Instrumentation & Measurement Magazine 25-1 - 91

the carrier frequency that is transmitted by the antenna can
cover as much of the entire frequency range of the satellite
transponder as possible. Considering a transponder with a
bandwidth of 72 MHz as an example, if the step size is 5 MHz,
a maximum of 15 frequency points can be measured. In (4),
 

 is the difference of the distance between the

BA
ss
tt
two antennas and the satellite; tt

BA
equ
equ

 is the differ
 
ence of the system error between the two antennas, which
can be measured and deducted in real time by using the satellite
simulator method. Due to the small distance between the
two antennas, the atmospheric propagation delay difference
 

 of the signal in the propagation process has

BA

tt
almost been cancelled out, so this part of the error can be ignored
compared to the previous error term;



BA is
00
 
tt
Fig. 4. Schematic diagram of the baseline distance reduction.
For a more intuitive presentation, the formula is used for
the derivation. Assuming that there are antenna A and antenna
B installed in parallel on station 1, the observation equation of
antenna A in " receiving its own station-disseminated signal "
mode can be obtained from (1). For ease of understanding, we
simplified (1) as follows:
   
A t tt t
equ
s
where 
A
s
and antenna A at time t, 
A
the transmitting and receiving channels of antenna A, 
A
equ
t
 t is the time delay of satellite transponder. Similarly, the
observation equation of antenna B at the same time can also be
obtained, as follows:
A
sat
   
B
s
 t tt t
s
 2  
B BB B
equ
    
t
 
 
  
sat
   
 
t tt
tt tt
t
BA
  s
s
 BA B
 t tt
  



00
2
ss
B
equ
 equ
A BA

  
  
A
(4)
(3)
After subtracting (2) and (3), the delay difference of the satellite
transponder can be obtained, as follows:
  2  
A AA A
   
t
(2)
 t is the geometric distance between the satellite
 t is the total equipment delay of

is the atmospheric propagation time delay of the signal, and

the geometric distance difference between the two antennas
and the satellite and is also the baseline distance correction
of the two antenna coordinates. This error has a greater impact
on the group delay measurement result and must be
corrected during calculation. The calculation method of the
geometric path error that is caused by differences in the antenna
coordinates is presented in Fig. 4.
According to the above figure, the baseline vector,
which is composed of the coordinates of the two sets of
antennas, is
  
 
AB BAr r . Projecting the baseline distance
into the viewing direction of the satellite and the antenna
yields:

 
AB A
B
0 00

AB 
SB

   
         

  

x
x x
BA B
x y y y y zz zzS
2 22
S
B
A BS B
x x y y zz
B
S
B
   
S BS
(5)
Via this approach, substituting (5) into (4) can yield the
measurement of the satellite transponder group delay.
A
B
  

t tt
SB
As discussed above, antennas A and B are used to observe
the same transponder of the same satellite. Antenna
A uses the center frequency of the transponder, while antenna
B uses the center frequency as the center. According
to the actual bandwidth of the transponder and the visibility
of the ground station, the step size is selected such that
February 2022
Fig. 5. For May 12, 2019, UTC time, the trajectory of the APSTAR-7 satellite,
as calculated from the TLE file.
IEEE Instrumentation & Measurement Magazine
91
Instrumentation & Measurement Magazine 25-1

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