Modeling and interpolation of the ambient magnetic field by Gaussian\n processes

Abstract

Anomalies in the ambient magnetic field can be used as features in indoor\npositioning and navigation. By using Maxwell's equations, we derive and present\na Bayesian non-parametric probabilistic modeling approach for interpolation and\nextrapolation of the magnetic field. We model the magnetic field components\njointly by imposing a Gaussian process (GP) prior on the latent scalar\npotential of the magnetic field. By rewriting the GP model in terms of a\nHilbert space representation, we circumvent the computational pitfalls\nassociated with GP modeling and provide a computationally efficient and\nphysically justified modeling tool for the ambient magnetic field. The model\nallows for sequential updating of the estimate and time-dependent changes in\nthe magnetic field. The model is shown to work well in practice in different\napplications: we demonstrate mapping of the magnetic field both with an\ninexpensive Raspberry Pi powered robot and on foot using a standard smartphone.\n