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.

翻译：我们提出一种利用近似高斯过程回归在室内环境中计算大规模磁场地图的映射算法。利用环境磁场空间变化信息可用于室内区域的定位算法。高斯过程回归因能提供新位置处磁场预测及其不确定性量化，成为构建此类地图的理想工具。由于全高斯过程回归的计算复杂度与数据点数量呈三次方增长，其近似方法已得到广泛研究。本文基于结构化核插值框架，通过高效利用Krylov子空间方法加速推理过程。具体而言，我们将含导数的结构化核插值方法集成至标量势模型用于磁场建模，并以线性于数据点数的复杂度计算预测均值和协方差。仿真结果表明，在逐渐扩大的制图区域中，本方法构建的磁场地图精度优于现有最优方法。在大规模实验中，我们可在标准笔记本电脑上于两分钟内利用多达40000个三维磁场测量值完成磁场地图构建。