This thesis scales methods for Gaussian process-based magnetic field mapping and localization
in five distinct ways.@en

Accurately estimating the positions of multi-agent systems in indoor environments is challenging due to the lack of Global Navigation Satelite System (GNSS) signals. Noisy measurements of position and orientation can cause the integrated position estimate to drift without bound. Previous research has proposed using magnetic field simultaneous localization and mapping (SLAM) to compensate for position drift in a single agent. Here, we propose two novel algorithms that allow multiple agents to apply magnetic field SLAM using their own and other agents' measurements.Our first algorithm is a centralized approach that uses all measurements collected by all agents in a single extended Kalman filter. This algorithm simultaneously estimates the agents' position and orientation and the magnetic field norm in a central unit that can communicate with all agents at all times. In cases where a central unit is not available, and there are communication drop-outs between agents, our second algorithm is a distributed approach that can be employed.We tested both algorithms by estimating the position of magnetometers carried by three people in an optical motion capture lab with simulated odometry and simulated communication dropouts between agents. We show that both algorithms are able to compensate for drift in a case where single-agent SLAM is not. We also discuss the conditions for the estimate from our distributed algorithm to converge to the estimate from the centralized algorithm, both theoretically and experimentally. Our experiments show that, for a communication drop-out rate of 80%, our proposed distributed algorithm, on average, provides a more accurate position estimate than single-agent SLAM. Finally, we demonstrate the drift-compensating abilities of our centralized algorithm on a real-life pedestrian localization problem with multiple agents moving inside a building.

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In this paper, a simultaneous localization and mapping algorithm for tracking the motion of a pedestrian with a foot-mounted inertial measurement unit is proposed. The algorithm uses two maps, namely, a motion map and a magnetic field map. The motion map captures typical motion patterns of pedestrians in buildings that are constrained by e.g. corridors and doors. The magnetic map models local magnetic field anomalies in the environment using a Gaussian process model and uses them as position information. These maps are used in a Rao-Blackwellized particle filter to correct the pedestrian position and orientation estimates from the pedestrian dead-reckoning. The pedestrian dead-reckoning is computed using an extended Kalman filter with zero-velocity updates. The algorithm is validated using experimental sequences and the results show the efficacy of the algorithm in localizing pedestrians in indoor environments.@en

In this work, our focus is on indoor localization using the indoor magnetic field as a source of position information. This relies on the fact that ferromagnetic materials inside buildings cause the magnetic field to vary spatially. We jointly estimate the pose of a combined sensor module (containing a magnetometer) as well as the magnetic field map. We show that our previously developed algorithm for magnetic field-based simultaneous localization and mapping can be adapted and extended into a general framework where a multitude of measurements can be included. We exemplify this using a foot-mounted inertial measurement unit where we additionally assume the availability of range measurements.@en

We present a computationally efficient algorithm for using variations in the ambient magnetic field to compensate for position drift in integrated odometry measurements (dead-reckoning estimates) through simultaneous localization and mapping (SLAM). When the magnetic field map is represented with a reduced-rank Gaussian process (GP) using Laplace basis functions defined in a cubical domain, analytic expressions of the gradient of the learned magnetic field become available. An existing approach for magnetic field SLAM with reduced-rank GP regression uses a Rao-Blackwellized particle filter (RBPF). For each incoming measurement, training of the magnetic field map using an RBPF has a computational complexity per time step of O(NpN2m), where Np is the number of particles, and Nm is the number of basis functions used to approximate the Gaussian process. Contrary to the existing particle filter-based approach, we propose applying an extended Kalman filter based on the gradients of our learned magnetic field map for simultaneous localization and mapping. Our proposed algorithm only requires training a single map. It, therefore, has a computational complexity at each time step of O(N2m). We demonstrate the workings of the extended Kalman filter for magnetic field SLAM on an open-source data set from a foot-mounted sensor and magnetic field measurements collected onboard a model ship in an indoor pool. We observe that the drift compensating abilities of our algorithm are comparable to what has previously been demonstrated for magnetic field SLAM with an RBPF. @en

We propose an application of magnetic field norm simultaneous localisation and mapping to measurements from a foot-mounted sensor for pedestrian navigation. The algorithm is, to the best of the authors’ knowledge, the first three dimensional drift-compensating indoor navigation method using only accelerometer, gyroscope and magnetometer measurements that does not rely on assumptions about the spatial structure of the indoor environment. We use a Rao-Blackwellized particle filter to simultaneously and recursively estimate the magnetic field norm map using reduced rank Gaussian process regression, and the position and orientation of the sensor. Our experiments demonstrate that our algorithm results in a drift-free position estimate using measurements collected from a foot-mounted sensor while walking around inside a hallway.@en