■A
■mi
J4
A 0,
e.
eA
Earth and will provide continuous worldwide precise
navigation for appropriately equipped users (fig. 2).
Unlike TRANSIT, GPS will have at least four satellites in
view, worldwide and at each moment, so that 3D-real-
time-navigation will be possible. Currently only six proto
type satellites are available which provide 4 - 6 hours
coverage daily with four satellites and 10 - 14 hours with
two satellites (fig. 3). Consequently GPS can be used in
a limited way already today.
10 11 1! 13 H 15 16 17 11 19 70 2! 22 23 25 UTCIH]
Fig. 3. Visibility of GPS satellites in Wageningen on September 18,
1984. Satellites 4 and 7 are not suitable for navigation. An additio
nal satellite 12 has been launched end of September 1984.
The basic navigation mode is realized by the measure
ment of so-called „pseudoranges" between the user
and four satellites (fig. 4). These ranges are determined
by cross-correlating a coded navigation signal, transmit
ted from the satellite, with an identical signal generated
in the receiver. They are affected by the synchronization
error between the user clock and GPS system time
z!Tb. The observation equation is then
Rj |p, - pB cz1Tb cT !(X - XB)2
i /O
(Y. - YB)2 (Z - zB)2! czitb. (1)
p, with the components X., Y., Z. is the position vector
of satellite i in an Earth-fixed reference system, pB with
the components XB, YB, ZB the position of the observer
(antenna phase center) in the same reference system
and c the signal propagation velocity.
SATELUT 2
SATELLIT 1
SATELLIT 3
SATELLIT 4
R2
R3
R1
ionospheric corrections from measurements on both
carrier frequencies can only be computed by those
users, who have access to the L2 carrier through P-code
knowledge. More information on data and signal struc
ture can be found in (Van Dierendonck et al, 19781.
Satellite orbits are determined from observations on four
monitor stations in Guam, Hawaii, Alaska and Vanden-
berg. Similarly to TRANSIT the predicted „Broadcast
Ephemeris" are of limited accuracy. Most likely, precise
ephemeris from post processing of worldwide distribut
ed observations will be available in the future.
3. Concepts of observation and computation
The basic concept for GPS measurements by „pseudo-
ranges" has already been discussed. This concept is
used for navigation and may, under favourable condi
tions, provide a real-time position accuracy of 10 m
within the reference system of the GPS Broadcast Ephe
meris. This reference system is believed to be the same
as for TRANSIT Broadcast Ephemeris.
For geodetic purposes the real-time positioning accuracy
from pseudoranges is generally not sufficient. By collec
ting data over a longer time span of several hours, the
mean positioning error can be reduced to a few metres.
A higher accuracy is available through differential tech
niques (like translocation with TRANSIT). Simulation
studies at the Institut für Erdmessung" (IFE), Hannover
have shown [Seeber, 1984] that for a baseline of 65 km
the co-ordinate differences can be determined after ten
hours of GPS observations with an accuracy of 10
cm. However, also this result is under todays conditions
not much better than with TRANSIT.
A much higher accuracy can be achieved through mea
surements of phases and phase differences of the carrier
wave. By this, the resolution is more than 100 times bet
ter than with code-measurements and allows cm- and
mm-accuracy. The observations are the carrier phase
0A on station A or the phase-differences A 0AB of the
same signal on two different antenna stations A and B.
The observation equation is
271
- (m.
'AB WA 1 Pi Pb I |fi I
tB - mA) A c(A Tb - A Ta). (2)
In this equation, A is the wavelength of the carrier, mA
and mB are the integer numbers of full wavelengths for
the distance between observer A, B and satellite i.
Fig. 4. Positioning with GPS through range measurements.
The measurement of „pseudo-ranges" requires a prior
knowledge of the signal code. The so-called P-code al
lows real-time navigation with an accuracy of 10 - 15
m; the less accurate C/A-code has an accuracy of
30 - 50 m. Currently both codes are free. After final com
pletion of the system, the P-code will probably be classi
fied and not available to nonmilitary users.
For the computation of positions, the orbital elements of
the satellites have to be known. These elements to
gether with information on satellite and clock behaviour
and on the orbits of all available satellites (almanac) are
transmitted within the datasignal, modulated on the car
rier frequency. Two frequencies are transmitted: the L1
(1,57 GHz) containing P- and C/A-code and the L2 (1,23
GHz) containing only the C/A-code. Consequently,
The ambiguity numbers mA, mB can be resolved by spe
cial observation and calculation strategies, for instance
through the formation of double and triple differences
between observing stations and satellites [Goad and Re-
mondi, 1984; Beutler et al, 1984].
For the application of phase measurements the carrier
must be „reconstructed" in the receiver. This can be
realized by means of a priori knowledge of the code (i.e.
Tl 4100 receiver) or by special squaring techniques with
out code knowledge (i.e. Macrometer).
In view of the high possible resolution of 1 cm or even
better, phase measurements are especially interesting
for geodetic applications of GPS.
A further possibility for the use of GPS signals is given
in the same procedure as used by VLBI through cross-
correlation of the incoming signals on two different sta
tions A, B. Observable is the difference in the time of
arrival At of the same signal at stations A and B. This
purely interferometric technique up to now did not
lead to an operational receiving system for geodetic use.
NGT GEODESIA 85
87
