Magnetic Field Mapping Using Spatial Derivative Measurements with Gaussian Process Regression

Abstract

Indoor localization is an active research area since traditional localization methods, such as global navigation satellite systems (GNSS), are ineffective in indoor environments. One promising solution is to make use of anomalies in the magnetic field caused by ferromagnetic materials within buildings. By constructing a magnetic field map in an indoor location, the spatial variability in the magnetic field can be utilized to aid in inferring the location. Gaussian process regression (GPR) is frequently used to model the magnetic field and provide magnetic field predictions as well as the corresponding predictive uncertainty. In addition to mapping an entire building or room, the existing literature has also been studying mapping in close proximity to the sensor, as this provides valuable information for odometry purposes. Magnetic field measurements are obtained using sensors known as magnetometers. Magnetometer arrays, which are typically two- or three-dimensional fixed structures that contain multiple magnetometers, are used to construct these local maps as they are capable of measuring the magnetic field at multiple locations simultaneously. However, the time complexity of GPR scales cubically with the number of data points. When these magnetometer arrays are used, the size of the data increases rapidly. As a result, GPR can quickly become computationally intractable in combination with arrays. In this thesis, building on prior work that demonstrated the use of spatial derivatives of arrays for odometry purposes, we instead analyze how effective the information on the array can be approximated using the spatial derivative of the magnetic field to alleviate some of the computational burden. We analyze this by examining the performance of using the spatial derivative computed from different array configurations in terms of the number of magnetometers, their spacing, and noise levels, and comparing it with using all magnetometer measurements on the array. Through simulations, we show that the spacing is a key factor in determining the spatial derivative, and that more magnetometers and less noise result in better estimates. It is shown that the spatial derivative is not an effective approximation to the full information on the array. At least for the arrays considered in this thesis, it did not reduce the computational burden sufficiently to justify the resulting loss in map quality. In addition to examining which array configurations perform best with spatial derivatives, we also evaluate which configurations yield accurate maps for existing odometry methods that rely on arrays. We show that the array configuration plays an important role and requires deliberate selection for optimal performance.