Feasibility of “Weak GPS” Real-Time Positioning and Timing at Lunar Distance

There are multiple Global Navigation Satellite Systems (GNSS's), comprising over 100 navigation satellites in the Earth's medium and high orbits. Most of these satellites have antennas that point nadir to earth, and transmit navigation signals so vehicles on Earth's surface and in its vicinity can perform trilateration and estimate its 3-dimenional (3D) positioning. The sidelobes of these antennas can occasionally point to the Moon. It is postulated that a lunar vehicle carrying a large enough receiving antenna can occasionally detects and receives four or more sidelobes of these weak GNSS signals, thus enabling the vehicle to perform 3D positioning using an onboard GNSS receiver. We propagate the orbits of the GNSS satellites from United States' Global Positioning Satellite (GPS) constellation, the Europe's Galileo constellation, and the Russia's GLONASS constellation, to a total of 81 satellites. We simulate the visibility of these satellites by a lunar vehicle in a Near Rectilinear Halo Orbit (NRHO), based on the assumption that the lunar vehicle is “in-view” of a GNSS satellite as long as it falls within the 40-degree beam width of the satellite. We also simulate the 3D positioning performance as a function of satellites' ephemeris errors and pseudo-range errors. The preliminary results show that the lunar vehicle can “see” 5 - 13 satellites, and achieve a 3D positioning error (one-sigma) of 200-300 meters based on reasonable ephemeris and pseudorange error assumptions. We also consider the case of using relative positioning to mitigate the GNSS satellites' ephemeris biases; that is, we assume a reference receiver with accurately known positioning that is close to the lunar vehicle and then compute the relative position of the lunar vehicle with respect to the reference.