On Calibration of Three-Axis Magnetometer

Abstract

Abstract-Magnetometer has received wide applications in attitude determination and scientific measurements. Calibration is an important step for any practical magnetometer use. The most popular three-axis magnetometer calibration methods are attitude-independent and have been founded on an approximate maximum likelihood estimation (ML) with a quartic subjective function, derived from the fact that the magnitude of the calibrated measurements should be constant in a homogeneous magnetic field. This paper highlights the shortcomings of those popular methods and proposes to use the quadratic optimal ML estimation instead for magnetometer calibration. Simulation and test results show that the optimal ML calibration is superior to the approximate ML methods for magnetometer calibration in both accuracy and stability, especially for those situations without sufficient attitude excitation. The significant benefits deserve the moderately increased computation burden. The main conclusion obtained in the context of magnetometer in this paper is potentially applicable to various kinds of three-axis sensors.

On Misalignment Between Magnetometer and Inertial Sensors

“…However, end users prefer to an in-situ calibration with no requirement of external equipment. This practical demand gives birth to a class of attitude-independent calibration methods [2,[8][9][10][11][12][13], first proposed in public literature by [11,12] and becoming popular in the last decade. These methods exploit the fact that the magnitude of magnetometer measurement is constant regardless of the orientation at the local position.…”

“…This paper focuses the cross-sensor calibration problem, and the three-axis magnetometer and the three-axis gyroscope are assumed having been intrinsically calibrated in their separate sensor frames by appropriate attitude-independent methods [2,8,10]. Figure 1 illustrates the magnetometer senor frame ( * m -frame) and the gyroscope sensor frame (b-frame), defined by the their sensors' physical sensitivity axes.…”

“…Among the three kinds of sensors, magnetometer requires special attention as it is prone to the magnetic disturbance in the surrounding environment, such as the ferromagnetic material and strong electric currents. When the magnetometer is placed rigidly on or near to ferromagnetic objects, its output is distorted and cannot measure the external magnetic field, so careful calibration is necessary each time the magnetometer is used [2]. The distortion can be divided into hard iron and soft iron effects.…”

Magnetometer Calibration Using Inertial Sensors

“…[9], [10]. Outside of these two classes, a large number of other calibration approaches is also available, for instance [11], where different formulations of the calibration problem in terms of an ML problem are considered.…”

“…To obtain a correct calibration, it is fortunately not necessary to identify all individual contributions of the different components in (11). Instead, they can be combined into a 3×3 distortion matrix D and a 3 × 1 offset vector o where…”