statusPublished - 2011
    Event1st Australian Control Conference, AUCC 2011 - Melbourne, VIC, Australia
    Duration: 10 Nov 201111 Nov 2011

    Publication series

    NameProceedings of the 2011 Australian Control Conference, AUCC 2011

    Conference

    Conference1st Australian Control Conference, AUCC 2011
    Country/TerritoryAustralia
    CityMelbourne, VIC
    Period10/11/1111/11/11

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