Machine-Learning Approach for Solving Inverse Problems in Magnetic-Field-Based Positioning

Abstract

Magnetic fields are often utilized for position sensing of mobile devices. In typical sensing systems, multiple sensors are used to detect magnetic fields generated by target devices. To determine the positions of the devices, magnetic-field data detected by the sensors must be converted to device-position data. The data conversion is not trivial because it is a nonlinear inverse problem. In this study, we propose a machinelearning approach suitable for data conversion required in the magneticfield-based position sensing of target devices. In our approach, two different sets of training data are used. One of the training datasets is composed of raw data of magnetic fields to be detected by sensors. The other set is composed of logarithmically represented data of the fields. We can obtain two different predictor functions by learning with these training datasets. Results show that the prediction accuracy of the target position improves when the two different predictor functions are used. Based on our simulation, the error of the target position estimated with the predictor functions is within 10 cm in a 2 m × 2 m × 2 m cubic space for 87% of all the cases of the target device states. The computational time required for predicting the positions of the target device is 4 ms. As the prediction method is accurate and rapid, it can be utilized for the real-time tracking of moving objects and people.

Effectiveness of Artificial Neural Networks for Solving Inverse Problems in Magnetic Field-Based Localization

“…Hereinafter, 𝑥 ( ) , 𝑦 ( ) , 𝑧 ( ) , 𝜃 ( ) , 𝜑 ( ) are referred to as "TX-state parameters" since they represent the physical state of the TX. The magnetic fields created at an arbitrary point (𝑥, 𝑦, 𝑧) by the TX coil placed at a coordinate origin can be calculated using the following equation [18,19]: 𝐵 𝑥, 𝑦, 𝑧, 𝜃 ( ) , 𝜑 ( ) 𝐵 𝑥, 𝑦, 𝑧, 𝜃 ( ) , 𝜑 ( ) 𝐵 𝑥, 𝑦, 𝑧, 𝜃 ( )…”

“…In this section, we describe the basic of calculation techniques required for magnetic field-based localization and formulate the inverse problems to be solved by machine learning [ 18 , 19 ].…”

“…The magnetic fields created at an arbitrary point by the TX coil placed at a coordinate origin can be calculated using the following equation [ 18 , 19 ]: where and denote the vacuum permeability and dipole moment associated with the TX coil, respectively. The dipole moment can be expressed by the parameters of an N -turn coil attached to the TX as follows: where and denote the current and area size of the TX coil, respectively.…”

“…To solve this problem, an effective method for preprocessing training data has been proposed [ 19 ]. The core idea of the method is to logarithmically transform the magnetic field values in the training data.…”

“…The third method involves the application of machine learning to solve the inverse problems [ 18 , 19 ]. We have demonstrated that the computational time required for calculating the target position is significantly reduced by adopting machine learning.…”