Second-order-optimal filters on Lie groups

A. Saccon, Jochen Trumpf, Robert Mahony, A.P. Aguiar

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

7 Citations (Scopus)
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We provide an explicit formula for the second-order-optimal nonlinear filter for state estimation of systems on general Lie groups with disturbed measurements of inputs and outputs. Optimality is with respect to a deterministic cost measuring the cumulative energy in the unknown system disturbances (minimum-energy filtering). We show that the resulting filter will depend on the choice of affine connection, thus encoding the nonlinear geometry of the state space. For the case of attitude estimation, where we are given a second order (dynamic) mechanical system on the tangent bundle of the special orthogonal group SO(3), and where we choose the symmetric Cartan-Schouten (0)-connection, the resulting filter has the familiar form of a gradient observer combined with a matrix Riccati differential equation that updates the filter gain.
Original languageEnglish
Title of host publicationProceedings of the 52nd IEEE Conference on Decision and Control (CDC), December 10-13, 2013, Florence, Italy
Place of PublicationPisacataway
PublisherInstitute of Electrical and Electronics Engineers
ISBN (Print)978-1-4673-5714-2
Publication statusPublished - 2013


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