Magnetic field optimization from limited data

Abstract

When a sensor coil is placed in the field of an electromagnetic transmitter, a voltage is induced and may be measured. The amplitude of this voltage depends on the distance from the transmitter and the angle between the axes of the transmitter and the sensor. This relationship between the state of the coil and the voltages, known as the dipole model, can be exploited to track sensor coils in the space. ElectroMagnetic Articulography (EMA) uses this principle. It consists in measuring and representing graphically the mechanics of speech using sensor coils moved through the magnetic field induced by electromagnetic transmitters. The Carstens AG-500 EMA machine aims to provide 3-dimensional tracking of coils with 5 degrees of freedom and is used in speech mechanics research. The tracking process relies on optimization algorithms run to minimize the error between the measured voltages and the predicted ones using the dipole model. However, there is evidence to suggest that the dipole model may not match the actual magnetic field and then induces inaccurate tracking.

In this project, the feasibility of building a trainable model of the magnetic field is investigated. Using data sets sampled from the dipole model, different neural networks were trained and their performances compared. The objective of having such a model of the magnetic field would be to allow further optimization given some new data. A solution based on a constrained tracking of several sensor coils and an Unscented Kalman filtering algorithm is presented. Several coils were fixed relative to each other on a rigid body and moved through the measurement field of the AG-500. Using the knowledge of the fixed arrangement of the sensors on the block, the movement of this rigid body could be tracked.

Finally, several methods to discover the arrangements of coils fixed on a rigid device were tested.

The three solutions described above are part of a potential new calibration procedure aimed at accommodating any magnetic field distortions created by perturbations from the environment.