Iterative observer based method for source localization problem for Poisson equation in 3D
Type
Conference PaperKAUST Department
Applied Mathematics and Computational Science ProgramComputational Bioscience Research Center (CBRC)
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Electrical Engineering Program
Date
2017-07-10Online Publication Date
2017-07-10Print Publication Date
2017-05Permanent link to this record
http://hdl.handle.net/10754/625674
Metadata
Show full item recordAbstract
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.Conference/Event name
2017 American Control Conference, ACC 2017Additional Links
http://ieeexplore.ieee.org/document/7963449/ae974a485f413a2113503eed53cd6c53
10.23919/ACC.2017.7963449