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

Muhammad Usman Majeed; Taous Meriem Laleg-Kirati

doi:10.23919/ACC.2017.7963449

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

Muhammad Usman Majeed, Taous Meriem Laleg-Kirati

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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.

Original language	English (US)
Title of host publication	2017 American Control Conference, ACC 2017
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3257-3262
Number of pages	6
ISBN (Electronic)	9781509059928
DOIs	https://doi.org/10.23919/ACC.2017.7963449
State	Published - Jun 29 2017
Event	2017 American Control Conference, ACC 2017 - Seattle, United States Duration: May 24 2017 → May 26 2017

Publication series

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

Conference

Conference	2017 American Control Conference, ACC 2017
Country/Territory	United States
City	Seattle
Period	05/24/17 → 05/26/17

ASJC Scopus subject areas

Electrical and Electronic Engineering

Access to Document

10.23919/ACC.2017.7963449

Cite this

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title = "Iterative observer based method for source localization problem for Poisson equation in 3D",

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.",

author = "Majeed, {Muhammad Usman} and Laleg-Kirati, {Taous Meriem}",

note = "Publisher Copyright: {\textcopyright} 2017 American Automatic Control Council (AACC).; 2017 American Control Conference, ACC 2017 ; Conference date: 24-05-2017 Through 26-05-2017",

year = "2017",

month = jun,

day = "29",

doi = "10.23919/ACC.2017.7963449",

language = "English (US)",

series = "Proceedings of the American Control Conference",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "3257--3262",

booktitle = "2017 American Control Conference, ACC 2017",

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Majeed, MU & Laleg-Kirati, TM 2017, Iterative observer based method for source localization problem for Poisson equation in 3D. in 2017 American Control Conference, ACC 2017., 7963449, Proceedings of the American Control Conference, Institute of Electrical and Electronics Engineers Inc., pp. 3257-3262, 2017 American Control Conference, ACC 2017, Seattle, United States, 05/24/17. https://doi.org/10.23919/ACC.2017.7963449

Iterative observer based method for source localization problem for Poisson equation in 3D. / Majeed, Muhammad Usman; Laleg-Kirati, Taous Meriem.
2017 American Control Conference, ACC 2017. Institute of Electrical and Electronics Engineers Inc., 2017. p. 3257-3262 7963449 (Proceedings of the American Control Conference).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Iterative observer based method for source localization problem for Poisson equation in 3D

AU - Majeed, Muhammad Usman

AU - Laleg-Kirati, Taous Meriem

PY - 2017/6/29

Y1 - 2017/6/29

N2 - 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.

AB - 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.

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M3 - Conference contribution

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EP - 3262

BT - 2017 American Control Conference, ACC 2017

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2017 American Control Conference, ACC 2017

Y2 - 24 May 2017 through 26 May 2017

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

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