Exploiting Terrestrial Signals of Opportunity for LEO Smallsat Individual and Swarm Precision Navigation and Timing

James Schatzman

Abstract: Just as DORIS transmissions are exploited by DORIS system spacecraft for navigation, large numbers of uncooperative terrestrial transmissions are available and can be exploited for LEO spacecraft precision navigation and timing. For an individual spacecraft, the Doppler history of reception for several transmissions can be measured by an onboard receiver and analyzed. As several transmitters are passed by, the collection of Doppler histories can be analyzed to determine the spacecraft's orbit, even when no initial approximation is available for the orbit, when the exact as-emitted frequencies of emission are unknown, and when the onboard LO or timing reference is not perfectly stable. The requirements for this scheme to work are that the onboard LO is reasonably stable over the duration of passes by some number of transmitters, the carrier frequencies of transmission are stable during each pass, the locations of the transmitters are known, the signals' modulations admit for a suitable degree of precision for carrier frequency estimation, and that sufficiently accurate orbital propagation is available to be integrated into the analysis. No long-term (multi-pass) stability of the terrestrial transmitters is required. Suitable accuracies and stabilities, and the required number of transmitter passes are determined by simulation. For example, 6-8 transmitter passes may be sufficient; more passes increases PNT accuracy. The onboard timing reference may be of the high stability OCXO type – an atomic clock is not required. Multiple algorithms for the model fitting were evaluated including least-squares and Unscented Kalman Filters. Effectively, the scheme achieves LO stability greater than that of the transmitters by averaging many of them, after compensating for Doppler. PNT accuracy increases with the number of transmitter passes in the modeling fitting only to a certain point. It is found that there is a “sweet spot” or optimal number of passes which is approximately 50 for a DORIS-like spatial distribution of terrestrial emitters and when high accuracy orbital propagation is available, equivalent to around 3-4 revs. In practice, this may be somewhat longer than what is possible for precision orbital propagation, due mainly to the lack of suitable real time space weather data in low earth orbit. Use of multiple transmitter frequencies can support approximate ionospheric correction. For a swarm of spacecraft, carrier differential phase measurements for the same transmissions can be used to determine the relative positions and velocities of the spacecraft. This scheme can provide absolute position accuracies under 1 meter, absolute velocity accuracies under 1 mm/sec, absolute timing accuracy under ADEV 10^- 12, and relative position, velocity, and timing accuracy an order or magnitude or more below the relative accuracies. This scheme supports spacecraft PNT in the absence of GNSS. It is purely passive except in the case of the carrier differential phase data, which requires that digital IF data be passed between spacecraft for differential phase analysis. For example, this could be done via optical means. Perhaps the most challenging requirement for this scheme to be successful is that the received signals must be associated with known transmitter locations. For DORIS this is simple, since the transmission encode a station ID. For the uncooperative transmitter case, other means for uniquely identifying the transmitter identify, and therefore its location, are required.
Published in: Proceedings of the 2023 International Technical Meeting of The Institute of Navigation
January 24 - 26, 2023
Hyatt Regency Long Beach
Long Beach, California
Pages: 241 - 251
Cite this article: Schatzman, James, "Exploiting Terrestrial Signals of Opportunity for LEO Smallsat Individual and Swarm Precision Navigation and Timing," Proceedings of the 2023 International Technical Meeting of The Institute of Navigation, Long Beach, California, January 2023, pp. 241-251. https://doi.org/10.33012/2023.18599
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