Navigation of Mariner spacecraft to Jupiter and beyond will require greater accuracy of positional determination than heretofore obtained if the full experimental capabilities of this type of spacecraft are to be utilized. Advanced navigational techniques which will be available by 1977 include Very Long Baseline Interferometry (VLBI), three-way Doppler tracking (sometimes called quasi-VLBI), and two-way Doppler tracking. It is shown that VLBI and quasi-VLBI methods depend on the same basic concept, and that they impose nearly the same requirements on the stability of frequency standards at the tracking stations. It is also shown how a realistic modelling of spacecraft navigational errors prevents overspecifying the requirements to frequency stability

Chao, C. C.

Fliegel, H. F.

English

NASA Technical Reports Server

PRECEDING PAGE BLANK NOT FILABD. N75 2 1 1 9 7  
FREQUENCY STANDARDS REQUIRFNENTS OF THE NASA 
DEEP SPACE NETWORK TO SUPPORT OUTER PLANET MISSIONS 
Henry F. Fliegel 
and 
C. C. Chao 
Jet Propulsion Laboratory 
California Institute of Technology 
ABSTRACT 
Navigation of Mariner spacecraft to Jupiter and beyond will require 
greater accuracy of positional determination than heretofore obtained 
if the full experimental capabilities of this type of spacecraft are to 
be utilized. 
by 1977 include Very Long Baseline Interferometry (VLBI), three-way 
Doppler tracking (sometimes called quasi-VLBI), and two-way Doppler 
tracking. It is shown that VLBI and quasi-VLBI methods depend on the 
same basic concept, and that they impose nearly the sam? requirements 
on the stability of frequency standards at the tracking stations. It 
is also shown how a realistic modelling of spacecraft navigational er- 
rors prevents overspecifying the requirements to frequency stability. 
Advanced navigational techniques which will be available 
************* 
Several papers delivered at this conference deal with Very Long Base- 
line Interferometry (VLBI), by which the difference between the times 
of arrival of a signal at two widely separated stations from a distant 
radio source is determined by cross-correlation of data tapes. The Jet 
Propulsion Laboratory is supplementing its VLBI program with a simpler 
technique, similar in principle but requiring far less data processing, 
which is informally called Quasi-VLBI (QVLBI). Although developed 
primarily to solve problems in spacecraft navigation, QVLBI can be used 
to compare the frequencies and time rates of change of frequency of 
widely separated oscillators. 
By the methods which are now conventional at JPL, only two kinds of 
data are available for the radio navigation from the Earth of a dis- 
tant spacecraft. The range may be determined by measuring the time 
381 
https://ntrs.nasa.gov/search.jsp?R=19750019125 2020-03-19T21:06:18+00:00Z
required for a radio signal to travel to the spacecraft and back; and 
the range rate can be obtained from the doppler shift of the returned 
signal. 
function, since the second is merely the time derivative of the first. 
The fundamental problem of spacecraft navigation is that, of the three 
coordinates which an astronomer would use to locate an object in space 
-- radial distance, right ascension, and declination -- only the first 
is measurable using a single antenna, and the angular position must be 
deduced. At best, this deduction is difficult. 
Of course, these two data types determine only one mathematical 
Several kinds of information are contained in the measurements of range 
rate, and only by combining them can the deduction of spacecraft posi- 
tion and velocity be made reliably. In Figure 1, bottom, the sinusoidal 
curve shows the effect of the rotation of the Earth on the frequency of 
the returned signal by the doppler effect. Where the spacecraft is be- 
low the horizon of the tracking station (that is, from spacecraft set 
to spacecraft rise), the plotted curve is dashed; the solid portion of 
the curve represents observable data. 
pends on spacecraft right ascension and the Earth's rotational angle 
(UTl), the right ascension can be determined if UT1 is known; simi- 
larly, spacecraft declination can be determined from the amplitude of 
the curve. The uncertainty in our ability to target the spacecraft is 
represented by an elliptical area in a plane constructed perpendicular 
to the vector of spacecraft motion, within which the spacecraft is lo- 
cated to a certain confidence level, as illustrated at the top of 
Figure 1. 
tational pull causes a rapid change in the measured range rate (bottom 
of Figure 1). 
in the gravitational acceleration of the spacecraft toward the Sun, 
which is a function of position of the spacecraft in its orbit, and 
which can therefore be used to infer that position. All these kinds of 
information have been used via the Double-Precision Orbit Determination 
Program (DPODP) at JPL to ascertain and then to correct the trajectory 
parameters of the Mariner and Pioneer spacecraft during the successful 
missions of the past twelve years. Until now, range and range rate 
information obtained by one tracking station at any given time (single 
station tracking) has been adequate to meet all mission requirements. 
Since the phase of the curve de- 
As the spacecraft approaches the target planet, the gravi- 
Not shown in Figure 1 is the small but measurable change 
However, as requirements become more stringent, the sources of error in 
single station tracking become quite serious. Consider the case illus- 
trated in Figure 2, in which a spacecraft is traversing a long path 
(say to Jupiter), and in which data is being accumulated for many days 
to render the gravitational bending of the vehicle toward the Sun most 
noticeable (the long arc method). This acceleration toward the Sun 
varies from only 6mm/sec2 to 0.2 mm/sec2 over the entire distance from 
Earth to Jupiter, and, over the last 100 million kilometers of distance 
travelled, changes by only 33%. Large uncertainties can be produced by 
small effects -- by non-gravitational forces such as gas leaks, by 
changes made to the spacecraft trajectory (maneuvers) if they cannot be 
382 
perfectly modelled, and by unforeseen events (meteor impact, sudden 
venting of gas, and the like). 
in controlling the spacecraft position determination through the di- 
urnal doppler signature can be corrupted by the ionosphere and by the 
uncertainty in station longitude. And the effect of the gravitational 
pull of the target planet usually appears too late to be helpful for 
use in guidance. The basic difficulty is that spacecraft position is 
very difficult to determine by range (or range rate) information from 
a single tracking station. 
The effect of the rotation of the Earth 
Figure 3 illustrates what can be measured when two antennas track the 
spacecraft simultaneously, and the logic is very similar to that of 
VLBI. In going from single station to two station tracking, we have 
passed from so-called two-way ranging to three-way ranging. Single 
station tracking is called two-way ranging because there is an uplink 
(station transmitting to spacecraft transponder) plus a downlink 
(transponder replying to station). If a second station listens, but 
does not transmit, there is a third link (called the "three-way down- 
link"). The physically significant quantity in the situation is the 
difference, T, in the time of arrival of spacecraft signal between the 
two stations; and if 3 is the baseline vector between the two stations, 
s1 is the unit vector indicating spacecraft direction, and c is the 
speed of light, then + + 
-+ 
B * s  
1 ,  T =  
C (1) 
which is the fundamental equation of VLJB. If the fractional frequencies of re- 
ceived signal at the two stations are differenced, this difference 
(called "two-way minus three-way doppler") is the dimensionless quan- 
tity 2 ,  the time rate of change of T. 
as reduced from two-way and three-way range and doppler data, are 
called Quasi-VLBI (QVLSI) . 
These new data types, T or i, 
The advantage of QVLBI for spacecraft navigation over single-station 
tracking is that the angular position of the spacecraft can be directly 
measured, and not merely inferred by the orbit determination program. 
But QVLBI also offers the possibility of measuring the frequency offset 
between the widely separated station oscillators. If these oscillators 
were perfectly synchronized, then one would measure 
I .  
= i = A cos wt (from the Earth's rotation) 
f /observed + atmospheric effects 
+ equipment delay effects 
The atmospheric effects are caused especially by the difference in 
charged pafticle content in the ionosphere over the two stations, and 
by the difference in water vapor content in the troposphere, which is 
383 
difficult to model. The equipment delays (for example, cable delays) 
will produce no effect if they are constant, but any variation 
example, temperature effects at sunrise) will map directly into the 
observed frequency offset. 
at different frequencies, then the last equation becomes 
(for 
If the station frequency standards operate 
+. . 
standard 
(F) = A cos ut + f 
observed 
where (. . .) represents the atmospheric and equipment effects. Notice 
that, given sufficient data (i.e., a sufficient number of observational 
equations of the form of Equation (3) one can solve for A and 
separately; furthermore, by expanding Afstandard in a Taylor Af standard 
series, one could in principle solve for any number of coefficients in 
the polynomial expansion of Af. In practice,- the atmospheric sources 
of error make it impractical to solve for tern higher than frequency 
and frequency rate; Equation (3) becomes 
= A cos ut+ A f  + t *(g) + .  . . 
(4) @bserved tandard 
These simplified QVLBI equations illustrate the basic principles. 
practice, solutions from real data have been made using the Double 
Precision Orbit Determination Program (DPODP), which estimates fre- 
quency standard and spacecraft trajectory parameters simultaneously. 
In 
In 1971, the Mariner 9 spacecraft was simultaneously tracked by the 
Echo Deep Space Station (DSS 12) at Goldstone, California, and DSS 41 
at Woomera, Australia, (no longer operational) during the month and a 
half prior to Mars encounter. 
technique was demonstrated with real tracking data, 
though promising, were not as conclusive as might be hoped due to the 
limited amount of data and inadequate knowledge about the behavior of 
the frequency and time system employed. Later in 1973, a series of 
short baseline ( d 5  km) two station doppler demonstrations with the 
Pioneer 10/11 spacecraf ts was initiated to understand better the 
nature of variations of the frequency and timing system. 
cate that the frequency offsets between stations vary slowly and lin- 
early with a long-term (=IO6 sec) stability on the order of 2 parts in 
1OI2 (Of /f) . A successful QVBLI demonstration with real tracking data 
was made in December 1973 during the Jupiter Encounter of Pioneer 10 
spacecraft. On the basis of this experience, a real-time demonstration 
of the QVLBI technique was planned and carried out during the Mariner 10 
mission to Venus and Mercury (MVM). 
It was the first time that the QVLBI 
The results, 
Results indi- 
384 
flVM was the first interplanetary mission using one spacecraft to fly by 
two planets (Venus and Mercury) with the assistance of the gravitation- 
al attraction of one of the two planets. 
successfully completed with the Mercury encounter of 29 March 1974, and 
was extended to have a second flyby of the planet Mercury on 21 Septem- 
ber. The trajectory of Mariner 10, which is shown in Figure 4, con- 
sisted of many segments, each segment terminated by either planetary 
encounter or a trajectory correction maneuver (TCM). Therefore our 
demonstration was divided into five portions according to the following 
time spans: 
The official mission was 
1. EM-1 to TCM-2 (from November 13, 1973 to January 21, 
1974) 
Orbital determination solutions from this segment 
were used for TCM-2 in order to bring the space 
probe to the desired aiming point at Venus encounter. 
2. TCM-2 to Venus encounter (from January 21 to February 
5, 1974) 
This segment covered the closest approach to Venus, 
so that the position of the probe was accurately 
determined and provided a reference to compare 
solutions from the differenced doppler technique 
with conventional data. 
3. Venus encounter to TCM-3 (from February 5 to March 16) 
This segment was to determine the trajectory 
to provide the parameters for TCM-3. 
4. TCM-3 to Mercury encounter (from March 16 to March 29) 
This provided another opportunity to demonstrate 
the short arc (10 - 12 days) orbital determination 
capabilities using differenced doppler data. 
5. TCM-4 to TCM-5 (from May 10 to June 24) 
This segment was in the extended mission phase 
(after Mercury flyby) and covered the superior 
conjunction, which offered an excellent opportunity 
to demonstrate how well the effects of noise from 
the solar corona could be removed. 
The demonstration was successful in providing estimates of spacecraft 
velocity and position free of corrupting influences. 
interesting to consider the estimates which the data provided of the 
offsets between frequency standards. 
It is especially 
Figure 5 illustrates two different types of estimate of frequency off- 
sets between oscillators at the participating stations. All results 
385 
are with respect to the DSS 14 (Mars) antenna frequency standard at 
Goldstone, California; other participating stations were DSS 12 (Echo) 
16 Ian south of Mars antenna at Goldstone; DSS 42 and 43 in Australia, 
which shared a single frequency standard; and DSS 62 and 63 in Spain, 
each with its own standard. All stations used Hewlett-Packard 5065A 
rubidium standards for MVM navigation. 
The first type of estimate is shown by the heavy black diamonds in Fig- 
ure 5, each of which gives the solution from a single day's tracking 
data for A f  in millihertz between Mars and Echo oscillators (12 minus 
14) at Goldstone. Since the tracking frequency is S-band (2.3 giga- 
hertz), 7 nillihertz corresponds to Af/f = 3 parts to the size of 
largest residual from the mean which occurred. Since these stations 
are so close (16 km.), both looked through virtually the same acmos- 
phere, and the relative longitudes are known to within 6 cm., so that 
the results are nearly the best attainable by the present technique. 
We believe that these results display the real offsets between the 
station oscillators, though the tendency of the data to return to the 
mean value from the highest residuals, rather than to execute a random 
walk, is perhaps suspicious. Every user of VLBI or related techniques 
--- for clock or frequency standard comparison must observe that what is 
measured is the offset of an entire system -- antenna, cables, cir- 
cuitry, and oscillator, under the local atmosphere -- rather than of 
the oscillator alone. In this case, we have no reason to suppose that 
effects other than frequency standard offset and drift are present, 
but the possibility cannot be ruled out completely. 
The second type of estimate is displayed by the open circles, 
and triangles in Figure 5. For each station, and for each of the time 
periods defined above, all tracking data were combined by the Orbit 
Determination Program, and estimates were formed of (1) frequency off- 
set (2) standard deviation of the estimated frequency offset (3) rate 
of change of offset, when the estimate for rate was believed to be 
statistically significant. 
agree fairly well with the black diamonds. The estimates for rate 
correspond fairly well with the differences between offsets estimated 
on different dates. 
termination Program using a priori values of station longitude uncer- 
tainty of 5 meters; this estimate probably errs on the pessimistic side 
for stations of the Deep Space Net (DSN), but gives a fair idea of the uncertainties 
to be expected when conditions are not optimal. 
on the right represent the data when the spacecraft was near the Sun as seen from 
Earth. 
squares, 
The estimates thus formed for DSS 12 and 14 
The error bars were estimated by the Orbit De- 
The extremely large errors bars 
These data indicate that frequency offsets can be measured to a pre- 
cision of 1 part in 10l2 under fair conditions (error bars, Figure 5 )  
to about 1 part in 1013 under the best conditions (scatter of black 
diamonds. ) 
38 6 
The experiments reported here have been very useful in studies of what 
precision of frequency standard is needed for navigation in the DSN. 
They indicate that the behavior of the frequency standards can be 
modelled using solve-for parameters, along with spacecraft state, and 
so prevent us from overspecifying DSN standards. It has been shown at 
JPL that the existing rubidium standards were adequate to the needs of 
the MVM mission, but that requirements for outer planet missions will 
require the use of H-masers. 
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Frequency standards requirements of the NASA deep space network to support outer planet missions

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