Is 9D localization possible with unsynchronized LEO Satellites?

In this paper, we ask if 9D localization (3D position, 3D velocity, and 3D orientation estimation) is possible with the signals received from low earth orbit (LEO) satellites. To answer this question, we define a system model that captures i) the possibility of a time offset between LEOs caused by having cheap synchronization clocks, ii) the possibility of a frequency offset between LEOs, and iii) multiple transmission time slots from a particular LEO. We transform the Fisher information matrix (FIM) for the channel parameters to the FIM for the location parameters and show the possible localization conditions. Subsequently, we derive the FIM for the 9D localization (3D position, 3D orientation, and 3D velocity estimation) in terms of the FIM for the 3D localization. With these derivations, we show that even in the presence of time and frequency offsets between the LEOs, it is possible to perform 9D localization (3D position, 3D velocity, and 3D orientation estimation) of a receiver by utilizing the signals from three LEO satellites observed during three transmission time slots received through multiple receive antennas.