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    Iterative observer based method for source localization problem for Poisson equation in 3D

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    Type
    Conference Paper
    Authors
    Majeed, Muhammad Usman cc
    Laleg-Kirati, Taous-Meriem cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computational Bioscience Research Center (CBRC)
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Electrical Engineering Program
    Date
    2017-07-10
    Online Publication Date
    2017-07-10
    Print Publication Date
    2017-05
    Permanent link to this record
    http://hdl.handle.net/10754/625674
    
    Metadata
    Show full item record
    Abstract
    A state-observer based method is developed to solve point source localization problem for Poisson equation in a 3D rectangular prism with available boundary data. The technique requires a weighted sum of solutions of multiple boundary data estimation problems for Laplace equation over the 3D domain. The solution of each of these boundary estimation problems involves writing down the mathematical problem in state-space-like representation using one of the space variables as time-like. First, system observability result for 3D boundary estimation problem is recalled in an infinite dimensional setting. Then, based on the observability result, the boundary estimation problem is decomposed into a set of independent 2D sub-problems. These 2D problems are then solved using an iterative observer to obtain the solution. Theoretical results are provided. The method is implemented numerically using finite difference discretization schemes. Numerical illustrations along with simulation results are provided.
    Citation
    Majeed MU, Laleg-Kirati TM (2017) Iterative observer based method for source localization problem for Poisson equation in 3D. 2017 American Control Conference (ACC). Available: http://dx.doi.org/10.23919/ACC.2017.7963449.
    Sponsors
    This work was supported by King Abdullah University of Science and Technology (KAUST), KSA.
    Publisher
    Institute of Electrical and Electronics Engineers (IEEE)
    Journal
    2017 American Control Conference (ACC)
    Conference/Event name
    2017 American Control Conference, ACC 2017
    DOI
    10.23919/ACC.2017.7963449
    Additional Links
    http://ieeexplore.ieee.org/document/7963449/
    ae974a485f413a2113503eed53cd6c53
    10.23919/ACC.2017.7963449
    Scopus Count
    Collections
    Conference Papers; Applied Mathematics and Computational Science Program; Electrical and Computer Engineering Program; Computational Bioscience Research Center (CBRC); Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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