Three-dimensional reconstruction of a comet nucleus by optimal control of Maxwell´s equations: A contribution to the experiment CONSERT onboard space craft Rosetta

COmet Nucleus Sounding Experiment by Radio Wave Transmission (CONSERT) is one of 20 experiments onboard the ESA mission Rosetta and aimed at the reconstruction of the unknown internal material parameter distribution of a comet nucleus. The details on the experiment setup can be found in [1], [2]. CONSERT consists of a lander module which attaches to the surface of the comet and an orbiter module which circulates the comet in space. An electromagnetic sounding of the comet nucleus will be achieved by a signal link between the lander and orbiter antenna system. We propose an optimal control approach to solve for the unknown 3D material parameter distribution of the comet nucleus. We optimize the computed electromagnetic field distribution at the receiver locations for the measured (observed) electromagnetic field distribution by controlling the material parameters. The target functional, the difference between computed and observed field for all receiver locations and time steps is minimized by means of a gradient-based quasi-Newton optimization algorithm. The optimal control problem is solved if the target functional yields its global minimum.