Determining position around an asteroid using communication relays and trilateration

In this paper we consider the possibility of using a communications system that is operating between probes on the surface of an asteroid and an orbiting satellite to determine their relative spatial positions. This is accomplished by measuring the round trip communication delay between the orbiter and various surface probes to estimate distance and, thus, the position. By measuring the time it takes for a signal to be transmitted from the spacecraft, received by the surface probe, and then retransmitted back to the spacecraft, it is possible to get reasonable distance estimates without the need for high-precision, synchronized clocks on the surface probes. From these distance measurements, position can be determined using trilateration - the same basic technique behind the earth-based GPS system.