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

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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