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Localization of Passive 3D-Coils as an Inverse Problem: Theoretical Analysis and a Numerical Method
IEEE Transactions on Magnetics ( IF 2.1 ) Pub Date : 2020-04-01 , DOI: 10.1109/tmag.2020.2968858
Martin DoB 1 , Leon Bungert 2 , Daniel Cichon 3 , Hartmut Brauer 4 , Rafael Psiuk 1
Affiliation  

This article provides both a theoretical analysis and a numerical method for the inverse source problem of locating multiple passive 3-D coils based on measurements of their superposed magnetic fields. In our context, a 3-D coil consists of three concentric circular coils being mutually perpendicular, and the term “passive” means that these coils are not connected to an active power source. Instead, their current is induced externally by a low-frequency alternating magnetic field which is generated by a closed exciter wire. The underlying inductively coupled system is modeled with regard to the 3-D coils as magnetic dipoles and their localization is formulated as an inverse problem. Since its ill posedness mainly arises from strong sensitivity to observational noise, an approximate upper bound for the localization error is derived mathematically by linearization. The Levenberg–Marquardt algorithm is applied as a method for localization and modified for better performance as well as the ability to estimate the number of 3-D coils in the localization area. Our method is tested with simulated and real data in order to confirm its capability of locating up to three passive 3-D coils within the front of a wooden shelf surrounded by the exciter wire and eight rectangular loop antennas.

中文翻译:

无源 3D 线圈定位为逆问题:理论分析和数值方法

本文针对基于叠加磁场测量的多个无源 3D 线圈定位的逆源问题提供了理论分析和数值方法。在我们的上下文中,3-D 线圈由三个相互垂直的同心圆形线圈组成,术语“无源”意味着这些线圈没有连接到有源电源。相反,它们的电流是由闭合的励磁线产生的低频交变磁场在外部感应的。底层电感耦合系统将 3-D 线圈建模为磁偶极子,并将它们的定位公式化为一个逆问题。由于其病态主要源于对观测噪声的强烈敏感性,定位误差的近似上限是通过线性化在数学上推导出来的。Levenberg-Marquardt 算法被用作一种定位方法,并进行了修改以获得更好的性能以及估计定位区域中 3-D 线圈数量的能力。我们的方法用模拟和真实数据进行了测试,以确认其能够在由励磁线和八个矩形环形天线包围的木架前部定位多达三个无源 3-D 线圈。
更新日期:2020-04-01
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