Article Figures & Data
Figures
- FIGURE 1
Example design choices, namely, the satellite clock, constellation size, and orbit, to be finalized during the design of a SmallSat-based LNCSS
- FIGURE 2
Architecture of this work’s SmallSat-based LNCSS with Earth-GPS time transfer that provides both navigation and communication services at the lunar south pole region
In this hybrid constellation design, only a few satellites among the LNCSS constellation are enabled to provide communication services, while all of the LNCSS satellites provide navigation services.
- FIGURE 3
Illustration of the navigation design criteria and their dependency on two performance metrics, namely, lunar UERE and GDOP
- FIGURE 4
Data communication between the lunar surface and Earth consists of two data links: One between the LNCSS and Earth (via the Ka-band) and one between the LNCSS and the lunar user (via the S-band)
Both data links together influence the total amount of daily data transfer possible between the lunar surface and Earth, also called the daily data volume.
- FIGURE 5
Three LNCSS case studies of a hybrid constellation type considered. All satellites provide navigation services and only 25% (highlighted in orange) provide both navigation and communication services (a) Case A: 6 navigation-only satellites and 2 navigation+communication-enabled satellites (b) Case B: 9 navigation-only satellites and 3 navigation+communication-enabled satellites (c) Case C: 12 navigation-only satellites and 4 navigation+communication-enabled satellites
The trade-off performance among case studies is analyzed in terms of design criteria and performance metrics for navigation and communication services, as well as SmallSat factors.
- FIGURE 6
Timing estimation errors in the Earth-GPS time-transfer filter architecture for an LNCSS satellite in an ELFO with an onboard CSAC, where a) demonstrates the clock bias errors for the entire experiment duration and b) demonstrates the zoomed-in errors for a smaller time segment of 1 day
An RMS error of σclk, LNCSS = 2.37 m is demonstrated in the Earth-GPS time transfer, based on which the lunar UERE is computed as σUERE,LNCSS = 3.86 m. The red vertical bars indicate regions of ECOP (i.e., no Earth-GPS satellites are visible).
- FIGURE 7
GDOP variation in the lunar south pole region for case C, with an elevation mask of 20°
For intuition, a few prominent craters in the lunar south pole region are also marked, namely, the Shoemaker, Shackleton, and Haworth craters. As expressed in Table 5, the worst-case grid point has an average GDOP of 7.24 for 20°.
- FIGURE 8
Variation in the minimum availability per day tS of one LNCSS communication satellite across the lunar south pole region (greater than 80° S latitudes) for case C, with an elevation mask of 20°
For intuition, a few prominent craters are also marked, namely, the Shoemaker, Shackleton, and Haworth craters.
Tables
- TABLE 1
Orbital Parameters Represented in the OP Frame for the Three LNCSS Constellation Case Studies The short-hand notation x : y : z indicates a series generated within the closed interval [x, z], with spacing between values given by y. Note that for any case study, all combinations of the RAAN and mean anomaly series are considered to generate the orbital parameters: e.g., the 8 satellites in case study A are given by the following [RAAN, mean anomaly] pairs: [0, 0], [0, 90], [0, 180], [0, 270], [180, 0], [180, 90], [180, 180], [180, 270].
LNCSS Case Study No. of Satellites Semi-Major Axis a (km) Eccentricity e Inclination i (deg) Argument of Perigee ω(deg) RAAN Ω Mean Anomaly M A 8 6143 0.6 51.7 90 0:180:180 0:90:270 B 12 6143 0.6 51.7 90 0:90:270 0:120:240 C 16 6143 0.6 51.7 90 0:180:180 0:45:315 - TABLE 2
Communication System Parameters Used for Computing the Attainable Data Rate for Transfer Between the LNCSS Satellite and Earth
Parameter Value Transmission frequency ftx (GHz) 27 Transmission power Ptx (W) 4.8 Receiver gain Grx (dB) 55 Phase modulation index β(°) 60 Noise temperature Trx (K) 29.2 Antenna efficiency 0.6 Antenna diameter (m) 1 - TABLE 3
Breakdown of Payload Equipment Onboard a Navigation-Only Satellite, with a CSAC as the Satellite Clock and the Corresponding Power Requirements (Parker et al., 2022; Pereira & Selva, 2020; Schmittberger & Scherer, 2020; Wertz et al., 2011)
Payload Required Power (W) Microchip CSAC (two units) 0.2 Earth-GPS receiver 14.7 Navigation signal generation unit 35 Frequency generation and upconversion unit 22 Remote terminal unit 12 Total payload power, Ppayload–nav 83.9 - TABLE 4
Navigation Service Performance Comparison for an Elevation Mask of 5°, with Lunar UERE σUERE,LNCSS = 3.86 m The columns of mean performance denote the mean RMS error (RMSE) across the array of grid points, whereas the columns of max performance denote the RMSE of the worst-case grid point for each case study. See Section 3.2.3) for details on how the performance metrics and design criteria are computed.
LNCSS Case Study (# sats) Performance metrics: At worst user grid point Design criteria: Avg across user grid points Availability (%) Failure Tolerance (%) Coverage (%) GDOP Horizontal Position RMSE (m) Vertical Position RMSE (m) Receiver Timing RMSE (μs) Mean Max Mean Max Mean Max A (8) 100 97.9 100 8.95 5.62 61.62 15.00 277.22 0.03 0.62 B (12) 100 100 100 5.51 3.84 5.67 10.15 18.16 0.02 0.04 C (16) 100 100 100 4.38 3.15 4.72 7.63 15.32 0.01 0.03 - TABLE 5
Navigation Service Performance Comparison for an Elevation Mask of 20°, with Lunar UERE σUERE,LNCSS = 3.86 m The columns of mean performance denote the mean RMSE across the array of grid points, whereas the columns of max performance denote the RMSE of the worst-case grid point, for each case study. See Section 3.2.3) for details on how the performance metrics and design criteria are computed.
LNCSS Case Study (# sats) Performance metrics: At worst user grid point averaged across time Design criteria: Avg across user grid points Availability (%) Failure Tolerance (%) Coverage (%) GDOP Horizontal Position RMSE (m) Vertical Position RMSE (m) Receiver Timing RMSE (μs) Mean Max Mean Max Mean Max A (8) 77.51 54.11 53.29 246.24 14.75 4740.24 85.36 25620.85 0.19 56.94 B (12) 100 100 85.1 16.19 4.61 12.30 17.14 55.17 0.04 0.12 C (16) 100 100 100 7.24 4.12 7.04 14.06 29.88 0.03 0.07 - TABLE 6
Communication Design Performance Comparison for an Elevation Mask of 5° and a Data Rate of dKa = 44.7 Mbps See Section 3.2.4) for details on how the performance metrics and design criteria are computed.
LNCSS Case Study (# comm. sats, # total sats) Performance metrics: At worst user grid point Design criteria: Avg across grid points Availability (%) Failure Tolerance (%) Coverage (%) Summed Daily Availability tKa of LNCSS–Earth Data Link (s) (minimum among 15 days) Daily Data Volume (GB) A (2, 8) 100 43.75 100 160320 895.79 B (3, 12) 100 80.15 100 246720 1791.24 C (4, 16) 100 100 100 336012 1378.55 - TABLE 7
Communication Design Performance Comparison for an Elevation Mask of 20° and a Data Rate of dKa = 44.7 Mbps See Section 3.2.4) for details on how the performance metrics and design criteria are computed.
LNCSS Case Study (# comm. sats, # total sats) Performance metrics: At worst user grid point Design criteria: Avg across grid points Availability (%) Failure Tolerance (%) Coverage (%) Summed Daily Availability tKa of LNCSS–Earth Data Link (s) (minimum among 15 days) Daily Data Volume (GB) A (2,8) 86.50 15.57 100 160320 895.79 B(3, 12) 100 51.22 100 246720 1791.24 C (4, 16) 100 88.32 100 336012 1378.55 - TABLE 8
Comparison of Space Segment Costs Across the LNCSS Case Studies
The heuristic relationships used to calculate the total development and production costs in Brown (2002), Pereira and Selva (2020), and Wertz et al. (2011) are relevant for 2010 costs; thus, an inflation factor from 2010 to 2025 of 1.35 is considered (Wertz et al., 2011).
LNCSS Case Study (# comm. sats, # total sats) Total Dev. Cost [FY2025$M] Total Prod. Cost [FY2025$M] Total Space Segment Cost of LNCSS [FY2025$M] Average LNCSS Satellite Cost [FY2025$M] Comm. Payload Nav.-Only Satellite Comm. Payload Nav.-Only Satellite A (2, 8) 39.52 19.92 11.15 64.03 134.62 16.83 B(3, 12) 39.52 19.92 15.21 87.33 161.98 13.50 C (4, 16) 39.52 19.92 18.96 108.85 187.25 11.70
Jump to section
Related Articles
Cited By...
- No citing articles found.