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 procedure are inspired by the Global Positioning System (GPS), with the main difference being the makeup and location of the trans-mitters. Cislunar PNT utilizing sidelobe transmissions from GPS satellites, i.e., “weak GPS”, was studied in prior work and it was shown to achieve a one-shot estimation error between 200 and 300 meters under the assumption that the individual pseudorange errors do not exceed 5cm. In contrast, we consider a system in which a set of Earth-based transmitters continuously transmit a PN ranging signal similar in structure to the GPS signals, but in a dedicated frequency band. A receiver in cislunar space must acquire and track signals from four separate transmitters before solving for its position and time offset via multilateration. Similar to the weak GPS concept, this system provides a passive PNT solution for vehicles in cislunar space. We assume that the receiver is derived from state-of-the-art GPS receivers and is modified to operate in a dedicated frequency band. The main trade space for this system consists of the location, output power, and antenna gain of the ground transmitters. Intuitively, compared to the weak GPS concept, an Earth-based transmitter should allow for increased output power and antenna gain when compared to a GPS satellite, resulting in increased SNR and thus a lower positioning error. However, the decreased maximum distance between two transmitters in the PPNT scenario results in less favorable geometry and increased position dilution of precision (PDOP), causing an increase in the positioning error. In this paper, we study these aspects of the trade space in detail, with a specific 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 distance of PPNT systems, the PDOP of PPNT systems is about one order of magnitude larger than the PDOP of weak GPS. Second, the performance of a PPNT system depends on the pointing strategy used. If a receiver falls out of the main lobe of the ground transmitters, performance is severely degraded. A weak GPS-based approach outperforms PPNT with naïve pointing, i.e., with all transmitters pointing their main lobes towards the moon, for most reasonable power levels. However, if the transmitters can keep the receiver with their main lobes, PPNT systems outperform weak GPS due to the advantage in SNR. In this case, a PPNT system is limited only by the decrease in PDOP and the combined effect of atmospheric and control segment errors; the SNR does not present a limit.