Steel studs, heating, ventilation, and air conditioning (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 handheld devices, such as 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 article, through the analysis of a large data set 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.

中文翻译：

---

身高对室内磁场定位的影响

钢钉，供暖，通风和空调（HVAC）系统，钢筋以及许多其他建筑组件会产生空间变化的磁场。磁力计可以测量这些场，并且可以与惯性传感器结合使用，以在室内定位机器人和智能手机等手持设备。当前用磁力计进行定位和映射的方法通常基于简化的假设，即磁场不会随高度变化。在本文中，通过分析在伊利诺伊大学校园内三座建筑物中收集的大量数据，我们量化了这种“平面假设”可能被违反的程度，并研究了室内定位的后果。第一的，我们显示出磁场的平面外变化在进行磁力计测量的位置的一半以上是显着的。其次，我们表明，当定位和制图均基于在相同高度进行的磁力计测量时，定位的绝对轨迹误差很小，但是即使这些高度之间的差异很小，误差也会显着增加。第三，我们表明，如果在给定的一组轨迹上求平均值，则选择测量高度（如果在定位和制图时都保持相同的高度）对绝对轨迹误差没有明显影响，尽管存在某些轨迹不同的测量高度会导致明显不同的误差。第四，