Identification of the orbit semi-major axis using frequency properties of onboard magnetic field measurements

In this paper a novel algorithm for estimating the satellite's semi-major axis is presented. The procedure makes solely use of measurements of the magnitude of the magnetic field and it is therefore independent of the satellite's attitude. Relying on the fact that the orbital motion is nearly periodic in nature and that the Earth's magnetic field has a spherical harmonic behavior, the magnetic signal measured on board is analyzed in the frequency domain. The identification procedure calculates characteristic frequencies of the satellite motion from the magnetic spectrum and relates them to the orbit semi-major axis. Simulations, hardware-in-the loop and real data analyses have been performed. They prove that the algorithm is capable of estimating the semi-major axis well within 1 km for a broad range of orbits. Considering the tiny requirements in terms of measurement and computational burdens, the procedure looks appealing especially for very small satellites.