Article Figures & Data
Figures
- FIGURE 1
Flow chart of the user algorithm
- FIGURE 2
Station map for variogram modeling
- FIGURE 3
Precipitation radar image for each data set
- FIGURE 4
Empirical variogram modeling of data set 1: (a) station map with ZTD; (b) modeling result
- FIGURE 5
Empirical variogram modeling of data set 2: (a) station map with ZTD; (b) modeling result
- FIGURE 6
Comparison of empirical variograms for each data set
- FIGURE 7
NRTK station map
- FIGURE 8
Residual error of single-baseline RTK (5/28/2022, sunny): (a) NCSW; (b) GAST
- FIGURE 9
Residual error of single-baseline RTK (5/26/2022, rainy): (a) NCSW; (b) GAST
- FIGURE 10
Residual error of NRTK for NCSW (5/28/2022, sunny): (a) LSM; (b) Kriging
- FIGURE 11
Residual error of NRTK for GAST (5/28/2022, sunny): (a) LSM; (b) Kriging
- FIGURE 12
NRTK ambiguity resolution results for NCSW (5/28/2022, sunny): (a) LSM; (b) Kriging
- FIGURE 13
NRTK ambiguity resolution results for GAST (5/28/2022, sunny): (a) LSM; (b) Kriging
- FIGURE 14
NRTK position error for NCSW in the ENU frame (5/28/2022, sunny): (a) LSM; (b) Kriging
- FIGURE 15
NRTK position error for GAST in the ENU frame (5/28/2022, sunny): (a) LSM; (b) Kriging
- FIGURE 16
Residual error of NRTK for NCSW (5/26/2022, rainy): (a) LSM; (b) Kriging
- FIGURE 17
Residual error of NRTK for GAST (5/26/2022, rainy): (a) LSM; (b) Kriging
- FIGURE 18
NRTK ambiguity resolution results for NCSW (5/26/2022, rainy): (a) LSM; (b) Kriging
- FIGURE 19
NRTK ambiguity resolution results for GAST (5/26/2022, rainy): (a) LSM; (b) Kriging
- FIGURE 20
NRTK position error for NCSW in the ENU frame (5/26/2022, rainy): (a) LSM; (b) Kriging
- FIGURE 21
NRTK position error for GAST in the ENU frame (5/26/2022, rainy): (a) LSM; (b) Kriging
- FIGURE 22
Residual error for NCSW (6/12/2023, rainy): (a) single-baseline RTK; (b) LSM; (c) Kriging
- FIGURE 23
Residual error for GAST (6/12/2023, rainy): (a) single-baseline RTK; (b) LSM; (c) Kriging
- FIGURE 24
Residual error for NCSW (6/19/2023, rainy): (a) single-baseline RTK; (b) LSM; (c) Kriging
- FIGURE 25
Residual error for GAST (6/19/2023, rainy): (a) single-baseline RTK; (b) LSM; (c) Kriging
- FIGURE 26
Simulation setting: (a) grid map; (b) tropospheric delay (PRN 29)
- FIGURE 27
Residual error map: (a) LSM; (b) Kriging
Tables
Data set Weather condition Date Time (UTC) 1 Sunny 5/28/2022 20:40 ~ 23:10 2 Rainy 5/26/2022 20:50 ~ 23:20 3 Rainy 6/12/2023 4:00 ~ 6:30 4 Rainy 6/19/2023 14:30 ~ 17:00 Note: UTC: universal coordinated time
Data set Sill Range Nugget 1 0.0005 m2 130 km 0.0002 m2 2 0.0030 m2 910 km 0.0002 m2 3 0.0030 m2 1123 km 0.0002 m2 4 0.0040 m2 1123 km 0.0002 m2 Station Name Receiver Antenna Altitude Baseline (from master) Master NCMA Trimble NetR5 TRM57971 559 m — Aux 1 SCUN Trimble Alloy TRM115000 168 m 150 km Aux 2 NCWJ Trimble NetR5 TRM57971 993 m 127 km Aux 3 NCMO Trimble Alloy TRM115000 265 m 173 km User 1 NCSW Trimble NetR9 TRM57971 658 m 34 km User 2 MARI Trimble NetR5 TRM57971 366 m 69 km User 3 NCSP Trimble NetR5 TRM57971 301 m 85 km User 4 NCNE Trimble NetR5 TRM57971 1,123 m 76 km User 5 GAST Trimble NetR5 TRM57971 212 m 147 km - TABLE 4
Comparison of RMS of Residual Error for All Users Using NRTK with LSM and Kriging (5/28/2022, Sunny)
Residual
[RMS, cm]NCSW MARI NCNE NCSP GAST LSM 2.09 1.54 1.42 1.43 1.00 Kriging 1.62 1.34 1.30 1.26 1.04 - TABLE 5
Comparison of Success-Fix Rate of All Users Using NRTK with LSM and Kriging (5/28/2022, Sunny)
Success-fix rate [%] NCSW MARI NCNE NCSP GAST LSM 95.1 98.8 99.9 100.0 100.0 Kriging 99.9 100.0 100.0 100.0 100.0 - TABLE 6
Comparison of RMS of the Residual Error of All Users Using NRTK with LSM and Kriging (5/26/2022, Rainy)
Residual
[RMS, cm]NCSW MARI NCNE NCSP GAST LSM 4.35 2.91 2.36 3.24 2.29 Kriging 1.95 1.71 1.40 1.93 2.18 - TABLE 7
Comparison of Success-Fix Rate of All Users Using NRTK with LSM and Kriging (5/26/2022, Rainy)
Success-fix rate [%] NCSW MARI NCNE NCSP GAST LSM 51.8 75.5 87.7 68.0 92.5 Kriging 96.1 96.2 99.3 94.3 94.1 - TABLE 8
Comparison of RMS of Residual Error of All Users Using NRTK with LSM and Kriging (6/12/2023, Rainy)
Residual
[RMS, cm]NCSW MARI NCNE NCSP GAST LSM 3.22 1.90 1.97 2.13 2.09 Kriging 2.07 1.42 1.39 1.92 2.07 - TABLE 9
Comparison of Success-Fix Rate of All Users Using NRTK with LSM and Kriging (6/12/2023, Rainy)
Success-fix rate [%] NCSW MARI NCNE NCSP GAST LSM 75.8 98.3 96.6 98.3 96.1 Kriging 95.7 100.0 98.9 99.8 96.5 - TABLE 10
Comparison of RMS of Residual Error of All Users Using NRTK with LSM and Kriging (6/19/2023, Rainy)
Residual
[RMS, cm]NCSW MARI NCNE NCSP GAST LSM 3.07 1.86 1.77 1.95 1.82 Kriging 1.48 1.29 1.09 1.70 1.72 - TABLE 11
Comparison of Success-Fix Rate of All Users Using NRTK with LSM and Kriging (6/19/2023, Rainy)
Success-fix rate [%] NCSW MARI NCNE NCSP GAST LSM 78.5 95.4 97.7 98.0 96.8 Kriging 99.9 100.0 100.0 100.0 98.1 - TABLE 12
Weightings of the Initial Epoch Calculated with the LSM and Kriging Weighting Model (Data Sets 1 and 2)
Weighting LSM Kriging (data set 1, sunny)
PRNKriging (data set 2, rainy)
PRN2 11 13 15 20 23 29 2 11 13 15 20 23 29 Aux1 –1.13 0.05 0.00 0.11 0.06 –0.05 –0.04 0.01 0.02 –0.01 0.07 0.03 –0.05 –0.04 0.00 Aux2 1.08 0.21 0.20 0.07 0.02 0.07 0.07 0.02 0.17 0.17 0.07 0.03 0.07 0.07 0.04 Aux3 1.05 0.14 0.15 0.28 0.31 0.28 0.23 0.32 0.17 0.18 0.27 0.29 0.27 0.23 0.30
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