Position and Orientation Estimation Uncertainty Using Magnetometer Arrays for Indoor Localization

Abstract

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.