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.
ThompsonD., Euldph: A new technique for making computer-assisted depth estimates from magnetic data, Geophysics47(1) (1982), 31-37.
2.
ReidA., AllsopJ., GranserH., MillettA. and SomertonI., Magnetic interpretation in three dimensions using euler deconvolution, Geophysics55(1) (1990), 80-91.
3.
HashiS., TokunagaY., YabukamiS., KohnoT., OzawaT., OkazakiY., IshiyamaK. and AraiK., Wireless motion capture system using magnetically coupled lc resonant marker, Journal of Magnetism and Magnetic Materials290 (2005), 1330-1333.
4.
HashiS., YabukamiS., KanetakaH., IshiyamaK. and AraiK., Wireless magnetic position-sensing system using optimized pickup coils for higher accuracy, Magnetics, IEEE Transactions on47(10) (2011), 3542-3545.
5.
ChibaA. and NaraT., 2-d localization of radio frequency identification tags from measurements of the weighted integrals of the magnetic flux density, IEEE Transactions On Magnetics50(9) (2014).
6.
PiniésP. and TardósJ.D., Fast localization of avalanche victims using sum of gaussians, in Robotics and Automation, 2006. ICRA 2006. Proceedings 2006 IEEE International Conference on, pp. 3989-3994, IEEE, 2006.
7.
PiniésP., TardósJ.D. and NeiraJ., Localization of avalanche victims using robocentric slam, in Intelligent Robots and Systems, 2006 IEEE/RSJ International Conference on, pp. 3074-3079, IEEE, 2006.
8.
NaraT., SuzukiS. and AndoS., A closed-form formula for magnetic dipole localization by measurement of its magnetic field and spatial gradients, Magnetics, IEEE Transactions on42(10) (2006), 3291-3293.
9.
NaraT. and ItoW., Moore-penrose generalized inverse of the gradient tensor in euler's equation for locating a magnetic dipole, Journal of Applied Physics115(17) (2014), 17E504.
10.
BeikiM., ClarkD.A., AustinJ.R. and FossC.A., Estimating source location using normalized magnetic source strength calculated from magnetic gradient tensor data, Geophysics77(6) (2012), J23-J37.
