Online One-Dimensional Magnetic Field SLAM with Loop-Closure Detection

Abstract

We present a lightweight magnetic field simultaneous localisation and mapping (SLAM) approach for drift correction in odometry paths, where the interest is purely in the odometry and not in map building. We represent the past magnetic field readings as a one-dimensional trajectory against which the current magnetic field observations are matched. This approach boils down to sequential loop-closure detection and decision-making, based on the current pose state estimate and the magnetic field. We combine this setup with a path estimation framework using an extended Kalman smoother which fuses the odometry increments with the detected loop-closure timings. We demonstrate the practical applicability of the model with several different real-world examples from a handheld iPad moving in indoor scenes.

Figures (5)

• Figure 1: Illustration of our method with top left (green) ground truth, top middle (red) odometry, top right (blue) estimation results. The blue circles indicate the locations at which loop closures are detected. In the bottom, we twice visualise the magnetic field measurements (in a body-fixed frame) over time, above and below the black dashed line. In grey we indicate the locations where the magnetic field is detected to be similar in which we use loop closures in our algorithm.
• Figure 2: Results on empirical proof-of-concept data with (top left) the trajectory including circles indicating the locations of detected loop closures, and (bottom and top right) the weights $w_{\text{m},t}^\text{fwd}$ in red, $w_{\text{p},t}$ in blue and the overall weights $w_t$ used for loop closures in black. These weights are shown for the entire trajectory (bottom) and zoomed in (top right).
• Figure 3: Results on empirical proof-of-concept data with (top) the trajectory including circles indicating the locations of detected loop closures, (middle) the weights $w_{\text{m},t}^\text{fwd}$ in red, $w_{\text{p},t}$ in blue and the overall weights $w_t$ used for loop closures in black, and (bottom) the magnetic field measurements in microtesla.
• Figure 4: Position RMSEs of 100 Monte Carlo simulations for different odometry accuracies: Varying gyroscope bias $b_\omega$ (left), varying position noise variance $\sigma^2_\text{p}$ (middle) and varying angular velocity noise variance $\sigma^2_\omega$ (right).
• Figure 5: Illustration of our method with top left (green) ground truth, top middle (red) odometry, top right (blue) estimation results. In the bottom, we twice visualise the magnetic field measurements over time, above and below the black dashed line. In grey we indicate the locations where the magnetic field is detected to be similar, resulting in loop closures in \ref{['alg:slam']}.