Surrogate modeling with Genetic Programming applied to satellite communication and ground stations

In satellite missions, there are many complex factors requiring complex software or hardware design; for example: orbital calculation, Doppler shift correction. In optimization and computer aided design, the use of surrogate models has been increasing lately. These models replace a complex calculation or simulation by a simpler one, with good approximation. Neural Networks, Support Vector Machines and DACE models have been used, but Genetic Programming is another way to create surrogate models and little research has been done about it. An advantage of using simpler models in small satellite missions, such as Cubesats, is that they are less demanding regarding circuits (both in money and in power consumption) and memory. If the approximation is good, the surrogate model could be enough. These savings could be multiplied by a factor of 20 or more if the surrogate models are applied into constellations of small satellites, with 20 or more individual satellites involved. In this paper, Genetic programming is compared against Neural Networks for creating surrogate models for orbital calculations and Doppler shift. The models are created by machine learning, that is, the method takes a set of experimental or calculated samples and it uses them to create a model that approximates those samples. Genetic Programming uses an evolutionary approach that evolves trees representing non-structured mathematical functions formed from a alphabet of basic operations (in this paper: constants, +, -, *, /, sin, cos, log, exp). The main metrics of success are the maximum absolute error, the MAE (medium absolute error) and RMSE (root mean square error) against a bigger set of validation samples.