Magnetic-field simultaneous localization and mapping (SLAM) using consumer-grade inertial and magnetometer sensors offers a scalable, cost-effective solution for indoor localization. However, the rapid error accumulation in the inertial navigation process limits the feasible exploratory phases of these systems. Advances in magnetometer array processing have demonstrated that odometry information, i.e., displacement and rotation information, can be extracted from local magnetic field variations and used to create magnetic-field odometry-aided inertial navigation systems. The error growth rate of these systems is significantly lower than that of standalone inertial navigation systems. This study seeks an answer to whether a magnetic-field SLAM system fed with measurements from a magnetometer array can indirectly extract odometry information - without requiring algorithmic modifications - and thus sustain longer exploratory phases. The theoretical analysis and simulation results show that such a system can extract odometry information and indirectly create a magnetic field odometry-aided inertial navigation system during the exploration phases. However, practical challenges related to map resolution and computational complexity remain significant.

Recently, it has been shown that odometry is possible only using data from a magnetometer array. In this work, we analyze the uncertainty of the pose change estimate using a magnetometer array. We derive an analytical expression for the pose change covariance to analyze the estimation uncertainty in Monte Carlo simulations. Under certain conditions, we demonstrate that using a magnetometer array, it is possible to estimate the position and orientation change with submillimeter and subdegree precision between two consecutive time-steps. Moreover, we also demonstrate that when constructing a magnetometer array, magnetometers should be placed in the direction of movement to maximize the positional and rotational precision, with at least four magnetometers per unit of length-scale. In addition, we illustrate that to minimize positional and rotational drift to under a few percentages and degrees of the distance traveled, submillimeter and subdegree magnetometer alignment errors are necessary. Similarly, bias errors smaller than a few percent of the magnitude of the magnetic field variations are necessary. The Monte Carlo simulations are verified using experimental data collected with a 30-magnetometer array. The experimental data show that when insufficient magnetic field anomalies are in close proximity, the changes in positions are estimated poorly, while significant orientation information is still obtained. It also shows that when the magnetometer array is in close proximity to sufficient magnetic field anomalies, the overall trajectory traveled by a magnetometer array can be accurately estimated with a horizontal error accumulation of less than a percentage of the distance traveled.

Ferromagnetic materials in indoor environments give rise to disturbances in the ambient magnetic field. Maps of these magnetic disturbances can be used for indoor localisation. A Gaussian process can be used to learn the spatially varying magnitude of the magnetic field using magnetometer measurements and information about the position of the magnetometer. The position of the magnetometer, however, is frequently only approximately known. This negatively affects the quality of the magnetic field map. In this paper, we investigate how an array of magnetometers can be used to improve the quality of the magnetic field map. The position of the array is approximately known, but the relative locations of the magnetometers on the array are known. We include this information in a novel method to make a map of the ambient magnetic field. We study the properties of our method in simulation and show that our method improves the map quality. We also demonstrate the efficacy of our method with experimental data for the mapping of the magnetic field using an array of 30 magnetometers.