Co-Chairs: Ella Atkins and James Cutler

The defense for Michael Gonzalez will begin shortly before at 12:30pm.

In person and on zoom: https://umich.zoom.us/meeting/register/tJYtcO2rrD8qHdNNXhL2i8RfLVVYlc4q6zMC

Abstract:
Earth's magnetic field is a ubiquitous signal commonly used to orient one's heading relative to North. Typical magnetic field navigation techniques assume the ambient field points Northward and remains constant in a local area. Both assumptions break down inside buildings due to distortions caused by ferrous materials in modern structural components. In this work, we show how to make maps of magnetic field distortions to improve our ability to orient and traverse through indoor spaces. Because the magnetic field is ubiquitous on Earth and magnetometers are present on most modern smartphones and IMUs (inertial measurement units), our methods can be applied nearly anywhere on Earth.

This dissertation presents three major contributions towards the use of magnetic fields for indoor navigation. First, we show how to use a small UAV (unmanned aerial vehicle) to measure the ambient field throughout a workspace and create three dimensional magnetic field maps. We leverage a machine learning tool called Gaussian process regression (GPR) as the backbone of our magnetic field maps to interpolate the field at unobserved locations.

Second, we use a multiplicative extended Kalman filter (MEKF) with our GPR-based maps to estimate the attitude (orientation) of a UAV. Here, we introduce the concept of spatial variation which describes how much the magnetic field changes locally. Results show that our magnetic maps yield a two-fold improvement of attitude estimates indoors (where there is high spatial variation), but are unnecessary for outdoor environments where a constant-field assumption is appropriate.

Finally, we use a particle filter to estimate the position of a UAV using indoor magnetic fields. This last innovation is important because GPS (a staple for position estimation outdoors) is not available inside buildings. Instead, we use our GPR-based magnetic field maps to track the UAV's motion through our mapped space. Our results give three-dimensional position estimates of a UAV within 0.2m for six of our eight test cases. In addition, we show how the amount of magnetic field's spatial gradient correlates with our position estimation accuracy.

With some improvements, our methods can be used to transform the way people navigate through buildings. Imagine an indoor route planning application that guides someone to their terminal at an airport, to a book at their local library, or to their office at a new job. Because magnetic fields are everywhere on Earth, we can apply our mapping and navigation techniques to any building on the planet. In addition, the presence of magnetometers in modern smartphones gives everyone the ability to benefit from the invisible field all around them.

To make this vision a reality, our methods need to be less sensitive to changes in the magnetic field. Although this dissertation does not investigate robust navigation or time-varying magnetic field mapping, it does present important foundations on the practice of creating magnetic field maps and their value in enabling indoor navigation.