Saying goodbyes to rotating your phone: Magnetometer calibration during SLAM

TL;DR

This work tackles magnetometer bias as a major impediment to MF-based indoor SLAM by introducing SLAMnC, a Rao-Blackwellized particle filter that performs simultaneous localization, mapping, and bias calibration without requiring a pre-collected MF map. Each particle maintains its own map and a bias estimate, with a per-particle Kalman filter updating the bias as loop closures occur; MF residuals guide the bias refinement while the map grows analytically from the trajectory. The approach is validated on smartphone data from a shopping mall and mobile-robot data from office/apartment environments, showing convergence of the bias to values comparable to manually calibrated references and MF map consistency similar to or better than OS-calibrated baselines. The results suggest that magnetometer calibration can be effectively integrated into SLAM, enabling robust indoor positioning when manual calibration is impractical and paving the way for combining calibration with other modalities in diverse platforms.

Abstract

While Wi-Fi positioning is still more common indoors, using magnetic field features has become widely known and utilized as an alternative or supporting source of information. Magnetometer bias presents significant challenge in magnetic field navigation and SLAM. Traditionally, magnetometers have been calibrated using standard sphere or ellipsoid fitting methods and by requiring manual user procedures, such as rotating a smartphone in a figure-eight shape. This is not always feasible, particularly when the magnetometer is attached to heavy or fast-moving platforms, or when user behavior cannot be reliably controlled. Recent research has proposed using map data for calibration during positioning. This paper takes a step further and verifies that a pre-collected map is not needed; instead, calibration can be done as part of a SLAM process. The presented solution uses a factorized particle filter that factors out calibration in addition to the magnetic field map. The method is validated using smartphone data from a shopping mall and mobile robotics data from an office environment. Results support the claim that magnetometer calibration can be achieved during SLAM with comparable accuracy to manual calibration. Furthermore, the method seems to slightly improve manual calibration when used on top of it, suggesting potential for integrating various calibration approaches.

Figures (9)

• Figure 1: Two-axis projections of the magnetic field signal during a calibration movement (top) and a trajectory in a shopping mall (bottom), illustrated in Fig. \ref{['fig:calib_estimation']}. The color indicates time in seconds. Bias $\mathbf{b} \in \mathbb{R}^3$ can be extracted from the calibration movement using sphere fitting methods. This paper demonstrates bias estimation from natural walk data.
• Figure 2: A pre-collected MF map and a mobile robot trajectory from DLR's laboratory from Siebler et al's work on Simultaneous Localization and Calibration (SLAC) siebler2023magnetic_robot. The authors are able to estimate the bias during positioning by using a factorized PF and a KF. Permission for reuse granted by IEEE (©2023 IEEE).
• Figure 3: (a-b) Estimated trajectory collected from a shopping mall and the produced MF map. (c) Corresponding bias estimation by particle-wise Kalman Filters. The dashed line is bias reported by the operating system. The band depicts three times the standard deviation of the bias over the particles.
• Figure 4: 2D map estimate construction at $d_{\text{curr}}$ from data points $d_1, d_2, d_3$. First, the calibration is applied to all data points. Then the readings are rotated to the world frame, in which the map estimate is computed (in this example the mean of kNN). Finally, the map estimate is rotated to $d_{\text{curr}}$ sensor frame, where it is used to obtain the residual for the PF and KF (vector difference inside the dashed circle).
• Figure 5: St James Quarter shopping mall in Edinburgh. Trajectories eight_1 and full from our shopping mall data set. Trajectory eight_2 is visualised in \ref{['fig:calib_estimation_traj']}.