Limited bene﬿t of cooperation in distributed relative localization

Wilbert Samuel Rossi, Wilbert Samuel Rossi, Paolo Frasca, Fabio Fagnani

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

    Abstract

    Important applications in robotic and sensor networks require distributed algorithms to solve the so-called relative localization problem: a node-indexed vector has to be reconstructed from measurements of differences between neighbor nodes. In a recent note, we have studied the estimation error of a popular gradient descent algorithm showing that the mean square error has a minimum at a finite time, after which the performance worsens. This paper proposes a suitable modification of this algorithm incorporating more realistic a priori information on the position. The new algorithm presents a performance monotonically decreasing to the optimal one. Furthermore, we show that the optimal performance is approximated, up to a $1 + \epsilon$ factor, within a time which is independent of the graph and of the number of nodes. This bounded convergence time is closely related to the minimum exhibited by the previous algorithm and both facts lead to the following conclusion: in the presence of noisy data, cooperation is only useful till a certain limit.
    Original languageUndefined
    Title of host publicationProceedings of the 52nd IEEE Conference on Decision and Control
    Place of PublicationUSA
    PublisherIEEE CONTROL SYSTEMS SOCIETY
    Pages5427-5431
    Number of pages5
    ISBN (Print)978-1-4673-5716-6
    Publication statusPublished - Dec 2013
    Event52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy
    Duration: 10 Dec 201313 Dec 2013
    Conference number: 52

    Publication series

    Name
    PublisherIEEE Control Systems Society

    Conference

    Conference52nd IEEE Conference on Decision and Control, CDC 2013
    Abbreviated titleCDC
    CountryItaly
    CityFlorence
    Period10/12/1313/12/13

    Keywords

    • EWI-24173
    • IR-88319
    • METIS-300255

    Cite this

    Rossi, W. S., Rossi, W. S., Frasca, P., & Fagnani, F. (2013). Limited bene﬿t of cooperation in distributed relative localization. In Proceedings of the 52nd IEEE Conference on Decision and Control (pp. 5427-5431). USA: IEEE CONTROL SYSTEMS SOCIETY.