h
f,
ly, the wet component leaves errors of the order of 1 or
2% of the total refraction effect.
This is the reason why during the processing, the mea
surements below 5 or 10 degrees elevation are system
atically rejected. We note also that when by the end of
this decade an accuracy of 10 cm or better should be ob
tained in positioning, the tropospheric refraction should
considerably be improved.
New models are in preparation. Some are still based on
the classical meteorological parameters measured at the
ground stations while others are based on radiometer
techniques allowing to deduce the vertical profile of the
water vapour distribution [Elgered, 1982; Claflin et al,
1979]. From results obtained by the experiments just
mentioned, it is expected that it is possible to monitore
the tropospheric refraction with residuals less than 1 or
2 centimeters.
2.2. The ionospheric perturbation
The higher part of the atmosphere is called the iono
sphere and as a consequence of the presence of free
electrons, it generates a perturbation of the radio signal.
The signal path is given by:
AR ^1 Üi (2)
f2 f3 f
where f denotes the frequency transmitted by the satel
lite and a„ a2, a3 are functions of the electron density
distributed along the signal path and of the magnetic
field.
The first term is the most important; it varies linearly
with the so-called Total Electronic Content (TEC) along
the path and it is inversely proportional to the square of
the transmitted frequency. It suffers considerable varia
tions between day and night (from 10"16 to 5.10 1S),
according to the season, the solar activity and the satel
lite elevation with respect to the local horizon. To esti
mate the main contribution of (2), knowledge of TEC is
thus of primary importance.
Table 3 presents an estimate of the ionospheric contri
bution on distance and range rate measurements, for
different frequencies and for mean or extreme values of
TEC [Saint-Etienne, 1981].
Type of
measure
ment
Error
400
Frequency in MHz
1600 2000
8000
Distance
- mean
50,
3,
2,
0,12
- value reached in less
than 10% of events
250,
15,
10,
0,6
- maximum value
500,
30,
20,
1,2
Range
- mean
17,
1,
0,7
0,04
rate
- value reached in less
than 10% of events
85,
5,
3,5
0,21
- maximum value
170,
10,
7,
0,43
Table 3. Effect of ionospheric perturbation on range (m) and range
rate (cm/sec.).
As no direct measurement allows the measurement of
TEC, positioning from space requires a dual frequency
operation which will remove the first order of the per
turbation:
a. Correction for distance measurements
With respect to the geometrical path the propagation
time delay is given by:
At AR/c (3)
Let zlr, and At2 be the corresponding time delay for
two transmitted frequencies f, and f2at first order we
have
d (At) zlr, - Zlr2
from the measurement of d (Ar), we can deduce suc
cessively zlr2 and TEC. The quantity d (At) is obtained
by the following procedure; the two frequencies are
identically modulated with reference pulses which are
simultaneously transmitted from the satellite. At the
ground station the arrival of the reference pulses is de
tected at both frequencies and the associated epochs
are noted. The difference between the epochs, related
to the same reference pulses, yields immediately d (At).
Such a procedure removes the main perturbation on the
order of a centimeter but it requires a high resolution
(0,01 nanoseconds) in the recording of epochs.
b. Correction for range rate measurements
At the observing site the range rate is estimated from the
Doppler effect observed at two transmitted frequencies.
The ionosphere introduces a complementary frequency
drift deduced from (2)
f dzIR
At
c dt
b1 b2 b3
f f2 f3
At the first order, denoting:
fit f»
f 1d ^2d
f-io i f2o
2e
'2d
the total drift of the two transmitted frequen
cies
the drift associated with the Doppler effect
the drift associated with the ionospheric re
fraction,
we can write the four equations
fit f 1 d f 1e f 2t f2d f2e
fgd ^2
fid fl fie
The third and fourth equation express that the initial fre
quencies are respectively proportional to the Doppler
effects and inversely proportional to the ionospheric per
turbation. The measurement of flt and f2t will allow to
solve the above system and to deduce the four un
knowns fid and fie (i 1,2). Using the dual frequency
approach, table 4 gives an estimate of the remaining
error for distance and range rate measurements.
However, a series of 10 years of station co-ordinates
determined in Brussels from observations of the
Type of
measure
ment
Error
Pairs of frequencies
1501400 400/2000 1227/1575 2000/8000
Distance
- mean
0,6 m 0,9 cm 0,3 cm 0,01 cm
- value reached in
less than 10% of
events
10, m 6,6 cm 1,7 cm 0,05 cm
- maximum value
36, m 22, cm 4,5 cm 0,11 cm
Range
- mean
0,3 3.10 3 2.10 3 3.10 s
rate
- value reached in
less than 10% of
events
6, 0,04 0,02 4.10 4
- maximum value
23, 0,14 0,06 1.10 3
Table 4. Ionospheric errors by using two frequencies for range and
range rate (cm/sec.) maeasurements.
76
NGT GEODESIA 85
