An orbit determination algorithm for small satellites based on the magnitude of the earth magnetic field

Autonomous attitude determination systems based on simple measurements of vector quantities such as magnetic field and the Sun direction are commonly used in very small satellites. However, those systems always require knowledge of the satellite position. This information can be either propagated from orbital elements periodically uplinked from the ground station or measured onboard by dedicated global positioning system (GPS) receiver. The former solution sacrifices satellite autonomy while the latter requires additional sensors which may represent a significant part of mass, volume, and power budget in case of pico- or nanosatellites. Hence, it is thought that a system for onboard satellite position determination without resorting to GPS receivers would be useful. In this paper, a novel algorithm for determining the satellite orbit semimajor-axis is presented. The methods exploit only the magnitude of the Earth magnetic field recorded onboard by magnetometers. This represents the first step toward an extended algorithm that can determine all orbital elements of the satellite. The method is validated by numerical analysis and real magnetic field measurements.