Tetrahedral satellite formation: Geomagnetic measurements exchange and interpolation

Abstract

This note presents a study of a four-satellite tetrahedral formation to collect, process, and exchange multipoint measurements of geomagnetic field in a near-polar orbit. The study is conducted as a series of numerical experiments based on simulated spacecraft orbits and corresponding geomagnetic field models output. The four satellites are assumed to move in near-circular orbits specifically chosen to maintain the tetrahedron quality. The satellites exchange their simulated magnetometers readings and the collected multipoint measurements are processed on board of any of them thus creating an instantaneous interpolated map of the geomagnetic field in the interior of the tetrahedron. Interpolation is carried out with the use of Kriging algorithms, known in geostatistics for capturing spatial correlation of the data and taking into account statistical properties of the interpolated variables. We propose a concept of a servicing formation, and analyze interpolation accuracy for different formation sizes. It is then discussed how the processed multipoint measurements can be provided as a service to other nearby satellites. Finally, we show that using the existing COTS magnetometers it is possible to obtain real-time interpolation data, which are more precise at a given point and time than a conventional onboard magnetic field model, thus ensuring better attitude determination routines performance in the serviced spacecraft.