Gaussian process for modelling the space environment from sparse data collected by massively distributed femtosatellite networks

Femtosatellites are an emerging spacecraft class characteristic for having a mass of less than 100 g, which makes them a competitive design choice for applications that require large spacecraft swarms. With their small mass enabling unprecedentedly large sensor networks in orbit for a relatively low cost, femtosatellite swarms have been proposed for massively distributed in-situ parallel sensing. While simulated missions have shown promising results in prior publications, the data generated by such systems presents challenges in processing that must be addressed; namely, data operations become intractable as the size of the swarm increases, measurements are sparse relative to the size of the volume being monitored, and any attempt to reconstruct an image from the data must address multiple input parameters. In this paper we demonstrate a way forward in these issues by the use of Gaussian Processes Regression to model the environment from data generated by distributed femtosatellite systems, after which the models are applied for interpolation to reconstruct the environment around the swarm. Both a spatial and a spatio-temporal model are constructed from measurements of a magnetic field in low Earth orbit, which were generated from a simulated femtosatellite mission. Both models were able to successfully demonstrate the ability to reconstruct field features from sparse data, with worsening performance in very low swarm density cases.