The Impact of Height on Indoor Positioning with Magnetic Fields

Steel studs, HVAC systems, rebar, and many other building components produce spatially varying magnetic fields. Magnetometers can measure these fields and can be used in combination with inertial sensors for indoor positioning of robots and of handheld devices like smartphones. Current methods of localization and mapping with magnetometers are often based on the simplifying assumption that magnetic fields do not vary with height. In this paper, through analysis of a large dataset collected across three buildings on the University of Illinois campus, we quantify the extent to which this "planar assumption" is likely to be violated and examine the consequences for indoor positioning. First, we show that out-of-plane variations in the magnetic field were significant at over half the locations where magnetometer measurements were taken. Second, we show that absolute trajectory error in positioning was low when both localization and mapping were based on magnetometer measurements taken at the same height, but that error increased significantly with even small differences between these heights. Third, we show that the choice of height at which to take measurements---if this height was kept the same for both localization and mapping---had no significant impact on absolute trajectory error when averaged across a given set of trajectories, although some trajectories existed for which different measurement heights led to significantly different errors. Fourth, we show that absolute trajectory error decreased when magnetometer measurements were aggregated across a small range of heights to produce a single, planar map and when measurements at the median height were used for localization.