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Research ArticleOriginal Article
Open Access

Time Transfer From GPS for Designing a SmallSat-Based Lunar Navigation Satellite System

Sriramya Bhamidipati, Tara Mina, and Grace Gao
NAVIGATION: Journal of the Institute of Navigation September 2022, 69 (3) navi.535; DOI: https://doi.org/10.33012/navi.535
Sriramya Bhamidipati
Stanford University
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Tara Mina,
Stanford University
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Grace Gao
Stanford University
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  • FIGURE 1
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    FIGURE 1

    GPS signal at lunar distances is received from the sidelobes and small parts of the main lobe; the received C/N0 depends on the gain pattern and power of the GPS satellite’s transmit antenna, occultation from Earth and the Moon, and free-space path loss.

  • FIGURE 2
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    FIGURE 2

    Architecture of our proposed time transfer from GPS that utilizes intermittently available GPS signals to correct the lower-grade clocks onboard the LNSS satellite

  • FIGURE 3
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    FIGURE 3

    High-level architecture of our timing filter; the LNSS satellite is equipped with a lower-grade clock and utilizes a GPS receiver with position and velocity aiding to correct for clock bias and drift errors.

  • FIGURE 4
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    FIGURE 4

    Our simulated setup with a) 31 GPS satellites and corresponding antenna gain patterns for b) Block IIR, c) IIRM, and d) IIF satellites; note that we only model off-boresight angles greater than 16°, which are not occluded by Earth.

  • FIGURE 5
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    FIGURE 5

    Illustration of three ELFOs considered for validating our proposed time-transfer technique, where ELFO #1 is at an altitude of 6,541.4 km, ELFO #2 is at 7,500 km, and ELFO #3 is at 9,750.5 km

  • FIGURE 6
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    FIGURE 6

    Our simulated spaceborne GPS receiver is equipped with a high-gain steering receiver antenna with 14 dBi at 0° off-boresight angle and a 3-dB beamwidth of 12.2°

  • FIGURE 7
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    FIGURE 7

    Received C/N0 from GPS PRN 7 at ELFO #1 simulated in STK; we observed intermittent availability of the GPS signal (i.e., when C/N0 lies above the 15 dB-Hz threshold).

  • FIGURE 8
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    FIGURE 8

    GPS satellite visibility (blue lines) and maximum ECOP (red bars) across ELFOs; ELFO #1 achieves the least maximum ECOP of 3,060 s (at ≈ 6.6157 days), while ELFO #3 had the greatest overall percentage of satellite visibility (≥ 1 satellite) at 99.2%

  • FIGURE 9
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    FIGURE 9

    Clock bias and drift errors across ELFOs for σeph, LNSS = 3 m; red bars indicate ELFO #1 ECOP regions. ELFO #2 exhibits the least maximum clock bias and drift errors of 0.26 μs and 0.24 ns/s, respectively.

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    TABLE 1

    Individual Error Components Considered for the Lunar UERE Formulation

    LNSS segmentError components (based on GPS UERE)Lunar UERE (based on 1σ error)
    Space/ControlBroadcast clockσclk, LNSS
    Differential group delayσgd, LNSS
    Broadcast ephemerisσeph, LNSS
    UserIonospheric delay-
    Tropospheric delay-
    Receiver noise and resolutionσrec, LNSS
    Multipath effects-
    • Note: This includes errors due to the broadcast clock, differential group delay, broadcast ephemeris, and receiver noise and resolution; other components, namely multipath effects, ionospheric delays, and tropospheric delays are considered to be negligible for the lunar environment.

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    TABLE 2

    Keplarian Parameters Associated With Three ELFOs Considered for an LNSS Satellite

    ELFO No.Altitude (km)EccentricityInclination (°)Argument of Perigee (°)RAAN (°)Mean Anomaly (°)
    #16,541.40.6056.29000
    #27,500.00.0540.09000
    #39,750.50.7065.59000
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    TABLE 3

    Comparison Analysis of Satellite Visibility and Maximum ECOP Across ELFOs

    ELFO No.Max ECOP (s)Satellite Visibility (%)
    ≥ 1≥ 4
    13,06098.188.0
    24,02098.888.6
    33,36099.292.1
    • Note: ELFO #1 exhibits the least value of maximum ECOP, while ELFO #3 exhibits the maximum duration of satellite visibility.

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    TABLE 4

    Comparison Analysis of Lunar UERE Across Three ELFOs for σeph, LNSS = 3 m With a CSAC Onboard the LNSS Satellite

    ELFO No.RMS timing error of CSACLunar UERE (m)
    Bias (m)Drift (m/s)
    18.511.37 × 10−29.02
    28.031.35 × 10−28.58
    37.941.32 × 10−28.49
    • Note: The estimated lunar UERE across all ELFOs had a comparable order of magnitude to that of the GPS UERE. Note that unlike Figure 9 that showcases maximum timing errors, this table reports the RMS errors with units of clock bias listed in m and that of clock drift in m/s.

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    TABLE 5

    Sensitivity Analysis of Lunar UERE Across Three ELFOs as the Broadcast Ephemeris Errors are Varied as σeph, LNSS = 0.3 m, σeph, LNSS = 3 m, σeph, LNSS = 30 m, and σeph, LNSS = 300 m

    ELFO no.Lunar UERE (m)
    0.3 m3 m30 m300 m
    15.669.0242.41766.66
    25.608.5841.13768.80
    35.308.4941.10752.05
    • Note: The estimated lunar UERE across all ELFOs exhibited a near-quadratic decrease in value as the broadcast ephemeris error decreased.

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NAVIGATION: Journal of the Institute of Navigation: 69 (3)
NAVIGATION: Journal of the Institute of Navigation
Vol. 69, Issue 3
Fall 2022
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Time Transfer From GPS for Designing a SmallSat-Based Lunar Navigation Satellite System
Sriramya Bhamidipati, Tara Mina,, Grace Gao
NAVIGATION: Journal of the Institute of Navigation Sep 2022, 69 (3) navi.535; DOI: 10.33012/navi.535

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Time Transfer From GPS for Designing a SmallSat-Based Lunar Navigation Satellite System
Sriramya Bhamidipati, Tara Mina,, Grace Gao
NAVIGATION: Journal of the Institute of Navigation Sep 2022, 69 (3) navi.535; DOI: 10.33012/navi.535
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  • Article
    • Abstract
    • 1 INTRODUCTION
    • 2 PROPOSED TIME TRANSFER FROM GPS TO LNSS
    • 3 MODELING THE LUNAR SIMULATION SETUP
    • 4 EXPERIMENTAL RESULTS AND ANALYSIS
    • 5 CONCLUSION
    • HOW TO CITE THIS ARTICLE
    • ACKNOWLEDGMENTS
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  • Resilience Monitoring for Multi-Filter All-Source Navigation Framework With Assurance
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Keywords

  • GPS
  • lunar navigation satellite system
  • time transfer

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