Instrumentation & Measurement Magazine 24-4 - 19

consist of 30 medium earth orbits (MEO) satellites and six
backup satellites in the future, and it will become the world's
most accurate positioning and navigation system.
This paper is based on the Galileo system, and presents the
precise products of satellite orbit and clock offset published by
GFZ, CODE and SHAO. The pseudo-range and carrier phase
observations of Galileo are measured by GNSS receivers in
time keeping laboratories, the Galileo PPP time comparison
experiment is studied, and the time difference between different
laboratories is analyzed and studied.
Algorithm of Galileo PPP Time
Comparison
Using the local time reference UTC(k) as reference signal,
Galileo PPP is studied based on two multi-system high performance
GNSS receivers. The observed data output by the GNSS
receiver include Galileo pseudo-range and phase data in real
time, and the observation equation can be expressed as [3], [4]:
  P cdt cdT d d d
 i 


L P cdt cdT d d d N

 /
i
    
i
r
r
s
s
trop
trop
ion mult
i
i
i
ion mult L/ i
i
      
In (1), the subscript i represents the Galileo carrier frequency
(i=E1,E5a). Other variables are: ρi
and Li
: The pseudo-distance
and carrier phase observations on a single frequency (in meters),
respectively;
P:
the true distance between station and satellite (in meters);
: the receiver clock offset correction (in meters);
: the satellite clock offset correction (in meters);
dtrop: the tropospheric delay (in meters); dion
cdtr
cdTs
: the ionospheric
delay (in meters);
mu / i
d
lt  and dmu / i: the pseudo-range and carrier phase mullt
L
tipath delay caused by different carrier signals (in meters)
respectively;
λi
Ni
: the phase integer ambiguity (in meters); and
ερi and εϕi
: the observation noise caused by the pseudo-range
and carrier phase measurement (in meters), respectively.
In order to reduce the effect of the first order ionospheric
delay, the dual-frequency ionospheric-free combination model
is used in (2) [5]:

Pr IF




,
fP fP

22
1 1 22

Lr IF
, 22
12
22
11 2 2
ff

fL fL


ff

22
12
where the Pr,IF is ionospheric-free pseudo-range combination,
and the Lr,IF
(2)
(1)
Table 1 - The data processing model
Content
Observed data
Sampling interval
Signal selection
Satellite orbit
Satellite clock offset
Ionospheric delay
Troposphere delay
Cut-off angle
Receiver clock model
Receiver position model
Relativity effect
Tidal correction
Result calculation
Modified model
Pseudo-range and phase
observation file
30 s
Galileo E1, E5a frequency
Products from GFZ/CODE/
SHAO [6]
Products from GFZ/CODE/
SHAO
Dual frequency ionosphericfree
combination
Saastamoinen + random
walking model [7]
10°
White noise
Static
Model correction
Model correction
Extended Kalman Filter
Estimation [8]
is ionospheric-free phase combination. Table 1
shows the observation model of Galileo PPP and the method
of data processing model.
The model correction algorithms are shown in Table 1, and
the principle of Galileo PPP time comparison is shown in Fig. 1.
According to Fig. 1, the Galileo carrier phase time comparison
method can be described as: the reference time frequency
signal of station A is RefT1, the reference time frequency signal
of station B is RefT2, and the uniform reference time is IGST.
June 2021
Fig. 1. The principle of Galileo PPP time comparison.
 fT IGST
tA
tB
Re 1
 fT IGST
Re 2
IEEE Instrumentation & Measurement Magazine
(3)
(4)
19

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