TY - GEN

T1 - Robust iterative observer for source localization for Poisson equation

AU - Majeed, Muhammad Usman

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

U2 - 10.1109/CDC.2016.7798870

DO - 10.1109/CDC.2016.7798870

M3 - Conference contribution

SN - 9781509018376

SP - 3972

EP - 3978

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

PB - Institute of Electrical and Electronics Engineers (IEEE)

ER -