Robust iterative observer for source localization for Poisson equation

Muhammad Usman Majeed; Taous-Meriem Laleg-Kirati

doi:10.1109/CDC.2016.7798870

Robust iterative observer for source localization for Poisson equation

Muhammad Usman Majeed, Taous-Meriem Laleg-Kirati

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

Abstract

Source localization problem for Poisson equation with available noisy boundary data is well known to be highly sensitive to noise. The problem is ill posed and lacks to fulfill Hadamards stability criteria for well posedness. In this work, first a robust iterative observer is presented for boundary estimation problem for Laplace equation, and then this algorithm along with the available noisy boundary data from the Poisson problem is used to localize point sources inside a rectangular domain. The algorithm is inspired from Kalman filter design, however one of the space variables is used as time-like. Numerical implementation along with simulation results is detailed towards the end.

Original language	English (US)
Title of host publication	2016 IEEE 55th Conference on Decision and Control (CDC)
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	3972-3978
Number of pages	7
ISBN (Print)	9781509018376
DOIs	https://doi.org/10.1109/CDC.2016.7798870
State	Published - Jan 5 2017

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Research work presented in this paper was funded by King Abdullah University of Science and Technology (KAUST).

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10.1109/CDC.2016.7798870

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title = "Robust iterative observer for source localization for Poisson equation",

abstract = "Source localization problem for Poisson equation with available noisy boundary data is well known to be highly sensitive to noise. The problem is ill posed and lacks to fulfill Hadamards stability criteria for well posedness. In this work, first a robust iterative observer is presented for boundary estimation problem for Laplace equation, and then this algorithm along with the available noisy boundary data from the Poisson problem is used to localize point sources inside a rectangular domain. The algorithm is inspired from Kalman filter design, however one of the space variables is used as time-like. Numerical implementation along with simulation results is detailed towards the end.",

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

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AU - Laleg-Kirati, Taous-Meriem

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: Research work presented in this paper was funded by King Abdullah University of Science and Technology (KAUST).

PY - 2017/1/5

Y1 - 2017/1/5

N2 - Source localization problem for Poisson equation with available noisy boundary data is well known to be highly sensitive to noise. The problem is ill posed and lacks to fulfill Hadamards stability criteria for well posedness. In this work, first a robust iterative observer is presented for boundary estimation problem for Laplace equation, and then this algorithm along with the available noisy boundary data from the Poisson problem is used to localize point sources inside a rectangular domain. The algorithm is inspired from Kalman filter design, however one of the space variables is used as time-like. Numerical implementation along with simulation results is detailed towards the end.

AB - Source localization problem for Poisson equation with available noisy boundary data is well known to be highly sensitive to noise. The problem is ill posed and lacks to fulfill Hadamards stability criteria for well posedness. In this work, first a robust iterative observer is presented for boundary estimation problem for Laplace equation, and then this algorithm along with the available noisy boundary data from the Poisson problem is used to localize point sources inside a rectangular domain. The algorithm is inspired from Kalman filter design, however one of the space variables is used as time-like. Numerical implementation along with simulation results is detailed towards the end.

UR - http://hdl.handle.net/10754/622793

UR - http://ieeexplore.ieee.org/document/7798870/

UR - http://www.scopus.com/inward/record.url?scp=85010748407&partnerID=8YFLogxK

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DO - 10.1109/CDC.2016.7798870

M3 - Conference contribution

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SP - 3972

EP - 3978

BT - 2016 IEEE 55th Conference on Decision and Control (CDC)

PB - Institute of Electrical and Electronics Engineers (IEEE)

ER -

Robust iterative observer for source localization for Poisson equation

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