Modeling and interpolation of the ambient magnetic field by Gaussian processes

TL;DR

This paper introduces a Bayesian Gaussian process model for accurately interpolating and extrapolating ambient magnetic fields, aiding indoor positioning with efficient computation and adaptability to changing magnetic environments.

Contribution

It presents a physically justified, computationally efficient Gaussian process model for magnetic field interpolation, incorporating a Hilbert space representation for improved scalability and real-time updating.

Findings

Effective magnetic field mapping with Raspberry Pi robot

Successful magnetic field interpolation using smartphones

Model adapts to time-dependent magnetic field changes

Abstract

Anomalies in the ambient magnetic field can be used as features in indoor positioning and navigation. By using Maxwell's equations, we derive and present a Bayesian non-parametric probabilistic modeling approach for interpolation and extrapolation of the magnetic field. We model the magnetic field components jointly by imposing a Gaussian process (GP) prior on the latent scalar potential of the magnetic field. By rewriting the GP model in terms of a Hilbert space representation, we circumvent the computational pitfalls associated with GP modeling and provide a computationally efficient and physically justified modeling tool for the ambient magnetic field. The model allows for sequential updating of the estimate and time-dependent changes in the magnetic field. The model is shown to work well in practice in different applications: we demonstrate mapping of the magnetic field both with an inexpensive Raspberry Pi powered robot and on foot using a standard smartphone.