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3. 00
~ME.MORANDUM REPORT NO. 1357
liii~
I 11h
DETERM I NATION OF ORB ITAL ELEMENTS AND REFRACTION
EFFECTS FROM SINGLE PASS DOPPLER OBSERVATIONS
waIluh
R. B. Patton, Jr.
V. W. Richard A S T 1 A
OCT? 0 19W
0 TODqmr,m of the Army Project No. 503-06-011
BAoLrLdnISanTcIeC M anRagEeSmEenAt RStCruHct utre Cu No. 5210.11. 143 LABORATORIES
ABERDEEN PROVING GROUND, MARYLAND
4. ASTIA AUIIABILrrY NOTICE
Qualified requestors way obtain copies of this report fro ASTIA..
This report vill be published in the proceedings of the
Symposium on Space Research and thereby will be available
to the public.
I
5. BALLISTIC RESEARCH LABORAT RI S
MEMORANDUM RPORT 710. 1357
JME 1961
IP ATI OF ORBr"AL ELKWTS AND FRACT!-!
EFFECTS FROM SINGIE PASS DOPPLER OBSERVATICKS
R. B. Patton, Jr.
V. W. Richard
Ballistic Measurements LAboratory
Presented at the Symposium on Space
Research, Florence, Italy, April 1961
jrdtAwmbD of Rthe Army roJect No. 503-06-011 DwEment tructure Coe No. 201Y1 A3
ABIRDZIN PROVING GROUND, MARYLAND
6. BALLItSTIC RESEARCH L13ORLT-OEIS
MENCRRSMN 30. 1357'
xima 19&1
ccma~ --tauLtv ty obsrfzim the CC a &+-iTas~s,
the Dev9 NN n h fteqmem of a rqlsd~ .tmIhfclk ts eofthe~r
Ist afOP1 a mal~ Cr 412e±A.L aectl=&m tR a CC~t~-
ble aet of rp- - u-fos ft~ the 1wrtalu piult~ and eotat±r acqpits.
a MLT awzb ooh~n gl rtl1n. rh latte hs been
-PfMF~ tM w~fm r~A eCqs tm E1109 ftemc zwmomom da-elcr
00fts ft taw twosvh~w A te~biqa f=- jmuii. ithe ,j-amr.&
u efbe Is &Q~~bd soiu Cr amv -al 1t acu~a
7. LODL TT.
A method has been deyelo ed for th" determination of a ccsletc set
of orbital parameters from a few minutes of Doppler data recorded in the
course of a single pass of a satellite. The source of the sinal may be
a transmitter in the satellite or a ground-based transmitter reflecting
a signal fro the satellite. The latter transmitting system requires
more costly and complex equipment but offers reliability, an accurately
known transmitter frequency, and a stronger ge try for a more accurate
orbital computation when the number of receiving stations is limited.
Since it was desired to develop a rapid, reliable, and moderately
accurate method of determining the orbital parameters of a satellite
tracked by a Doppler system eploying a m4inm of receiving stations,
ephasis was placed on the development of a solution from single lass
observations recorded at fron e to three receiving sites. The single
pass limitation vas conslazd to present a challenging and worthy
problem for which there would be numerous mpplications if a reasonable
solution could be developed.
in the past, Doppler data have been used primarily to measure the
slope and time of inflection of the frequency-time curve to obtain slant
range and time-of-closest-approach information. This is considered to
be only an elemntal use of the information in the Doppler data. eingle
pass observations from one receiver have been demonstrated to contain
sufficient information for satellite orbital determinations of suffl' -it
accuracy for many applications.
For exaa ple, it may be desirable to know the orbital parameters as
quickly as possible after launching a satellite. The orbital parameters
of a newly launched satellite could be computed within i-u" after the
beginning of its free flight. Again, after attempting to deflect or
steer a satellite into a different orbit, it may be desirable to kncY
the new orbital pwaieters within a matter of minutes.
The fllcwing sections will digcusa 4'e practicality of orbit cie-terminations
from DoppIle data alone end will indicate limitations as
well as the obvious advantages for zhis conceptually simple technique.
5
8. DESCRIICN OF TRACNG EQU~eNT AND DATA
Doppler observations cnu ist of recordings of Doppler frequency, as
a function of time. Here the Doppler frequency is defined to be the fre-quency
obtained by heterod~yning a locally generated signal against the
signal received from the satellite followed by a correction for the fre-quency
bias introduced as a result of the difference between the frequency
of the local oscillator and that of the signal source. 3h tais report,
the Doppler frequency is defined to be negative when the satellite is
approaching the receiving site and positive when it is receding. If the
Doppler frequency, as defined, is plotted as a function of time, one
obtains a curve of the form shown in Figure 1, usually referred to as an
IS" -curve. The aoymnietry of the curve is typical for a tracking system
with a ground-based transmitter and a receiver separated by an appreciable
distance. Oly for a satellite whose orbital plane bitecta the base line
will the Doppler data produce a symtrical "S" curve with a reflection
system. With a satellite-borne tranmitter, the "8" curve is very nearly
symmetrical, being modified slightly by the Earth's rotatin and the
refractive effect of the ionosphere. If continuous observations are made
and sampled at frequent intervals, such as ore per second, Figure 1 (a)
illustrates an analog plot of the data avaiL. le for ccmputer input.
However, with a ground based transmitter it may be necessary to limit the
number of observations in order to minimize equipnt cost and coplexity.
For example, it is possible to use only three antenna beams and provide
three sections of the "S" curve as shown in Figure 1 (b). Another possi-bility
is the use of a scanning antenna beam to provide discreet observations
at regular intervals as shown in Figure 1 (c). Such data could be obtained
by an antenna with a thin, fan-shaped beam which scanned the sky repeti-tively.
The data in any of the forms suggsted above my be used readily as
input for the computing proct-dure. Whenever possible, thl input con-sists
of the +otal 1N-ppler cycle count over a variable time interval re:t
than the Doppler frequency itself (i.e. the arca *a2u:i the curves or arcs
of curves presented in Figure 1 (a) and 1 (b)).
6
9. TIME
(a)
CIM
(c)
Fig.I-Doplfere uenc-tie cuves
7E
10. In order to handle the Doppler date rapidly and mccurtely, the
DOppler frequency is automatically counted and digitized at the receiving
sites. Figure 2 shows a simplified block diagram of a DOPLOC receiving
syntem. Automatic, real-time counting rf the Doppler frequency requires
a signal of high quality, that is one with very sm rand- errors intro-duced
by noise. Doppler data, which are essentially noise free, are made
possible in the DOPLOC system by use of a very narrw bandwidth, phase-locked,
trackiug filter (ref. 1) following the receiver. Significant
improvements in the signal-to-noise ratiL& of noisy received signal are
realized by extreme reduction of the system bandwidth tlrugh the use of
the filter. Bandwidths adjustable from 1 to 100 cycles per s-cond are
available. The filter is capible of phase-locked operation when a signal
is an weak as 36 decibels below the noise, (i.e. a noise-to-sign- power
ratio o 400). The filtering action is obtained by use of a frequency-controlled
oscillator that is correlated or phase-locked to the input
signal. The basic block diagram of the tracking servo loop is shown in
Figure 3. Tracking is accomplished with an electronic servo system designed
to force the frequency-controlled oscillator to follow the vriatiocns of
frequency and phase of the input signal. Correlation is maintained with
respect to input signal phase, frequency, first tie derivative of frequency,
and with a finite but smll phase error, the second tim derMytive of
frequency. This is done by a cross-correlation detector cona:sting of the
phase detector and filter, or equalizer network. Ubder dynoaf£c conditions,
the control voltage to the oscillator is so filtered in the equalizer net-work
that tracking faithfully reproduces the rate of change of the input
frequency. An inherent feature of this design is an effective acceleration
memory wbich provides smooth tracking and extrapolation through signal
dropouts. Experience with signal reception fro Earth satellites has barne
out the necessity for this amory feature, since the ree$V.id signal ampli-tude
my vay widely and rapidly. The filter works through signal null
periods very erfectively without losing lnIr. In addition, ti s .
provides effective tracking of the desired Doppler signl in the -'-esene
of interfering rignals when several sateili+s are within receiving range
at the same time.
, , s I I I I I I I8
12. 0
w-Jg-
N
'Al
I-CD
Co
'Ii
I-N
0 Ii.
w U
4
I-.
U
U,
S
WI0-
CO 0
a
I-
0. z
:0
13. The signal-to-noise power imprcirenent furnished by the tracking
filter is equal to the ratio of tLe irput source noise beadwidth to
the filter bandwidth. The internal noise generated by the filter is
negligibly small at all bandwidths. The relation between input and
output signal-to-noise is shown in Figures 4 and 5. In a typical case
wii h a receiver bandwidth of 10 kc and a filter bandwidth of 5 cps, a
signal buried 27 db down in the noise will appear at the filter output
with a 6 db signal-to-noise rat.'o. An experimental investigation
(ref. 2) has been made of the relation between signal-to-noise ratio
and the uncertainty or random error in measuring the frequency of a
Doppler signal. The test results showing R.M.S. frequency error as a
function of signal-to-noise ratio and tracking filter bandwidths are
shown in Figure 6. For the example cited previously, a signal 27 db
down In the noise can be read to an accuracy of 0.15 cps. An integration
time or counting time interval of one second was used for these measure-ments.
The tracking filter can be equipped with a signal search and autcma-tic
lock-on system. Signals 30 db down in the noise at typical Doppler
frequencies, from 2 to 14 kc, can be detected within a fraction of a
second and the filter phase-locked to the signal. With this equipment,
signal acquisition and lock-,= have become routine in field operations.
The DOPLOC system has been used extensively for satellite tracking.
The inherent high sensitivity of the receiving system to signals of very
low energy (2 x 10O2 0 watts, - 197 dbw, or 0.001 microvolts across gn ohms
for a threshold signal at 1 cps bandwidth) has permitted the use of con-ventional,
low gain, wide coverage, antennas to achieve horizon to hori-zon
tracking at great ranges. It has been found to be practical to chaige
bandwidths over the selectable range of 1 to 100 cps in accordance with
the information content of the signal and thus achieve maximum signal-to-noise
ratio. Since the key to successful determination of orbits lies in
obtaining data with small values of random an. systematic error, t:t high
quality dr.t o,'? ut of the DOPLOC system has been an imjortao 4 eature.
An orbital solution, develuped specifica.,1y for this system, has yielded
relatively accurate results with a surprisingly small number of DOPLOC
tracking observations.
i1
14. -V- . T14 T1 1 FT4, 1 f
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7j
z
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Till
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7 7 z
M-N
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12
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- k 042 L - 0 5 3:Z 09
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13
16. INPUT SIGNAL TO NOISE RATIO
VS.
OUTPUT SIGNAL TO NOISE RATIO
AND
RMS FREQUENCY ERROR
x .3
2
'.00
INP OISE SOION TO 0 61 - AI
-M -4 -I 14 -It --
17. THE ORBITAL SO. -2CQ
The method of solution consists of a curve-fitting procedure, in
which a compatible set of approximations for the orbital jArameters,
are improved by successive differential corrections. The latter are
obtained from a least-squares treatment of an over-determined system
of equations of condition. The imposed limitation of single pass
detection permits several assumptinns which considerably simplify the
computing procedure. Among these is the assumption that the Earth
may be treated dynamically as a sphere while geometricully regarding
it as an ellipsoid. In addition, it is assumed that no serious loss
in accuracy will result if drag is neglected as a dynamic force. With
these assumptions, it is apparent that the satellite may be regarded
as movlg in a Keplerian orbit. An additional simplification in the
reduction of the tracking data is warranted if the frequency of the
system exceeds 100 megacycles; for it then becomes feasible to neg-lect
both the atmospheric and ionospheric refraction of the transmitted
signal.
In formulating the problem matieatically, it is helpful to regard
the instrumentation as an interferoeter. In this sense, the total
number of Doppler cycles observed within any time interval will provide a
measure of the change in slant range from the receiver to the satellite
if the transmitter is air-borne, or in the sum of the slant ranges from
both the transm-itte.' and receiver to the satellite if the signal origi-nates
on the ground and is either reflected or retransmitted by the
satellite. Assuming the latter for the discussion which follows, let
g (t) be defined as the change in the sum of the two slant ranges.
It follows fra Figure 7 that
(1t2 ) - S+Rs) - (+ I(1)
where T is the position of the transmitting sit-, R, the location om -=ae
Ith recriver, S. u position of the satellite at time t,, and S the
15
19. position a!- +ine t 2 . gj (t 1 2 ) is th- cbnnge in the sum of the raant
ranges from the satellite to the transntter and to the jth receiver
in the time interval from t to t It is worth noting that, if
this time interval is equal to one second and . is the wavelength of
the transmitted signal, [g j (t 1 2 ) "+ X is equivalent to the Doppler
frequency for the jtth receiver at the time, (t I + 0.5 sec.).
The mathematical development )f the computing procedure has been
presented in reference 3 and will not be repeated here. Rather, we
will confine our remarks to a sumry of the more important phases of
the method. The solution consists of improving a set of position and
velocity components which have been approximated for a specific time.
The latter will be defined as t o and in general, will be within the
time interval over which observations have been recorded. The com-puting
procedure is outlined in Figure 8. Initial approximtions for
position and veloci.ty uniquely define a Keplerian orbit which may be
described in tems of the following orbital -ters:
a semi-m&jor axis,
e a. eccentricity,
a a mean anomaly at epoch,
i j inclination,
n- right ascension of the ascending node,
c a argument of perigee.
After these parameters have been determined, the position of t tc
satellite, and then g3 (t), may readily be computed as a function of
time. Comparing the computed values of gj (t) with the observed values
of the same quantity and assuming more than six observations, a set
of differential corrections for the initial approximatin.- cr position
and velocity may then be obtained from a standard least-sqares treatment
of the resulting over-determined system of equations. The correctinis
are applied to the initial approximations and thc computation is ite&ated
until convergence is achieved.
17
20. U)
0o
0
w
CL 0 A4 w I
0
z - a a 2 00
I--M
0
b
I.&1 0
0 *
It 0
S 0
21. This computing procedure essextis.aly determiies oly those seg-ments
of the orbit confined within the intervals of observation. By
constraining the satellite to Keplerian motion, the parametersa a, e, a,
i, n, and w are likewise determined in the course of the computation;
and these serve to provide an estimate of mot~.on over the entire orbit.
On the other hand, it has been found Iqpractical to fit an entire ellipse
to the observations by solving fc- the oibital parameters directly.
19
22. n'TTTAL ORBITAL APPOX &T. I8NS
Convergence of the computation resta primarily upon the adequacy
of the initial approximations for position asd velocity. It has been
establibhed that, for a system consisting cf a single reeeiver and an
earth-bound transmitter at opposite ends of a 400 mile base line, con-vergence
is assured when the error in each coordinate of the initial
estimate is not in excess of 50 to 75 miles and the velocity components
are correct to within 1/2 to 1 mile per second. When the signal source
is carried by the satellite a unique solution is impossible with obser-vations
from a single receiver. However, if single pes measurements
are available from two or more receivers, with either a ground-based or
a. air-borne transmitter, the system geometry is greatly strengthened.
Convergence anii then be expected when the initial apwimtions are
within 150 to 200 miles of the correct value in each coordinate and
1 to 2 miles per second in each velocity component. larger errors my
occasionally be tolerated, but the figures presented are intended to
specify limits within which convergence may be reasonably assured.
Therefore, it has been necessary to develop a supporting ccuputa-tion
to provide relatively accurate initial approximtims to position
and velocity for the primary computation. Several successful methods
have been developed for this phase of the problem; but discussion will
be confined to a few applications of a differential equstion, derived,
in reference 3, to approximately relate the motion of the satellite to
the tracking observations. If the transmitter is earth-bound, this
equation In of the form
A -,2
S -. + (2)
where the slant ranges from the transmitter and the receiver to the
satellite are respectively pT and pi. Wj is the secon time derivative
of t he function dpfinel by equation (1). In derivinx equation (2),
It was ass-li that:
20
23. 1) in angular measurement, the ek,tAlite is within ten degrees
of the instrumentation site,
2) the Earth is not rotating,
5) the satellite moves in a circular orbit.
With these assumptions, A may be shown to be appraximately equal to
v 4/(GR) and hence, constant for a circular orbit since R is the
Earth's radius, v is the velocity c the satellite, and G is the mean
gravitationajl constant.
The first application to be considered will be for a system in
which the transmitter is carried by the satellite. For the jth receiver
in such a system, equation (2) reduces simply to
Aj 2
(3)
.j
If measurements of the rate of change of the Doppler frequency, fj, are
made for two different times, to and t1 , and Doppler frequencies, f,
are observed at regular intervals between to and t , we note that
(t ~ f(t)0'
P*j ((t) to1 - x r (t0 ), t1,t )
Pj (t1) - PJ (to) + f f (t) dt,
t
0
where X is the wavelength of the siguaL and, p3 (t1 ) and p i (t,) are thn
only unImowns. Combining equations (4) with equation (3) yiclds
t5
(t, 2 - ~ (t 2 1 + Ff' t j(t)dt!
Pj (tc) L r0
L (to (t1)j
21
24. which vith the last relation of equations (1) determines elant rang
as a fimction of time. These results mu¢- *. used with equatio () to
establish a value for A from Vhich an excellent approxaimtion of the
velocity of the satellite mey be obtained. No additional InformLtion can
be extracted when observations are limited to those from a mingle receiver.
However, if measurements f three or more receivers overlap in time,
a set of approximations to the position and velocity components Wy be
determined by a straightforward trinculation procedure. When data from
only two receivers are available, an estimate of position and velocity
may still be obtained for a time which lies within the interval of obser-vation
of both receivers, if the results of the corxtation described by
equat.on (5) are coabined vith the ass mption of circular notion. For an
epoch time, selected so that the satellite Is near the zenith of the
instrumentnUon site, we mW safely assume that the vertical component
of velocity Is sll and can well be approximated by zero. Using the
reaults of the computing procedure described above, slant ranges for the
epoch time may be computed for each receiver; and in the process, 4n
estimate for the velocity of the satellite will be obtained. Coabining
these three results with the Doppler frequency meanurments fr the two
receivers for epoch time, we my readily determine the remain'n velocity
components and anl three position coo-dLiates, in this development, no
account has been taken of the difference In frequency between the trans-itter
In the satellite and the reference oscillator on the ground. If
both are stable, a constant frequency error, or bias, wll be introduced.
n general, this error is so large that it must be corrected before applying
the above procedure. Moat methoda, for determining the bias, assum
ayi*try about the inf'.ectlon point and use this characteristic of the "S*
curve to determine the inflection time as accurately as possible. Sance
the latter Is also the time of closest approach of the satellt e to the
receiver, the Doppler frequency should be zero. 9Therefore, the basa is
simply the observed frequency at the inflection time.
22
25. The second application considers a _7y3tem in which the trans-mitter
is earth-bound so that the signal travels fron the EaFth'
surface to the satellite and back to one ur more receivers on the
Earth's surface. For thLs problem, equation (2) applies. Let us
define a right-hand rectangular coordinate system as shown in Figure
9 with the origin at the transmitter and the Z-axis positive in the
direction of the vertical. The y-axis is formed by the intersection
of the tangent plane at the transmit ter with the plane determined by
the transmitter, the Ith receiver, and the Earth's center. The re-ceiver
will then be at the known pcint (0, Yji, zj). If the variable
point (x, y, z) indicates the position of the satellite, the slant
ranges from the transmitter and the Ith receiver are respectively
given by
T + y + z ,
(6)
P - l + 2 ( xY-yj)2 + z- J2) 2
from which it follows that
* +. Yy + z
AT PT(7)
xi + (y -y ) y + (z -.zj) .
j pi
In the three-beam mode of operation, the satellite will be approximately
in the yz-plane at to, which is defined as the tine halfway between the
initiation and termination of tracking in the center beam. Let the
satellite's position and velocity at this time be defined as (xo1 , Yo, zoj
and (* o' o), respectively. Obviously, x may be approximted by zero
end as before, 1'o may also be met equal to zero. Equations (7) then reduce
to
23
26. zV
CTE
*EOITP FO0DE0RMNIN
ot APR XMA N sNoIA
coxiFIUR *I5,Y~j
27. °To =
2Y + Zo0
(8)
= (YoYj) ko
P~~/(Yoo -yj)f+ (-ZJ)7j
Let fjo and fJo be the Doppler frequency and rate of change of frequency
for the Jth receiver at t . It follows that
fJOTo fo (6 + j
)
(9) From equation (2), we conclude
A 2 A 2
jo I POoT OoJ + jo (10o)
Expressing equations (9) and (10) in terms of the position coordinates
and velocity compcnents of the satellite at time, to, yields
~JOXF~ -o) (yo - .(%YJ)(
- v + ( L., ,) )
2 = A 1 2 j
JYo 2 (3o Y() ko 2 A-ky2 O021 A[ (Y' " 2 + (°z,
jo" 'y + + V~ o . )X Z) (12)
XV y 0 + zo X" Y"- j7 + (2.o'b
Let us assume a specific orbital inclination. With our previous
assumption of circular motion, jo may readily be computed as a fVm-tion
of Yo and z o . Than equations (11) and (12) will likewise provi~e fjo
25
28. and fo as functions of position in the ,z-Plane. Thus, for a given
inclination, families of curves may be computed and plotted in the
yz-plane for both fjo and f Figure 10 presents such a plot, for an
incliration of 80 , with the transmitter and receiver separated by
434 miles and with both located 350 off the equator. To attain symmetry
and simplify the construction of such charts, z3 was assumed to be zero,
which is a reasonable appruximation for this approach to the problem.
If similar charts are prepared for a number of inclinations, satisfactory
initial approximatlons may be rather qLckly and easily obtained by the
following operations:
1) Assume an inclination. This, of course, is equivalent to
selecting a chart. Accuracy is not casential at this stage
slAce the estimate may be in error by 150 without preventing
convergence.
2) Enter the chart with the observed values of f and fi to
determine an appropriate position within the yz-plano.
3) Approximate the velocity components. These should be consistentt
with the assumption of circular motion, the height determined
in step 2), and the assumed inclination.
4) Determine the position and velocity components in the coordi-nate
system for the primary solution by an appropriate
coordinate transformtion.
In addition to the graphical method, a digital solution has been
devised for equations (11) and (12). As in the previous development,
we have two measurements available and desire to determine three unknowns.
In this approach, one unmown is determined by establishing an upper bound
and assuming a value which is a fixed distance fro this bound. The
distance has been selected to place the variable between its ,;per and
lower bounds in a position which is favorable for convergence of the
primary computation. In this method, we chose to start by approxiiating
z0 . It may be observed in Figure 10 that, for larger values of it3o the
maximum value or zc occurs above either the tr'mumitter or receiver whiie,
26
29. SIX -
30 CPSAS
.j 40 CP/
x 4
70
TRANSMITTER micIVER
Y-AXIS (EAST IM MILES)
OOPLOC FREQUENCY AND RATE 0F CHANGE
OF FREQUENCY AS A FUNCTION OF
POSITION IN THE YZ - PLANE
(FOR SD. INCLIN..4rION)
FIGURE 10
T7
30. for smaller values f f e the maximum value of zo occurs over the mid-point
of the base l±ne. The first step in tte computation is to determine
a maximum value for z0 . To this end, ko is eli-inated from equations (11)
and (12) to yield an expression which varies only in yo and z0 . A appears
in this expression, but it is also a function of these variables. The
resulting equation may be solved by numerical methods for z with YO-knd
then, solved a second time for z with Yo -al/2Y j. The larger of
these results is to be used as a value for (zo)M which is defined to be
the maximum possible value of z . Assuming the altitudes of all satellites
0
to be in excess of 75 miles, we may conclude free the general characteristics
of the family of curves for f in Figure 10, that the satellite's altitude
will differ from (z o)M by no more than 100 miles. Since an error of 50
miles may bc tolerated in the approximtion for tach coordinate, E Zo) - 50 i.a suitable value for z0 . With the altitude thus determIned,
we may solve equations (11) and (12) for Yo and Yo" In the process A, and
hence the velocity, will be determined. With i assumed as zero, i ms& be
00
readily evaluated to complete the initial approximations which consist of
the position (0, yo, zo) and thc velocity (*o, ko, 0). It is worth noting
that there is a pair of solutions for y0 and Y " Further, the method does
not determine the sign of x . If, in addition, we accept the possibility
of negative altitudes for the mathematical model, we arrive at eight
possible set3 of initial conditions vhich are approximtely syemetrical
with respect to the base line and its vertical bisector, It is an interesting
fact that all eight, when used as input for the primary camputation, lead
to convergent solutions which exhibit the same type of syimtry as the
ipproximations themselves. Of course, it is trivial to eliminate the four
false solutions which place the orbit underground. Aurther, two additional
solutions may be eliminated by noting that the order in which the satellite
passes through the three antenna beams determines the sign of i. :a the
two remaining possibilities, Jo is observed to have opposite sins. Since
the y-axis of the DOFLOC system has been oriented fram west to east, the
final ambiguity may be rezolved by assuming an eastward cacm~nent of
28
31. velocity for the satellite - certain.Ly a valid armmpticn to date. In
any event, all ambiguity may be roved rrom the solution by the addition
of one other receiver. Moreover, this would significantly improve the
gecetry of the system and thereby strenithen the solution.
The first method presented in this section is intended for use with
a satellite which carries its own transmitter. These data are generally
recorded continuously as in Figure la. The other two methods have been
developed for a system which provides observations of the type displayed
in Figure lb where the siga source Is on the Earth's surface. The plot
shown in Figure le is also for a system with an earth-bound trantter;
and the last tvo methods may be applied to such data if minor modifications
are made in the procedures. Indeed, with any tracking system that provides
observatlow of satellite velocity components, equation (2) furnishes an
adequate base for establi&hlng an approximate orbit to serve as an initial
solution which may be refined by more sophisticated methods.
29
32. RESULTS OF ORBITAL COGMUTATIO
Numerous convergent solutions have been obtatned with actual field
data from a system consisting of a transmitter a. Fort Sill, Oklahoa,
and a single receiver at Forrest City, Arkansas. This system complex
provides a base line of 434 miles. In addition, several orbits have been
established from field data for satellites which carried the signal source.
For the latter mode of operation, receivers werve available at both porrest
City, Arkansas, and Aberdeen Proving Ground, Maryland, providing a base
line of 863 miles. Results will be presented for both types of tracking.
The initial successful reduction for the Fort Sill, Forrest City
sstem wa, achieved for Revolution 9937 of Sputnik iII. The D0PrX obser-vations,
as well ae the results, axe presented in Figure 11. Measurements
were recorded for 28 seconds in the south antenna beam, 7 seconds in the
center beam, and 12 seconds in the north beam, with two gaps in the data
of 75 seconds. Thus, observations were recorded for a total of 7 seconds
within a time interval of 3 minutes and 17 seconds. Using the graphical
method described in the previous section to obtain initial approximtions,
convergence was achieved in three iterations on the first pass through
the computing machine. It will be noted, in the comparison of DOPLOC and
Space Track results, that there is good agreement in a, e, i, and n, par-ticularly
for the latter two. This is characteristic of the single pass
solution when the eccentricity In small and the computational input is.
limited to Doppler frequency. Since the orbit is very close to being
circular, both a and w are difficult for either the DOPLOC System or Space
Track to determine accurately. Hoever, as a result of the mall eccen-tricity,
(co + a) is a good approximation of the angular distance alon the
orbit from the equator to the position of the satellite at epoch ti-'. .v
as such provides a basis of comparison between the two systems. A compari-son
of this quantity is included in Figure 11. To summarize, vha limited
to single pass, single-receiver observations, the DOPLUC 8-sta provides
an excellent deterriwnat-In o,f the orientation of the orbital plane, a
good determination of tt.e shape of the orbit, and is 'f.ir-to-poor determi-nation
of the orientation of the ellipse ithin the orbital plas.
30
33. - - -j
N
II7 -Z -~0
.0 ~ IL
0 A
IrI
oa) A000 0P z~s, I
in~~~2 ---to- -- w',0 c
w wi
ILI
II 4pI
34. Although c and w have been accurately Letermlned cm occasion, the
interim DOPLOC system with its limitations fails to provide consistently
good results for these two quantities. Therefore, only a, e, i, and n
will be considered in presenting the remaining DOPLOC reductions. The
observations recorded for the Fort Sill, Forrest City coMplex are plotte
in Figure 12 for six revolutions cf Discoverer XI including 172, the lad.,
known revolution of this satellite. The DOPLOC determined position for
this pass indicated an altitude of 82 miles as the satellite crossed the
base line 55 miles west of Forrest City. A conpsrison of the Space Track
results with the DOPLOC reductions for these observations is presented
in Figures 13 through 16. In addition, DOPLOC reductions havt been
included for three revolutions in which the receivers at rest City and
Aberdeen Provg Cround traced the air-borne transmitter in the satellite.
In Figures 17 through 20 a similar comparison is presented for six separate
passes of Transit 1B. In these, all observations consist of data obtained
b) receivers at Forrest City and Aberdeen Proving Ground while tracking
the on-board transmitter.
Finally, in Figure 21, results are tbuated for a reduction based
on only seven frequency observations. These have been extracted from the
complete set of observations previously presented for Sputnik 1I1. They
were selected to serve as a crude example of the type of reduction required
for the proposed DOP1DC scanning-beam system. The example shows that the
method is quite feasible for use with periodic, discrete measurements of
frequency. Of course, the proposed system would normlly yield several
more observations than were available in the example.
It is noteworthy that numerous solutions have been obtained with
field data from a single receiver during a single pass of a satellite.
Further, these measurements have been confined to three short Periods of
observation within a two to three minute Interval. Additional receivers
spread over greater distances would, of course, considerably enhance the
accuracy of the results. For example, a system with t'ro receivers ane a
36. 1 g1
0 1i
to
1
II--
0 _
z~~ Z Z it_
0o 0
W, w I- &
Eu. 4c~ 4c-at0
0. ME
0
11 0 3393
0.4 Z49
S33M3Eln NOILVunON
37. w w __
0 0c
z a: w~
zz Z
Wo, oZzg
0Z 4 0
o 9- cc
00 z 0
0. zo
4- I,
S338930 NI WO0N O)NION30SV JO NOIEN338V ALHOUN
38. CoY
hiw
J w +
z0) t___ 0
Z _ 0
c z
z 4
w- 0 !E
1+Z ra .
w _ _ _ _ _ _o 09ccc
w ww
- ______r a =__ 0
__ 4IW
1' q
56 I ~V M i~WI3 meI
39. w 0
to 0
00
0 ar
ZZ
Z 0 0
WCC aa
cc a w 0
0 Cdw i w
I- L9
Lu +
U
0
U I 0
0
0
A1131HIN3003
.37
40. Z -~0
20
2W
z 4
0 W.....g a _ _
7 -
z, i
9L a
SflMG3O NI NOILVNIIDNI
38
41. w 0.
z I-z
3 z
z Io-~
hi 40
I- -
202
z0 4c N S3M3 I30 NO3OVd OSIS 10
42. w
w
w cc
go _ - _ 0__
z
z -
0 N
z
La - _
a 20 z
*2
x w 81
4cO
coo
w 4
(0j
0, z
04
43. - F I-II-W
z
0 w
>o s
coo -~ J 1
z -d u w3C
4W-II-z
I
44. 00
00
o ~I ..
* I.
b0-
~a%
04.
a- ' -
$43 A SMV PA5ld.0Q
45. ground transmitter would reduce . 'rrOr PrOP~aio to in the ccmA~ptIoMS approximately a tenth of that to be expected for a system ; 4th a single receiver. Removing the restricti on Of single pass determination would further enhance the accuracy of i he results.
COaU"t~ng time$ have been found to be quite reasonable. Convergent solutions have requiredl 20 to I40 ainutee on the Ballistic Research lAboratories. O-RDVAC vhlt:h requires the coding to include floating decimal sub-routines. Mom modern nOlsIes, such as the DNLEM, -nov under con- structiOn at the Ballistic Research laboratories, will perfom the Sam computation In 2 to J4 minutes. Bence, It Is realistic to claim that the system potentially has the capabiity of orbit deterninatioU Within, five m:!zutes of the observation time. in conclusion, the method In general =d, therefore, need be confined to neither Doppler fequazneies nor KePlee-Aa orbits, In partlcuALr, if the limitatton of Keplerlmn motion may be retained, onay minor modificatIon is required to use the method 14h all.oer types of satellite observatins
143
46. ICIOSPREC MMAsRM D.MS
Oue of the methods used for studying the ionosphere is derived
from the measurement of its effect on radio waves propagted through it.
One effect observed is the increase in propagation phase velocity above
that occurring in free space (i.e. the wavelength is longer in the medium
than in free space). At the frequcncies used, 30 to 300 mc., the index
of refraction ez' be =pressed as
4o.25 N
f 2 (13)
0
where N• is the electron density in electrons per cubic meter an& f 0 is
the tranmmitt+-d frequency. Thus, the index of refraction Is less than
unity in an ionized medium and the aunt by which the index of refraction
is changed is inversely proportional to the squa-re of the frequency.
Use is made of the dependece of the refractive index on frequency to
determine ionosphere electron content. Data with which to make the electron
content computation are obtained by measuring the Doppler frequency shift
on two harmonically related signal frequencies transmitted front & satellite.
The Doppler frequency, superimosed upon the lower of the two frequencies,
is multiplied by the ratio of the two sina' frequencies employed; and then
the result is subtracted frm the Doppler observations of the higher fre-quency
signal to yield dispersive Doppler data. The dispersive Doppler
frequency is proportional to the time rate of change of the total clectr-t
content along the propagation path,
0
where IrNedr is the total electron content along the propasLion path, r;
ThL& a measure of the clatzgv in electron content, over & time interval of
interest, is obtained by integration of the disp rulve Doppler frequenc.-.
which Is simply a eye?! count over the specified Interval.
1414
47. Instrumentation has been develcped for measuring and recording
dispersive Doppler frequency. Satellites carrying radio tzunswitters
whose frequencies are harmonically related serve as signal sources. In
order to receive signals frcm stellites at great distances and provide
output data of high quality it is necessary to us.. extremely sensitive
receiving systems. Narrow bandwidth, phase-locked, tracking filters are
used to provide essentially noise-free Doppler frequency data. Two
channels are used to receive the two iarmonically related sign&". The
multiplication of the Doppler frequency on the lower frequency signal takes
place at the output of the tracking filter so as not to degrade the signal-to-
noise ratio. Frequency multiplication prior to the final narrow-band-widthi
filter would seriously degrade the signal-to-noise ratio of the
Doppler signal. A special broadband frequency multiplier (ref. 4) has been
developed for multiplying audio frequencies. The technique developed is
unique in that it achieves multiplication of an Audio frequency Doppler
signal, which varies many octaves, but maintains a sinusoidal output wave-form.
The multiplication factor can be any product of two's %od three's
(i.e. 2, 3, 4, 6, 8, 9, ---. ). This frequency multiplier is basically a
combination of an aperiodic frequency doubler, push-push, circuit and a
bridge configuration tripler circuit. Anxiliary circuits with functions
of automatic gain control; clipping, differentiation and phase-locked
trcking filtering make possible a iinusoidal output waveform.
Figure 22 shows a block diagiam of a receiving system for ionospheric
measurements using the broadband frequency multiplier (ref. 5). Dispersive
Doppler, Faraday rotation and satellite rotation effects on the signal can
be separated automatically and directly recorded as nhown in Figure 23.
This is a portion of a record from an upper atmosphere sounding rocket
flight in which a two frequency transmicter was carried.
Dispersive Doppler data recorded in a form similar to that shown in
Figure 23 can be counted to an accuracy of - 0.1 cycle. The total electron
content can be expresed in terms of dispersive D.ippler cycles as
45
48. : u-Il
a.w~~EJjHJj~J i:J I
I a U
*~ :.- aa4 0
a -~ 1- .3
9- ~ I'
ma ~a- * 2
agZ --
-
a- I-I
t-~ I m
0 g j ~Z .3 -
4
1:3 3; :~
- I3 3~a, * I - e
-- * 0 [iJI~ mm - g
S
I4~I g
1mb.. -z
3 mm liii- 0 a- m~ 2
a: ~:i1 I
:3 -
-
ma
-a
S.
50. N dr (IF- (15) 1) 13.4 x i0
where (0 - K01) is the integrated dispersive Doppler frequency, PI is
the lower transmission frequency, F2 is the higher, K is the ratio F2/F I .
Consider the Transit satellite (1960 Eta), where F, - 54 me and F2 = 324 mc.
The incremental change in total electron content for each dispersive
Doppler cycle is
N-d ..3..2.4. ..3...24 x 108 x lo-8 " 6.9 x 1013 seqlueacrter omnes ter ":(16)
Therefore. t;,e counting accuracy of t 0.1 cycle represents a measuroing
sensitivity to the change in ionosphere electron content of 6.9 x 1012
electrons/square meter. This sensitivity is high enough to detect s1l
irregularities in the ionosphere. A plot of dispersive Doppler data and
integrated dispersive Doppler frequency is shown in Figure 24. for a pass
of the Transit satellite (1960 Eta) on 17 November 1960. Irregular hori-zontal
gradients in the ionosphere are clearly shown by the variations in
the dispersive Doppler frequency that are evident during the second half
of the satellite pass. ibis curve normally has a relatively smooth "S"
shape under undisturbed geo.gnetic conditions. It is of considerable
interest to note that this record was made following the period of an
extremely severe geomagnetic disturbance. Severely disturbed radio cou.
ditions existed fro November 12 through 18. One of the most active solar
regions observed in recent years was reported by the North Atlantic Radio
Warning Service of the National Bureau of Standards. The A-index (a
measure of geomagnetic activity) on November 13 w 280, thehi.hest recorded
in this solar cycle. An A-index of 25 is considered a disturbed condition,
therefore 280 represents an extremely disturbed condition. An unusua.ly
high magnetic field intensity vas recorded at the .5llistic Research
Ibcratorims rmW.#c,, -cer station on November 12 and 13 Vhich is -' .n 'n
48
52. Figure 95. Thus the qualitative agreement between the irregularly shaped
dispersive Doppler curve in Figure 24 and the disturbed ionosphere is well
established.
The Faraday rotation effect can also be used to determine total
ionosphere content. Techniques have been developed for separating Faraday
rotation effects from satellite rotation effects by the use of opposing
circularly polarized antennai. and a sequence of electronic mixers as shown
in Figure 22. When the satellite spins very slowly, a simpler method of
determining Faraday rotation cycles by counting received signal amplitude
nulls can be used. A linearly polarized receiving antenna is used in this
case. A plot of ionospheric electron content is shown in Figure 26, obtained
by tsing reneived signal amplitude null data from a pass of the Transit
satellite (1960 Eta). The ccmputation methods of Bowhill (ref. 6) and
Garriott (ref. 7) were used in the earliest studies. A complete ray
tracing program based on that of Little and Lawrence (ref. 8) is in preps-ration
to provide more acciuracy and to eliminate several assumptions and
restrictions of the early methods.
50
53. WAL it:mv ON .k 13 No. fme
~J ±." E 4. ........
75
55. CONCLSIONS
The infomtion on the Ionosphere, 0 ained by the met. ds Aes-cribed,
makes it possible to correct refr,tion errors and obtain more
accurate orbital parameters fru Doppler lata. An interesting example '
the ionospheric effect on orbital accuracy was ooserved in the computation
of the orbital parameters shown in Figures 17, 18, 19, and 20. The
computation was first attempted using the complete "S" curve including
the relatively constant frequency limbs. The limbs represent data ob-tained
during the emergence of the satel.ite from the horizon and recession
into the horizon. The orbit obtained was appreciably different from that
published by Space Track. Another computation was made using only the
center pwrtion of the "S" curve, while disregarding the limbs. The so-lution
was qxeatly improved and the results agreed very well with Space
Track data. This points out the large refractive effect the ionosphere
iiLroduces &L low elevation angles of transmission. Fortunately, an
orbital solution can be compute, from Doppler datAL obtained at quite high
elevation angles, thereby minimizing the refractive crror.
A program has been initiated to combine Doppler frequency observations
with electron content data in an iterative computing process to Increase
the accuracy of tna orbital determination. The comutation will be initi-ated
by determining an orbit from the uncorrezted Doppler observations.
The electron content data and this approxlmate orbit will be combined to
compute corrections for the original Doppler frequency aesurezits.
Usiag the latter, the process will be iterated until the refractive error
has been minimized in the Doppler data and hence, in the conputcd orbital
parameters as well.
. B. PATTON, JR.
V. W. RIM"
55
56. REmFCES
1. Richard, Victor W. DOPIOC Trackirs .'ilter, BRL Me.-orandum Report
1173, October 1958, Ballistic Resesar ch Laboratories, de -n
Proving Ground, Maryland.
Dean, William A. Precision Frequeney easurement of Noicy Doppler
Signal, BRL Memorandum Report 1.10, June 1960, Ballistic Research
laboratories, Aberdeen Proving Ground, Yryland.
Patton, Robison B., Jr. Orbit Determination from Single Pas-3
Doppler Observations, 17E Transactiona on Military Electronics,
Vol MIL-4, Numbers 2 & 3, pp 37r-344, April - July, 1960.
4. Patterson, Kenneth H. A Broadband Frequency Multiplier and Mixer
for Dispersive Doppler Measurements, BRL Memorandum Report 1343, March
1961, Ballistic Research laboratories, Aberdeen Provi" Ground,
Mar-land
5. Crulckehank, William J. Instruwntatior Used for Ionosphere Electron
D.nsity Meaurements, BRL Technical Note 1317, May 1960, Ballistic
Reseerch laboratories, Aberdeen Proving Ground, Maryland.
6. Bowhill, S. A. The Paraday Rotation Rate of a Satellite Radio
Signal, Journal of Atmospheric and Terrestrial Physics, 13 (1 and
2), 175, 1958.
7. Garriott, 0. K. The Determination of Ionospheric Electron Content
and Distribution from Satellite Observations, Theory and Results,
Journal of Geophysical Research 65, 4, April 1960.
8. Little, C. G. and Lawrence, H. S. The Upe of Polarization Fading
of Satellite Signals to Study Electron Content and Irregularltle3
in the Ionosphere, National Bureau of Standards JournlI of Research,
v64D, No. 4, July - August 1960.
5,4
57. DIST RI=BjION LIST
No. of No. or
Chief of Ordnance Cosmander
ATTN: ORDIB - Bal See Electronic Systems Divisioa
Department of the Army A-'M: CCSIN (Spicetrack)
Washington 25, D.C. L.G. Hanscom Field
Bedford, Massachusetts
Comanding Officer
Diamond Ordnance Fuze Laboratories 2 Cmmsanding General
ATM: Technical Information Office, Army Ballistic Missile Agency
Branch 041 ATTN: Dr. C.A. Lundquist
Washington 25, D.C. Dr. F.A. Speer
Redstone Arsenal, Alabama
10 Cosander
Armed rervices Technical 2 Director
SiLformation Agency National Aeronautics and
ATTN: TIPCR Space Administration
Arlington Hall Station ATE: Dr. Robert Jastrow
Arlington 12, Virginia Mr. John T. Mengel
1520 H.Str-et, N.W.
10 Ccoander Washington 25, D.C.
British Army Staff
British Defence Staff (W) 1 Chief of Staff, U.S. Army
ATTN: Reports Officer Research and Development
3100 Massachusetts Avenue, N.W. ATM: Director/Special Weapons
Washington 8, O.C. Missilee & Space Division
Washington 25, D.C.
4 Defence Research Member
Canadian Joint Staff 1 Electrac Space Electronics laboratory
2450 Massachusetts Avenue, N.W. 53T B West Valencia
Washington 8, D.C. Fuller )n, California
Coimander 1 Tnternational Duiness Machine Corp.
Naval Missile Center Federal Systems Division
ATTN: Mr. Lloyd 0. Ritland, Code 3143 ATTm: Mr. D.C. Sising -
Point Mugu, California Systems Development Library
7230 Wisconsin Avenue
Comander Pethesda, V*,-'iwnd
Air Force Systems Cownd
ATTX: CRS 1 Philco Corporation
Andrews Air Force Base Western rxDvelopment Laboratory
Washington 25, D. C. PTfI7: Mr. Peter L. . ,t
3871 Fabian Way
Palo Alto, CJlV" .i%
55
58. DI" IBWEYC, LIST
No. of 1o. of
Conies Organization Copes Organization
Space Technology Laboratories, 1 Mr. Arthur Eckstein
Incorporated U.S. Army Signal Research and
Informatlon Services Acquisition Dey-lopment Laboratory
Airport Office Building Astro-Electronics Division
83029 Sepulveda Boulevard Fort Monmouth, New Jersey
Los Angeles 45, California
1 Dr. Roger Gallet
1 Westinghouse Electric Corporation National Bureau of Standards
Friendship International Airport Central Radio Propagation Lab.
ATTN: Mr. F.L. Rees - Mai! Stop 649 Boulder, Colorado
P.O. Box 169r
Baltimore 3, Mryiand 1 Dr. Wa. H. Guier
Howard County Laboratory
Mr. Edvir C. Admas Applied Physics Laboratory
Cook L-.ectric Company Silver Spring, Maryland
Cook Technological Center
.6401 Oakton Str-t 1 Professor Robert A. Helliwell
Morton Grove, Illinois Stanford University
Electronics Filding
Dr. O.J. Baltzer, Stanford, California
Tec nical Director
Textron Corporation 1 Dr. Paul Herget
Box 907 University of Cincinnati
Austin 17, Texas Cincinnati, Ohio
Mr. W.J. Botha 1 Mr. L. Lambert
c/o N. I. T. R. Columbia University
P.O. Box 10319 632 W. 125th Street
Johannesburg, South Afrtca New York 27, New York
Dr. R.N. Buland 1 Dr. A.J. MalLinekrodt
Ford Motor Company 1.4141 Stratton Avenue
Aercnutroic Division Santa Ana, California
System Analysis Department
Fora Road 1 Mr. D.J. Mudgvsy
Newport Beach, California Electronic Techulques Group
Weapsn Beseur, --.- 4blisbeent
Mr. David M. Chase P.O. Box 1424 H
TGR Incorporated Salisbury, South Australia
2 Aer.al Way
Syosset, Long Island, New York 1 Mr. .W. O'Bzien
Radio Corporation o Aerica
Dr. G.M. 17'.7r- . Servo Su.-Unit
U.S. Naval Observatory "'oatton 101-203
Washington 25, D. C. Moorestown, New Jerocy
56
59. DISTRIBUTION LIST
No. of
Organization NCoo.p ieoAr Organization
Mr. B It. Rhodes
Midwest Research Professor George W. Swensun, Jr. Institute UhiYersity of Illinois 4?Ks Vityr 1liesri Department of Electrical Kansas City 10, Missouri Engineering
BDor.e inTgh oAmlarsP pla. neR oCnao mpny DUrr.b ana, Illinois V. G. Szebehely
Aero-S~ace Division
Org. 2-5410, Ml1 Stop GnrlEeti opn 22-99 General Electric CcSyt P. 0. Box 3707 Missile and Ordnance Syste eattle 24, Washingtonepartment
3198 Chestnut Street
Prfessor Willlam j. Ross Philadelphlia, Pennsylvania
AsEsolecciatrteic aP. roEfenssionre eofr1g Dr. James . Warwick
The Pennsylvania University of Colorado State University High Altitude Ot rvatory University Park, Pennsylvmnla Boulder. olorado
Mr. William Scharfman
Stanford Research Institute Dr. Fred L. Whipple Antenna Labratorny Sitsonlan Institute
Menlo Park, Astrophysical Observatory California
60 Garden Street
Mr. E. H. Sheftelman Cambridge 38, Massachusetts
AVCO Manufacturing Corporation
R:3earch and Advanced
Development Division 201 Lowell Street
Wilmington, Massachusetts
57
60. I3 tJ t t
*w 00SdS
0 .5. -
h. 0 .1
O~~~s 0 C-f
18
A 'S iii; P.__
~ - ! ujre
~~: V -
v 4 I
r. n
