A Stable Adaptive Observer for Hard-Iron and Soft-Iron Bias Calibration and Compensation for Two-Axis Magnetometers: Theory and Experimental Evaluation

Abstract

This letter addresses the problem of on-line estimation and compensation of the hard-iron and soft-iron biases of a 2-axis magnetometer under dynamic motion, utilizing only biased measurements from a 2-axis magnetometer. The proposed adaptive observer formulates the relation between the true magnetic field vector and the magnetometer measurements as an algebraic system where the unknown biases enter linearly. The observer is shown to be globally stable. When the magnetometer measurements are persistently exciting (PE), the system is shown to be globally asymptotically stable, and the biases are shown to converge to their true values. The estimated biases are used to provide a calibrated magnetic field direction vector which is utilized to estimate magnetic geodetic heading. The adaptive observer is evaluated in a numerical simulation and a full-scale vehicle trial. For the proposed observer: $(i)$ knowledge of the instrument attitude is not required for sensor bias estimation, $(ii)$ zero a priori knowledge of the local magnetic field vector magnitude or vector direction is needed, $(iii)$ the system is shown to be globally stable, $(iv)$ the error system is shown to be globally asymptotically stable when the measured magnetometer signal is PE. $(v)$ magnetometer hard-iron and soft-iron bias compensation is shown to dramatically improve dynamic heading estimation accuracy.