  We present a method for scalable and fully 3D magnetic field simultaneous
localisation and mapping (SLAM) using local anomalies in the magnetic field as
a source of position information. These anomalies are due to the presence of
ferromagnetic material in the structure of buildings and in objects such as
furniture. We represent the magnetic field map using a Gaussian process model
and take well-known physical properties of the magnetic field into account. We
build local maps using three-dimensional hexagonal block tiling. To make our
approach computationally tractable we use reduced-rank Gaussian process
regression in combination with a Rao-Blackwellised particle filter. We show
that it is possible to obtain accurate position and orientation estimates using
measurements from a smartphone, and that our approach provides a scalable
magnetic field SLAM algorithm in terms of both computational complexity and map
storage.
