A Truncated Singular Value Decomposition approach for locating a magnetic dipole with Euler's equation

Issue title: Proceedings from the 17th International Symposium on Applied Electromagnetics and Mechanics (ISEM 2015)

Guest editors: Fumio Kojima, Futoshi Kobayashi and Hiroyuki Nakamoto

Article type: Research Article

Authors: Higuchi, Yusuke^* | Nara, Takaaki | Ando, Shigeru

Affiliations: Department of Information Physics and Computing, The University of Tokyo, Tokyo, Japan

Correspondence: [*] Corresponding author: Yusuke Higuchi, Department of Information Physics and Computing, The University of Tokyo, Tokyo, Japan. E-mail:yusuke_higuchi@alab.u-tokyo.ac.jp

Abstract: It is known that Euler's homogeneity equation provides a system of linear equations for localizing a magnetic dipole from measurements of the magnetic field and its gradients. In this paper, we show that a solution of the equations obtained by Truncated Singular Value Decomposition (TSVD) always gives the true position of the dipole regardless of the singularity of the coefficient matrix. Hence, we can localize a magnetic dipole robustly without estimation bias by TSVD.

Keywords: Inverse problem, magnetic dipole, Euler's equation

DOI: 10.3233/JAE-162202

Journal: International Journal of Applied Electromagnetics and Mechanics, vol. 52, no. 1-2, pp. 67-72, 2016