  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.

Machine Learning;Machine Learning