Instrumentation & Measurement Magazine 25-5 - 32

is the ionosphere-free combination of the B1C pilot
component (C1P) and the B2a pilot component (C5P), and the
BDS DCB precision products released by IGS is used to eliminate
the delay of pseudo-ranges at different frequency points.
Equation (2) can be described as [10]:
P ,r IF  r   
k12
 DCBkk12
P P2 3
 (3)

12
c dt dT m ZWD
1


13


r
s
11
DCB PP
In (3),
k12



1575.42
1176.45
is a factor related to frequency, the DCB C P C I
PP 56 . The same principle, the ionospherePP
16 , and
13
  
the DCB C P C I
  
23
free combination of carrier phase observation equation [11] is
shown in (4):
L ,r IF

fL fL

ff

22
12
22
11 22
(4)
In this paper, the algorithm of Kalman filtering is used to estimate
the parameter, the observation and state equations can
be expressed using (5) [12]:
 

k =
  
k kk k
X Xw
L HX v
kk k ,1 1 k 1
where Xk is the state variable at time k, Φk,k-1
sition matrix from time k-1 to time k, wk
(5)
of the system, Lk is the observation vector at time k, Hk
coefficient matrix of the observation equation, and vk
is the state tranis
the noise vector
is the
is the observation
noise. The process noise and observation noise of the
system have the following statistical properties:





E w Cov w w E w w Q
E v
Cov w v E w vT

,
kj
 
 

k  0,
k ,
k ,

j 
k j
k  0, Cov v v E v v Rkj
k k   0
j   
T

k j
 kj
T
(6)
where V is the observation residual vector, H is the coefficient
matrix, l is observed minus computed, the state vector X includes
receiver position coordinate increment ( ,,
xy z
NN1  are the carrier phase
m
IF 12 ,, IF12
ambiguity. The state vector X is shown in (10) [12], [13]:
12
X x y z cdt ZWD N N    
1
m
, , ,
r ,
, ,, IF12
IF
  ),cdtr
is the receiver clock bias correction, ZWD is the zenith tropospheric
wet delay, and
(10)
Fig. 2 shows the principle of BDS-3 PPP time comparison
[11], [16], and the model correction algorithms are listed in Table
1. The BDS PPP time comparison method can be described
as follows: the local reference time frequency signal of station
A is T1ref
is T2ref
, the local reference time frequency signal of station B
, and the common reference time is IGST:
1
t T IGSTref
A
t T IGSTref
2
B
(11)
(12)
Here, t A is the time difference between T1ref and IGST, t B is
the time difference between T2ref and IGST. Therefore, the time
difference between station A and station B is derived from (11)
minus (12):
The Q and Rare the variance matrices of system noise and
observation noise, respectively, and it is assumed to be known
with white noise. The δkj
kj  


is the Kronecker function, and



1
kj
kj

.

The state transition matrix can be express as:
4 4 44

kk 0I4 4 44
/1


II


dt

(7)
where I is the diagonal matrix, and dtis time interval between
adjacent epochs. The coefficient matrix can be expressed as:
32
t   ref
ref
A B
(1
t T IGST T IGST
T IGST T IGST t
) ( 2
Testing and Analysis
The BDS-3 new signal PPP time comparison was studied based
on the observation data (NTSC and TP) obtained July 3-6,
2020. The BDS receiver was connected to the 1 PPS and 10 MHz
signals from a local laboratory. The laboratory had suitable environmental
conditions where the temperature and humidity
are kept at about 23 °C and 45%, respectively, for a long time.
Meanwhile, the BDS precise orbit and clock products published
by GFZ were used. Based on the algorithm and principle introduced
previously, the receiver short-baseline and high-precision
IEEE Instrumentation & Measurement Magazine
August 2022
   12   AB
 ref
ref
)
(13)
2
where ax
,ay
r
where Pr,IF
H 














a a a MF
a a a MF

xy z
xy z


i ii
1 11
1 11

aaa MFi 0 0  (8)
  
xyz 1
xyz 1
xy z
xy z
n nn
n nn
 
 0 1
0 0
a a a MF
a a a MF
1
1
,as
n 0 0
n 0 0


are the cosines of the satellite-ground direction.
Based on (3) and (4), it is assumed that m satellites are observed
at the time t, and observation equations are established.
The error equation is shown in (9):
V =HX l
(9)
0 0  0
0 1 0 0

aaa MFi
i ii
  
0 0 0
  
0 0 0 0
 
1
1
1
1
0 0
0 1
 
 
0 0
0 0

Instrumentation & Measurement Magazine 25-5

Table of Contents for the Digital Edition of Instrumentation & Measurement Magazine 25-5
