Large-scale magnetic field maps using structured kernel interpolation for Gaussian process regression

TL;DR

This paper introduces a scalable Gaussian process-based method using structured kernel interpolation and Krylov subspace techniques to efficiently create large-scale magnetic field maps for indoor localization, achieving high accuracy and speed.

Contribution

It develops a novel SKI-based approach with derivatives for magnetic field modeling, enabling linear complexity inference with large datasets.

Findings

Achieves better accuracy than existing methods on magnetic field maps.

Constructs maps from up to 40,000 measurements in under two minutes.

Demonstrates scalability and efficiency for large indoor environments.

Abstract

We present a mapping algorithm to compute large-scale magnetic field maps in indoor environments with approximate Gaussian process (GP) regression. Mapping the spatial variations in the ambient magnetic field can be used for localization algorithms in indoor areas. To compute such a map, GP regression is a suitable tool because it provides predictions of the magnetic field at new locations along with uncertainty quantification. Because full GP regression has a complexity that grows cubically with the number of data points, approximations for GPs have been extensively studied. In this paper, we build on the structured kernel interpolation (SKI) framework, speeding up inference by exploiting efficient Krylov subspace methods. More specifically, we incorporate SKI with derivatives (D-SKI) into the scalar potential model for magnetic field modeling and compute both predictive mean and covariance with a complexity that is linear in the data points. In our simulations, we show that our method achieves better accuracy than current state-of-the-art methods on magnetic field maps with a growing mapping area. In our large-scale experiments, we construct magnetic field maps from up to 40000 three-dimensional magnetic field measurements in less than two minutes on a standard laptop.