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Evaluation of Triple-Frequency GPS/Galileo/Beidou Kinematic Precise Point Positioning Using Real-Time CNES Products for Maritime Applications

Mohamed Abdelazeem
Mohamed Abdelazeem
 and 
Rahmi N. Çelik
Rahmi N. Çelik
   | Jan 19, 2024
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Published Online: Jan 19, 2024
Page range: 314 - 329
Received: Jan 14, 2023
Accepted: Oct 24, 2023
DOI: https://doi.org/10.2478/arsa-2023-0012
Keywords
© 2023 Mohamed Abdelazeem et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1.

Vessel trajectory
Vessel trajectory

Figure 2.

Number of tracked satellites (left) and PDOP values (right)
Number of tracked satellites (left) and PDOP values (right)

Figure 3.

Positioning errors in longitude, latitude, and altitude, respectively, for dual-frequency real-time PPP solutions
Positioning errors in longitude, latitude, and altitude, respectively, for dual-frequency real-time PPP solutions

Figure 4.

Positioning errors in longitude, latitude, and altitude, respectively, for triple-frequency real-time PPP solutions
Positioning errors in longitude, latitude, and altitude, respectively, for triple-frequency real-time PPP solutions

Figure 5.

Distribution of the differences between the dual-frequency PPP solutions and the differential solution in the three components
Distribution of the differences between the dual-frequency PPP solutions and the differential solution in the three components

Figure 6.

Distribution of the differences between the triple-frequency PPP solutions and the differential solution in the three components
Distribution of the differences between the triple-frequency PPP solutions and the differential solution in the three components

Figure 7.

STD of the PPP solutions in the three positioning components
STD of the PPP solutions in the three positioning components

Figure 8.

STD of the 2D position for the proposed PPP solutions
STD of the 2D position for the proposed PPP solutions

Processing parameters for both PPP and differential solutions

Parameter PPP solution Differential solution
Dual frequency Triple frequency
GNSS system G, E, C G, E, C G
Observations Code and phase Code and phase Code and phase
Mathematical model Undifferenced ionosphere-free Undifferenced ionosphere-free Differenced
Frequency

G: L1/L2

E: E1/E5a

C: B1/B2

G: L1/L2/L5

E: E1/E5a /E5b

C: B1/B2/B3

 L1/L2
Sampling rate 1 Hz 1 Hz 1 Hz
Elevation mask 10° 10° 10°
Orbit and clock CNES (RT) CNES (RT) IGS (final)
Tropospheric model Saastamoinen model
Mapping function Vienna mapping function 1 (VMF-1)
Parameter estimation Kalman filter

IMO accuracy requirements for GNSS positioning (IMO, 2002)

Navigation phase Horizontal accuracy (m) Integrity
Alert limit (m) Time to alarm (seconds) Integrity risk (per 3 h)
Ocean 10 25 10 10−5
Coastal 10 25 10 10−5
Port approach 10 25 10 10−5
Inland waterways 10 25 10 10−5
Track control 10 25 10 10−5
In port navigation 1 2.5 10 10−5
Automatic docking 0.1 0.25 10 10−5

Maximum 2D position error and 2D RMSE at 95% confidence for the PPP solutions

PPP solution Statistical parameter (m) PPP solution Statistical parameter
Maximum RMSE95%2D {\bf {RMSE}}_{{\bf {95\% }}}^{{\bf {2D}}} Maximum RMSE95%2D {\bf {RMSE}}_{{\bf {95\% }}}^{{\bf {2D}}}
G-DF 0.346 0.420 G-TF 0.162 0.265
GE-DF 0.215 0.242 GE-TF 0.149 0.190
GC-DF 0.236 0.279 GC-TF 0.243 0.314
GEC-DF 0.168 0.221 GEC-TF 0.221 0.175

Statistical analysis of 2D position for different PPP solutions

PPP solution Statistical parameter (m) PPP solution Statistical parameter (m)
Mean RMSE Mean RMSE
G-DF 0.140 0.172 G-TF 0.107 0.109
GE-DF 0.084 0.099 GE-TF 0.073 0.078
GC-DF 0.097 0.115 GC-TF 0.123 0.129
GEC-DF 0.064 0.085 GEC-TF 0.092 0.068
eISSN:
2083-6104
Language:
English
Publication timeframe:
4 times per year
Journal Subjects:
Geosciences, other
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