The GPS orbit determination was studied to see how well the radial coordinate for altimeter satellites such as TOPEX could be found by on board measurements of GPS signals, including the reconstructed carrier phase. The inclusion on altimeter satellites of an additional high accuracy tracking system is recommended. It is suggested that a sidetone ranging system is used in conjunction with TRANET 2 beacons

Bender, P. L.

Larden, D. R.

English

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(NASA- CR-169694) TOPER ORBIT GETERNINATION
	 983-14606
USING GPS SIGNALS FLCS A SILFTCNF SINGING
SYSTER (Joint Inst. for Lab. Astrophysics)
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TOPEX ORBIT DETERMINATION USING GPS SIGNALS PLUS A SIDETONE RANGING SYSTEM
Peter L. Bender * and Douglas R. Larden
Joint Institute for Laboraf-ry Astrophysics
National Bureau of Standards and University of Colorado
Boulder, CO 80309
ABSTRACT
One reason,for carrying out our GPS orbit determination study was to see
how well the radial coordinate for altimeter satellites such as TOPEX could
be found by on-board measurements of GPS signals, including the reconstructed
carrier phase. Preliminary results are very encouraging. However, the Inclu-
sion on altimeter satellites of an additional high accuracy tricking system
seems desirable. A suggestion is made for using a sidetone ranging system in
	 ?
conjunction with TRANET 2 beacons.
INTRODUCTION
The accuracy of the altimeter on the proposed TOPEX (Topographic Eacperi-
ment) satellite is high enough so that 3 cm accuracy for determining the ra-
dial coordinate would be very desirable if it can be achieved. One attractive
approach is to use signals from the GPS (Global Positioning System) satellites
to determine the orbit. However, until the schedule for launching the neces-
sary number of GPS satellites is definite and there are assurances that dith-
ering of the satellite signals or other factors will not degrade the achievable
accuracy , a combination of two approaches muet he planned for. The redundancy
provided by a dual approach would be helpful in any case, if the cost is not
too high.
Preliminary results for the GPS method are given briefly in the next sec-
tion. This is followed by discussion of a possible sidetone ranging system,
probably at S-band, which could be used to provide accurate ranges to MPEX
from a number of ground stations. TRANET 2 tracking data would be used also
to determine the ionospheric correction and for ambiguity resolution. The
sidetone ranging system could be developed by modifying a pair of USS (Unified
S-Band) transponders if desired.
*Staff umber, Quantum Physics Division, National Bureau of Standards,
Boulder, Colorado.
1253
CPS APPROACH FOR TOPEX ORBIT DETERMINATION
One of the two purposes in our study of the CPS orbit determination
problem has been to investigate how accurately CPS signals can be used to de-
termine the orbits of altimeter satellites (Larden and Bender, 1982x). Geo-
metrical arguments indicated that the radial coordinate for TOPEX could be
solved for accurately if the horizontal coordinates of the CPS satellites were
kn:.%.n co about 20 cm. Our results (Larden and Bender, 1981, 1982b) indicate
that this CPS orbit accuracy can be achieved with 2 to 6 hours of tracking
from 20 well-distributed ground stations, even when reasonable allowances for
uncertainties in the nongravitational forces on the satellite and in the low
degree terms of the gravitational field are made. Although measurements of
the CPS signals actually would be made nearly continuously at the ground sta-
tions, we have assumed in the simulations that measurements are made only in-
frequently in order to avoid unreasonably large reductions in the measurement
errors due to averaging. For the 4 hour case (Larden and Bender, 1982b), a
se r of measurements was included every 30 minutes. This interval might corre-
spond roughly to the time scale for changes in the errors of water vapor cor-
rections obtained with water vapor radiometers.
As a preliminary case, we added single differences in range between TOPEX
and a reference ground station for each CPS satellite visible to TOPEX at the
middle of our 4 hour run. TOPEX was taken to be at 2° south latitude, 97°
east longitude, and 1300 km altitude. Eleven CPS satellites could be observed
with elevation angles of greater than -27% The uncertainty in each single
difference was assumed to be 1.4 cm. Clock offsets for TOPEX at its one ob-
serving time and for all but one of the 20 assumed ground stations at each
measurement time were solved for. The results for the TOPEX coordinate uncer-
tainties are given in Table 1. Most of the total uncertainty comes from the
assumed 3 cm uncertainty in each coordinate for each of the ground stations.
Results of a somewhat different approach to simulating the TOPEX orbit
determination problem using CPS signals have been reported recently by
Ondrasik (1981, and personal communication, 1981). In particular, the TOPEX
radial coordinate uncertainty was calculated based on one set of measurements
per minute over only a 10 min observing period, with the uncertainties in the
positions of three ground stations located at DSN (Deep Space Net) sites taken
to be 10 cm in
Table 1
TOPER COORDINATE UNCERTAINTIES
Spherical	 Formal error	 Total uncertainty
coordinate	 (cm)	 (cm)
Latitude	 1.0	 3.1
Longitude	 1.0	 2.7
Radial position	 1.3	 3.0
7RKUNAL PAS
Of POOR QU	 1135
each coordinate. The positions of up to ten additional ground stations at
TRANET 2 sites were solved for, as well as the GPS satellite positions. The
TOPEX orbit was determined, rather than just the instantaneous position. It
is interesting that the TOPEX radial coordinate uncertainty increased by less
than 80% for a particular 10 min arc involving only two DSN sites when the
other nine ground stations for this case were left out. This result appears
to indicate that a smaller number of CPS tracking stations than the 20 we have
initially assumed may be sufficient when data are also available from an addi-
tional satellite which can see many of the GPS satellites.
SIDETONE RANGING SYSTEM APPROACH
Despite the encouraging results of simulations based on observing GPS
signals with TOPEX, we believe that an additional accurate orbit determination
method is needed, as discussed in the introduction. One fairly obvious ap-
proach would be to add an S
-band or X-band sidetone ranging transponder to the
TRANET 2 beacon on TOPER, and range to it from a substantial number of ground
stations. Some of these would be at existing or planned TRANET 2 stations.
Others could be at fixed laser ranging or VLBI sites used it crustal dynaraics
measurements, but some additional stations in particularly desirable sites
probably would be needed.
An example of the type of sidetone ranging system which might be used
is shown in Figure 1. It is derived from standard USB transponders, with the
Input frequencies v 1 and v 2 received from the ground being roughly 2100 and
2030 MHz respectively. Transponder 11 would be essentially unmodified. It
operates by taking the output from a voltage controlled oscillator (VCO), mul-
tiplying it by a fixed ratio of integers (M I /N 1 ) to obtain the same frequency
as v 1 , and then phase locking the VCO with a phase sensitive detector so that
the two inputs to the phase sensitive detector maintein a fixed phase relation-
ship. The output from the locked VSO is then multiplied by another ratio of
integers (M2 /N2) and sent to a transmitter for re:roadcast to the ground. The
integer ratios are chosen so that the output frequet.cy v 3 of about 2280 MHz is
just (240/221) times vI.
For transponder i2, the modifications are more substantial. The VCO in
it is locked so that (M I /N I ) times its frequency is phase locked to the re-
ceived frequency v 2 of about 2030 MHz. However, a third VCO is added. Its
frequency is multiplied by (M 2/N2) and sent through the transmitter in trans-
ponder #2 to the ground. The frequency of the third VCO is chosen so that the
transmitted frequency v 4
 is about 2210 MHz. Some of the signals at frequen-
cies v 1 and v 2 going to the phase sensitive detectors in the two transponders
are taken out and mixed to give a roughly 70 MHz reference signal, and a simi-
lar ?0 MHz beat frequency is generated by mixing v 3 and v4 . An additional
phase sensitive detector operating at 70 MHz is then used to adjust the third
VCO so that the two 70 MHz signals have a fixed phase relationship. To the
extent that phase delays within the system remain constant, the phase differ-
ence between the two output frequencies v3 and v 4 will be fixed with respect
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One reason for discussing the example of a possible sidetone ranging
system derived from USB transponders is that there is a substantial amount of
information on the phase stability of such transponders. In particular, a USB
transponder was used in Gravity Probe A, which was a test of the gravitational
frequency shift for a hydrogen maser flown in a rocket to an altitude of about
10,000 km (Vessot and Levine, 1979; Vessot et al., 1930). The frequency of
the hydrogen maser as a function of time during the flight was compared with
that of a second hydrogen maser on the ground using a three-frequency S-band
system. It appears from analysis of the results, reversing the original point
of view and assuming general relativity is corrict, that the time delay sta-
bility of the USB transponder used for one uplink and one downlink frequency
was 10 picosec per day (Allan et al., 1982). In addition, thermal tests car-
ried out at the Marshall Space Flight Center on two similar transponders indi-
cated a phase shift at S-band with temperature of only 13° per Kelvin. Also,
If the temperature coefficient of the initial preamplifiers and phase sensi-
tive detectors for the two parts of the sidetone ranging system were similar,
the temperature coefficient for the phase shift of thz 70 MHz beat between v3
and v 4 with respect to that between v i and v 2 should be quite small.
In the example discussed, the range from the ground station to the satel-
lite would be measured in terms of the wavelength for the 70 MHz beat between
the two S-band f7equencies used. This means that the ambiguity length for the
one-way distance would be 2.1 meters, and the ambiguity could be resolved from
the TRANET 2 tracking data. It appears likely that the combination of TRANET
2 information on the ionospheric delays from the same ground stations with S-
band ranges would be sufficient to accurately determine the ionospheric cor-
rection. However, careful studies of this question would be needed before
deciding between S-band and X-band for the sidetone ranging system. If an X-
band system is not necessary, the S-band phase could be used to improve the
precision of the range measurements, with the ambiguity resolved by the 70 MHz
beat frequency.
The additional equipment needed at a ground station to make sidetone
range measurmements has not yet been investigated. However, semi-automatic
operation seems quite possible. A water vapor radiometer looking along the
line of sight to the satellite will be needed in any case to achieve high
accuracy. This requirement appears to preclude operation at unmanned sites
because of maintenance requirements. Thus the number of ground stations
needed is an important question, which should be studied carefully.
rANr.1.11ST0NC
Both the GPS approach and the use of a sidetone ranging system along with
TRANET 2 data appear to be attractive possibilities for tracking TOPEX and
other satellites for which accurate orbits are required. Because of present
uncertainties concerning possible modifications of the GPS signals and the
completion date for the system, as well as to provide redundancy, we believe
that the inclusion of a sidetone ranging system on TOPEX and the development
of prototype ground station equipment should be pursued. Studies of the num-
ber and distribution of ground stations required with the sidetone ranging
system also are needed. It would be particularly desirable if most of them
ORIGINAL PAGE W
1258	
OF POOR QUALITY
could be, at 1i.ANET 2 sites or at any additional sites needed for CPS satellite
orbit determination.
ACKNOWLEDGMENTS
We wish to thank R. F. C. Vessot of the Smithsonian Astrophysical
Observatory for valuable conversations concerning Gravity Probe A. Informa-
tion from V. J. Ondrasik and S. C. Wu on the Jet Propulsion Laboratory simu-
lations of the TOPEX orbit determination problem using CPS signals also is
appreciated. This work was partially supported under NASA order No. W-15,
068.
REFERENCES
Allan, D. W., C. 0. Alley, N. Ashby, R. Becher, R. F. C. Vessot, and G. M. R.
Winkler, Ultra-accurate international. time and frequency comparison via an
orbiting hydrogen-maser clock, in Proc. Third Int. Symposium on Frequency
Standards and Metrology, 5-7 October-, 1981, Aussois, France (C. Audoin,
ed., Editions de Physique, Orsay, F::ance, 1982).
Larden, D. R., and P. L. Bender, Achievable accuracy of CPS orbit determina-
tion from worldwide tracking data, Trans. Amer. Geophys. Union 62, 840
(1981).
Larden, D. R., and P. L. Render, Predicted future CPS orbit determination
accuracy, in Abstracts, Fourth Annual Conference on the NASA Geodynamics
Program, Greenbelt, MD, January 26-29, 1982, p. 33 (1982a).
Larden, D. R., and P. L. Render, Preliminary study of CPS orbit determination
accuracy achievable from worldwide tracking data, in Proc. Third Int. Geo-
detic Symposium on Satellite Doppler Positioning, Las Cruces, NM, February
8-12, 1982 (1982b).
Ondrasik, J., Ne:.rly instantaneous subdecimeter orbit and station location
determinations using receive only radiometric data and low precision
clocks, Postdeadline paper, Fall Meeting, Amer. Geophys. Union, December 7
(1981;; abstract published in Trans. Amer. Geophys. Union 63, 156 (1982).
Vessot, R. F. C., and M. W. Levine, A test of the equivalence principle
using a space-borne clock, General Relativity and Gravitation 10, 181-204
(1979).
Vessot, R. F. C., M. W. Levine, E. M. Mattison, E. L. Blomberg, T. E. Hoffman,
G. V. Nystrom, B. F. Farrell, R. Decker, P. B. Eby, C. R. Baugher, J. W.
Watts, D. L. Teuber, and F. D. Wills, Test of relativistic gravitation
with a space-borne hydrogen maser, Phys. Rev. Lett. 45, 2081-2084 (1980).


TOPEX orbit determination using GPS signals plus a sidetone ranging system

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