Article Figures & Data
Figures
- 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
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
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
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
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
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
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
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
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.
Tables
LNSS segment Error components (based on GPS UERE) Lunar UERE (based on 1σ error) Space/Control Broadcast clock σclk, LNSS Differential group delay σgd, LNSS Broadcast ephemeris σeph, LNSS User Ionospheric delay - Tropospheric delay - Receiver noise and resolution σrec, 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.
ELFO No. Altitude (km) Eccentricity Inclination (°) Argument of Perigee (°) RAAN (°) Mean Anomaly (°) #1 6,541.4 0.60 56.2 90 0 0 #2 7,500.0 0.05 40.0 90 0 0 #3 9,750.5 0.70 65.5 90 0 0 ELFO No. Max ECOP (s) Satellite Visibility (%) ≥ 1 ≥ 4 1 3,060 98.1 88.0 2 4,020 98.8 88.6 3 3,360 99.2 92.1 Note: ELFO #1 exhibits the least value of maximum ECOP, while ELFO #3 exhibits the maximum duration of satellite visibility.
- 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 CSAC Lunar UERE (m) Bias (m) Drift (m/s) 1 8.51 1.37 × 10−2 9.02 2 8.03 1.35 × 10−2 8.58 3 7.94 1.32 × 10−2 8.49 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.
- 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 m 3 m 30 m 300 m 1 5.66 9.02 42.41 766.66 2 5.60 8.58 41.13 768.80 3 5.30 8.49 41.10 752.05 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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