Mathematical modeling and simulation of the earth's magnetic field: A comparative study of the models on the spacecraft attitude control application

In this paper, the Earth's magnetic field models which are widely used in spacecraft attitude control applications are modeled and extensively compared with a reference model. The reference model is obtained utilizing coefficients from the last generation of International Geomagnetic Reference Field (IGRF-12). The validity of this model is verified with the World Magnetic Model (WMM) in terms of intensity and direction of the field. The reference model is then used to evaluate lower-order and approximating models while the influence of effective parameters such as expansion order of modeling, orbit height, inclination, latitude and longitude on accuracy of modeling is investigated. The simulation results for several scenarios are presented and discussed. The linear and nonlinear transformations of the models from orbital frame to spacecraft body frame are compared for a wide range of attitude angles in order to investigate the sensibility and validity of linear transformation. Simulation of a spacecraft attitude control maneuver is performed to demonstrate the importance of the accuracy of the magnetic field model which is implemented in the attitude control system. The results indicated a meaningful increase in control effort when a simplified model was used. This research was aimed to investigate the borders of different geomagnetic field models and transformations for spacecraft attitude control applications. The presented results may lead to a proper choice of the Earth's magnetic field model based on the space mission requirements.