Passive Positioning, Navigation, and Timing (PPNT) in Cislunar Space using Earth-based Transmitters

We study the feasibility of a passive system for Positioning,Navigation, and Timing (PPNT) in the cislunar environment.The signal structure and position estimation procedureare inspired by the Global Positioning System (GPS), with themain difference being the makeup and location of the transmitters.Cislunar PNT utilizing sidelobe transmissions fromGPS satellites, i.e., “weak GPS”, was studied in prior work andit was shown to achieve a one-shot estimation error between200 and 300 meters under the assumption that the individualpseudorange errors do not exceed 5cm.In contrast, we consider a system in which a set of Earth-basedtransmitters continuously transmit a PN ranging signal similarin structure to the GPS signals, but in a dedicated frequencyband. A receiver in cislunar space must acquire and tracksignals from four separate transmitters before solving for itsposition and time offset via multilateration. Similar to theweak GPS concept, this system provides a passive PNT solutionfor vehicles in cislunar space. We assume that the receiver isderived from state-of-the-art GPS receivers and is modified tooperate in a dedicated frequency band. The main trade space forthis system consists of the location, output power, and antennagain of the ground transmitters. Intuitively, compared to theweak GPS concept, an Earth-based transmitter should allowfor increased output power and antenna gain when comparedto a GPS satellite, resulting in increased SNR and thus a lowerpositioning error. However, the decreased maximum distancebetween two transmitters in the PPNT scenario results in lessfavorable geometry and increased position dilution of precision(PDOP), causing an increase in the positioning error. In thispaper, we study these aspects of the trade space in detail, with aspecific focus on the impact of the transmitter-to-user geometry,i.e., PDOP, on the positioning error.The main findings of this study can be summarized as follows.First, due to the limited maximum inter-transmitter distanceof PPNT systems, the PDOP of PPNT systems is about oneorder of magnitude larger than the PDOP of weak GPS. Second,the performance of a PPNT system depends on the pointingstrategy used. If a receiver falls out of the main lobe of theground transmitters, performance is severely degraded. A weakGPS-based approach outperforms PPNT with naïve pointing,i.e., with all transmitters pointing their main lobes towardsthe moon, for most reasonable power levels. However, if thetransmitters can keep the receiver with their main lobes, PPNTsystems outperform weak GPS due to the advantage in SNR. Inthis case, a PPNT system is limited only by the decrease in PDOPand the combined effect of atmospheric and control segmenterrors; the SNR does not present a limit.