Instrumentation & Measurement Magazine 25-5 - 37

parameters, the different single navigation system time are
unified to the same system time, and the multi-GNSS fusion
PPP long-distance time comparison is realized. This research
takes GPS system time as a reference, in the multi-GNSS PPP
calculation, and the receiver clock bias according to the GNSS
system time are all unified to the GPS system time. It can be expressed
as:
dt t tC
  E


      
dt t t  t t  
CG
r
EE
r
  
  
t tG G C
G G E
t
t
t t dt ISBGC
t t dt ISBGE
(18)
where the ISB is inter-system bias between different navigation
system. Therefore, based on (1) and (18), the observation
model of the GNSS multi-GNSS fusion PPP time comparison
is shown in (19) and (20) [12], [21]:




G


P,, cdt cdTs MFr ZWD Ir ,1  rf
C      ,
E      ,
GG G
rf rf
P,, cdt cISB cdTs MF ZWD Ir ,1  r f
GE
r
    ,
C
P,, cdt cISB cdTs MFr ZWD Ir ,1  r f
 rf rf
rf rf
E



 G
L





C
 rf r
L

E
L ,r f       C
E
r f,      f
C
r
r
,        f rf r f

E
cdt cISB cdTs MF ZWD I N E
G
r
GE
r
E
E
r
E
f
r ,1
,,
The parameter vector X of the model to be estimated is:
,, ,
=   ,
,
 (21)
G GC
Gn Cm
G
cdt cdT MF ZWD I N 
G
G
r
r
G
s
GC
r
G
r
s
r
,1 
cdt cISB cdTC MF ZWD I N 
C
f rf r f
C

C
f
r  f rf rf
E E
,,
,1
C C
GE
r
E
E
E
f
E
G
G GG G
r
,, (20)
G
r
G
r
r
r
G
G
f
GCCC C
f
C
G
C
(19)
Fig. 13. The number of satellites were observed at NTSC.
X x, y z dtr ISB ISBGE ZWD N N N,, ,,, ,rf rf rf
Eq
T
where n is the number of GPS satellites observed, m is the
number of BDS satellites observed, and q is the number of Galileo
satellites observed. Since there are two observations for
each satellite in the traditional model, for each epoch there
are (2n+2m+2q) observation equations. The principle of multiGNSS
data fusion PPP calculation process is similar to the
principle introduced previously, and the equal weights for observations
from different GNSS, in the error equation of (9), the
coefficient matrix Hcan be described in (22):
H 














 
a a axy z


a a a
a aax yz
2 22
nG
nG

a
a
2 22
mC
mC
1 11

E EE

1 11
G GG 10 

x yz nG
1 11
C CC
  
x yza a mC
x yza a

a qE2 22
qE
x yza a qE
11
10



 
10
MFE 
2q
In (22), the first three columns are the coefficients of after linearization
of the observation equation, the fourth column is
August 2022
Fig. 14. The numbers of satellites were observed at TP.
IEEE Instrumentation & Measurement Magazine
37
 MFE 
 MFC 
1
2m
(22)
10
11
MFG 
1
  


MFG 
1
2n
MFC 
the coefficient of receiver clock, the fifth and sixth columns are
coefficients of inter system bias, and the seventh column is the
coefficient of tropospheric parameters.
In this paper, based on the multi-GNSS observation data at
NTSC and TP, the GPS+Galileo+BDS-3 fusion PPP time comparison
experiment is carried out. Fig. 13 and Fig. 14 show
the number of visible satellites at NTSC and TP in different
moments, including the numbers of multi-GNSS and single
system satellites observed at NTSC and TP on July 3, 2020. It
can be seen that the number of visible satellites in multi-GNSS
fusion is more than twice the number of single GNSS. The
multi-GNSS fusion can reduce the observation noise caused
by low elevation angle, especially important since the observation
station is located in the forest, city, or canyon and has
poor quality environment. The multi-GNSS links can ensure
the stability of time comparison and reduce the dependence
on a single system.
The multi-GNSS fusion PPP time comparison experiment
between UTC (NTSC) and UTC (TP) was carried out, and
the observation data of GPS, Galileo, and BDS-3 within 300 s
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