Satellite navigation system - geodesy progra

Kershner, R. B.

English

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NAVIGATION SATELLITES RICHARD B. KERSHNER
Applied Physics Laboratory
The Johns Hopkins University
One of the earliest suggestions for a practical oper-
ating satellite system to accomplish a practical ter-
restrial objective to receive financial support was a
system for global navigation. The system, supported
initially by the Department of Defense's Advanced
Research Projects Agency, was the outgrowth of work
done by William Guier and George Weiffenbach at
the Applied Physics Laboratory of The Johns Hopkins
University in the very sophisticated analysis of the
doppler shift from the first Sputnik. The specific
suggestion for a possible navigation system, based on
a similar precise analysis of the doppler shift result-
ing from the relative motion of an artificial satellite
and a ground observing station to yield an accurate
determination of the position of the ground station
from a knowledge of the satellite orbit, was due to
Frank McClure of the Applied Physics Laboratory,
and the first special NASA award for contribution to
space technology was given to Dr. McClure for this
concept.
The detailed system to accomplish global naviga-
tion with the aid of special artificial satellites was em-
bodied in a program under the code name of Transit
in 1959, and responsibility for the development was
transferred from ARPA to the Navy in 1960. The
proposed system concept, as widely described at that
time, is shown in figure I. It includes a constellation
of four satellites in polar orbits, with orbital planes
at 45 ° intervals, which transmit two coherent stable
frequencies. Also, modulations are imposed on
these frequencies which signify the contents of a
satellite memory which can be loaded from the ground.
This transmission is a simple communication channel
which makes available to the user a recent determina-
tion of the satellite orbit. In addition to obtaining
the orbit information, the user also measures the dop-
pler shift exhibited on the received frequency from
the stable satellite oscillator because of the relative
motion of the transmitter (satellite) and receiver
(ground point fixed on a rotating earth). Because of
the transmission and reception of two coherent fre-
quencies, it is possible to make a good approximate
correction for the major ionospheric refraction effect.
Progress on this system, as reported in the open
literature up to 1963, was very encouraging. In par-
ticular, enough was published during this period to
establish the fact that the limitation on accuracy for
the system would be determined by the knowledge of
geodesy since the largest uncertainty would result from
the knowledge of the satellite orbit which, in turn,
was limited by our knowledge of the force field which
controls the satellite orbit. Unfortunately, in March
1963, a change in policy resulted in the classification
of this project so that we can not report in an un-
classified manner the current status of this specific
program.
NASA has been observing the progress of this
program to determine whether or not it would meet
general civilian and commercial needs for a global
navigation system. It has tentatively determined that
the program has certain disadvantages, as far as gen-
eral purpose, nonmilitary use is concerned, that are
sufficiently restrictive to warrant a serious search for
alternative systems. Quite recently there has been
announced the results of a study program, carried out
by General Electric (GE) that proposes an alterna-
tive system that is believed, by some, to more nearly
meet the needs of a general-purpose civilian system.
The general concept of the GE system is to estab-
lish a system of a large number of satellites distributed
with random phase about four different orbits at an
altitude of some 6,000 miles. In addition, the system
has six ground stations strategically located about the
globe. It can be shown that with an appropriate,
127
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128 
- . .  r 
PEACEFUL USES OF SPACE 
FIGURE 1.--Operationai Navy satellite navigation system. 
relatively large, number of satellites there will always 
be essentially, for any potential user, two satellites 
which are simultaneously within his line of sight and 
within the line of sight of one of the six ground sta- 
tions. When a user desires his position he sends out 
a simple signal which is relayed by all satellites within 
line of sight. A ground station which receives this 
request for position from two separate satellites re- 
sponds by sending out a time impulse. This time 
impulse is relayed by the two satellites from which 
the request was received on to the user and is simply 
echoed back by the user via the same two satellites to 
the ground station. By measurement of the time dif- 
ference in these paths, the ground station, which, of 
course, knows the satellite position, can compute a 
triangulation for the user and establish his position, or 
at least two alternative positions. This information is 
then sent to the user, again by a satellite as a relay 
point. The user generally can readily select the correct 
one between the two possible positions since they 
usually differ quite widely. 
The considerations which lead to this system pro- 
posal were, of course, quite different from those which 
dictated the system selection of the Navy. In the case 
of the Navy's system, the entire cost of establishing 
and maintaining the system and paying for user equip- 
ment is all carried by the same organization, and the 
proper consideration is to meet the objectives with a 
minimum overall cost of system plus user equipments. 
There also are a relatively small number of user equip- 
ments, so that it is quite reasonable to pay a substan- 
tial amount for user equipment if by so doing the 
system establishment and maintenance costs can be 
reduced. For a general-purpose civilian system, how- 
ever, in which user equipment cost must be paid by 
the private shipowners, the system will attract users 
only if shipboard equipment cost can be held quite 
low. Thus, in principle, it is reasonable to consider 
systems which are appreciably more expensive to es- 
tablish and maintain if this more complex system can 
result in greatly reduced user-equipment cost. But, of 
course, the deeper question of whether it is appropri- 
ate for the Government to provide such a service as a 
subsidy or whether, alternatively, the economic con- 
siderations should provide for eventual amortization 
of the system costs by charges to the user must, of 
course, be decided ultimately by the Congress or the 
President. 
The purpose for raising this issue, at this time, is 
simply to take the opportunity to suggest to all within 
earshot that the economic considerations will, or at 
least should be, very important in the decision-making 
NAVIGATION SATELLITES 129
process to come, and that it may not be too late to
consider alternatives which could make an exceedingly
large effect on the outcome of these economic con-
siderations.
First, it is apparent that NASA, in making a de-
termination of the suitability of the Navy's navigation
approach for civilian needs, simply considered the sys-
tem as proposed and did not investigate the question
as to whether it was possible to modify or augment the
system to meet the requirements of civilian use for
considerably less money than would be required by
the development of a totally new system. Secondly,
and perhaps more important, if the pattern established
in the past is followed, the decision with regard to
implementing a civilian navigation system will be
made on the premise that a satellite system as a
navigation aid will have to justify itself economically
on the assumption that it accomplishes nothing else.
Now the fact is that the satellite system required to
implement the GE navigation proposal is to all in-
tents and purposes simply another intermediate alti-
tude, random-orbit communication system. It may
have rather specific requirements with regard to repro-
Aucibility of time delay but this is a minor technical
detail. If the United States does establish, through
the ComSat Corp., or in any other way, a midaltitude,
random-orbit communication satellite system, adding
to these satellites the requirement that they be able to
accept and relay the signals and messages required for
a navigation system of the GE type might make very
little difference in the design and costs of the satellite.
In this case, the economic consideration involved be-
comes markedly different.
It is granted that the exceedingly complex gnvern-
mental and industrial boundary conditions that exist
in the communication satellite area make this sugges-
tion very difficult to implement, but surely somewhere
there is a big enough system.
Whatever system is used to establish navigation on
a worldwide basis with the aid of artificial satellites,
it is clear that the accuracy of the system is depend-
ent, among other things, on the accuracy with which
the satellites can be tracked. And this, in turn, is
dependent on the precision with which the forces,
primarily gravitation, which act on the satellite, are
known. In short, an accurate description of the gravi-
tational force field is a prerequisite to accurate navi-
gation by satellites.
Although it is not quite so obvious, actually the
same information is required to establish an Earth-
based global navigation system. In fact, since the
Earth is largely water covered and elevations, even on
land, are based on "sea level," the "shape" of the
Earth is controlled by the gravitational field; that is,
the liquid surface of the Earth will form an equipo-
tential surface in the gravitational field (with proper
allowance for the effect of rotation). Thus, knowing
the gravity field is equivalent to knowing the shape
of geoid, i.e., the equipotential surface. And know-
ing the shape of the Earth is obviously necessary to
provide accurate global navigation even by Earth-based
systems such as Omega.
In summary, progress in global navigation accuracy,
with or without satellites, is dependent on progress in
geodesy. For this reason, it seems appropriate to in-
dicate here the current status of geodesy. It is particu-
larly appropriate to discuss this matter since geodesy
constitutes another of the practical applications of artifi-
cial satellites for accomplishing a terrestrial objective.
Before the advent of artificial satellites, the Earth
was considered to be an oblate spheroid, that is, an
ellipsoid of revolution with a circular equator but a
polar flattening. The first major departure from this
shape was the determination by O'Keefe that there
was an appreciable peaking at the north pole and flat-
tening at the south pole which constituted a north-
south dissymmetry. This fact, referred to in the press
by the phrase "pear-shaped" (figure 2), was deduced
FIGURE 2.--Pear-shaped Earth.
130 PEACEFUL USES OF SPACE
from satellite tracking. The next major announced
departure from the earlier model was given by Izsak
with the statement that optical satellite tracking clearly
indicated that the earth's equator was elliptical. This
fact has been determined independently by Newton at
the Applied Physics Laboratory, based on doppler
tracking results.
It is customary, in geodetic research, to express the
gravitation field in terms of a series expansion in
spherical harmonics:
V(r, q0,X) --
7K I °° lm --I -rlJt" Yml 1- 1 + :_ :_ (_, x)/=2 =
]2,o _____1st oblateness term ",5)
J4,o ___2nd oblateness term ",5:)
]3.0 = Pear-shaped term ",5,e)
]5.o;[7: = Higher order odd-harmonics ",s,°
/e _-- Higher order even harmonics _T)
J2,_;[2:2 = 1st elliptic equator term (s,9,1°)
In this expansion, the terms which are longitude in-
dependent are called zonal harmonics and those which
depend on longitude (like the elliptic equator term,
/2..-0 are nonzonal harmonics. The announcement of
the pear shape of the Earth and of the elliptic equator
corresponded to an approximate determination of Js,o
and ]2.2, respectively.
In 1963, Guier, of the Applied Physics Laboratory,
used data from the doppler tracking of three satel-
lites at different inclinations to make a determination
of all nonzonal harmonics through the fourth order.
Table I summarizes the data used, and table II indi-
cates the data fit obtained with this determination. It
is of interest that the overall data consistency of about
0.06 nm (nautical mile) is contrasted with about 0.2
(nm) 1 year earlier and something like 1 nm 4 years
earlier.
At about the same time, Cohen (at Dahlgren),
Kaula, and Izsak also made determinations of some
TABLE I.--Summary of doppler data used.
Satellite
designation
Inclination,
deg
1961a_1 .......... 32.4
1962fl#1 .......... 50.1
196101 ............ 66.8
Semi-
major Eccen-
axis, tricity
km
7410 0.010
7510 .007
7320 .008
Totals ...............................................
No. of
individual
satellite
passes
No. of
distinct
station
location
No. data
groups,
satellite
orbits
AV.
no. of
passes per
group
Av. time
span per
group (hr)
87 9 8 11 15.9
199 15 9 22 22.7
155 13 10 16 23.3
441 18 27
T^BLE II. Final data root-mean-square residuals
Satellite
1961a_1 .....
1962fl_1.....
196101 .......
Symmetric
component
(along-track),
Miles
78.1
62.0
73.6
Antisymmetric
component
(slantrange),
Miles
81.9
60.7
84.6
Total residuals
Nautical
Miles miles
113.2-=--0.061
86.8=0.047
112.3=0.061
or all of these harmonic coefficients. The results are
shown in tables lII, IV, and V.
Shortly after this determination of the harmonic
coefficients through the fourth order, a polar satellite,
which could be tracked accurately with doppler, be-
came available. The results were quite surprising;
namely, that the same geodetic coefficients which made
possible the tracking of three separate satellites to a
consistency of about 0.06 nm could allow no better
than about 0.15 nm in tracking a polar satellite. At
this point Newton made a new determination of theRMS total 102.3 = 0.055
NAVIGATIONSATELLITES 131
TABLE III.--Nonzonal harmonic coefficients
of the geopotential, n = 2
Value (x 10 _)
TABLE V.--Nonzon,J harmonic coefficients
of the geopotential, n = 4
Value (x 10")
Coefficient
1
C 2 ....
1
S 2 ....
2
C 2 ---
2
S 2 ---
Guier Cohen Kaula Izsak
* (0.0178) ...........................................
*(-0.0348 ...........................................
1.680 1.836 1.19 0.968
--0.638 --0.987 --1.10 --0.400
*Ct2 and S t2 should be negligible. They are listed in this
table as one indication of the accuracy of the results.
TABLE IV.--Nonzonal harmonic coefficients
of the geopotential, n = 3
Value (x 10e)
Coefficient
I
C3---
I
S 3 ---
2
C3---
2
S 3 ....
3
C 3 ---
3
S 3 ---
Guier
1.768
0.194
0.2858
--0.025
0.1480
0.1410
Cohen
etal.
Kaula
0.115
0.027
--0.043
0.102
lzsak
1.12
0.06
mm
0.091
--0.183
0.071
0.124
zonal harmonics (which were not well determined by
Guier's approach) and improved the tracking of the
polar satellite to about 0.1 nm without hurting the
tracking of the lower inclination satellites (table VI).
The geoid that results from these investigations is
shown in figure 3. We are approaching the point of
being able to make a new determination, based on
very high-quality data from four satellite inclinations,
Coefficient
1
C4---
1
S 4 ---
2
C 4 ---
2
S 4 ---
3
C 4 ---
3
S 4 .....
4
C4---
4
S 4 ---
Cohen
Guier
etal.
--0.5688 --0.6785
-- .4597 -- .3757
.05987 .1011
.2661 .2688
.0790 .1580
.0028 --0.036
-- .00785 ..............
0.00656 ..............
Kaula
--0.199
+ .436
-- .0067
.0755
.0299
.0096
-- .0051
0.0116
lzsak
.035
.123
.0215
.0148
.0097
0.0163
TABLE VI.--Determinations o/the odd harmonics
units of I0 -_
Harmonic 1 2
--2.673
Ja--- {+_ .059
_--0.088
Js--- 5- .038
$--O.439
J'-- {_+ .042
---' ........... ' ...........
--2.676
+ .055
--0.086
_ .035
--0.442
± .044
--2.703
± .27
--0.052
"+- .34
--0.507
4"-- .63
+0.055
± .51
Kozai
--2.562
± .007
--0.064
"4- .007
--0.470
± .010
+0.117
__ .001
including one in polar orbit, of all coefficients through
sixth order. However, it is clear that the needs of the
geodesy program can only be met by firing still more
satellites, specifically instrumented to enable precision
tracking, in a variety of orbits.
132 PEACEFUL USES OF SPACE
o
_ "30
o
FIGURE 3.--Doppler geiod of satellite (Guier, 1963).


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