Determination of orbital elements and refraction

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00

~ME.MORANDUM REPORT NO. 1357

DETERM I NATION OF ORB ITAL ELEMENTS AND REFRACTIONEFFECTS FROM SINGLE PASS DOPPLER OBSERVATIONS

R. B. Patton, Jr.V. W. Richard A S T 1 A

liii~ I

11h waIluh

OCT? 0 19W

0 TODqmr,m of the Army Project No. 503-06-011ordnance Management Structutre Cu No. 5210.11. 143BALLISTIC RESEARCH LABORATORIES

ABERDEEN PROVING GROUND, MARYLAND

ASTIA AUIIABILrrY NOTICE

Qualified requestors way obtain copies of this report fro ASTIA..

This report vill be published in the proceedings of theSymposium on Space Research and thereby will be available

to the public.

I

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 SpaceResearch, Florence, Italy, April 1961

twmb of the Army roJect No. 503-06-011jrdADR DwEment tructure Coe No. 201Y1 A3

ABIRDZIN PROVING GROUND, MARYLAND

BALLItSTIC RESEARCH L13ORLT-OEIS

MENCRRSMN 30. 1357'

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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

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

TIME

(a)

CIM

(c)

Fig.I-Dople freuenc-tie cuves

7E

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.

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00

h0 z

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_j Iw a

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w U

4

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:0

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

wi ih 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.

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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

12 (t ) - - (+ 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

PROBLEM GEOMETRY

FIGMJE 7

16

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, wewill 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 and in general, will be within theo

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

U)0o0

w

CL 0 A4w I

0

z - a a

2 00I--M

0

b

I.&1 0

0 *It 0

S 0

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

n'TTTAL ORBITAL APPOX .&TI8NS

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 -,2S -. + (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

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 ~ 0' f(t)

* (t) - r (t0 ),P j (to 1 x t, 1t)

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) yicldst5

(t, 2 - ~ (t 21 + Ff' t j(t)dt!P j (tc) L 0 r

L (to (t1)j

21

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

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- J)2 2

from which it follows that

* +. Yy + zAT 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

zV

CTE

*EOITP FO0DE0RMNINot sNoIA APR XMA N

coxiFIUR *I5,Y~j

°To =2Y + Zo0

(8)= (YoYj) koP~~o j/(Yo-yj)f+ (-ZJ)7

Let fjo and fJo be the Doppler frequency and rate of change of frequency

for the Jth receiver at t . It follows that

fo (6 + ) (9)fJOTo j

From equation (2), we conclude

A 2 A 2

TOoJjo I POo + jo (10o)

Expressing equations (9) and (10) in terms of the position coordinates

and velocity compcnents of the satellite at time, to, yields

~JOXF~ (yo - YJ)(- v + ,) ( )

= 2 A -o.L ) (%., 1 2 j

JYo 2 (3o Y() ko 2A-ky2 O021 A[ (Y' " 2 + (°z,

jo" 'y + + V~ o )X . Z) (12)X Vy 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

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 consistent t

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 appropriatecoordinate transformtion.

In addition to the graphical method, a digital solution has beendevised 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 it3 o themaximum value or zc occurs above either the tr'mumitter or receiver whiie,

26

SIX -

30 CPSAS

.j 40 CP/

x 4

70

TRANSMITTER micIVERY-AXIS (EAST IM MILES)

OOPLOC FREQUENCY AND RATE 0F CHANGEOF FREQUENCY AS A FUNCTION OF

POSITION IN THE YZ - PLANE(FOR SD. INCLIN..4rION)

FIGURE 10

T7

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 satellites0

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& be00

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 thetwo 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

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

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

-- -j

N -~0

-ZII7.0 ~ IL

0 A

IrI

oa) 00 PA00 z~s, I

in~~~2 to ------ w',0 c

w wi

ILI

II4pI

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

2

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ground transmitter would reduce . 'rrOr PrOP~aio in the ccmA~ptIoMSto approximately a tenth of that to be expected for a system ; 4th asingle receiver. Removing the restricti on Of single pass determinationwould further enhance the accuracy of i he results.COaU"t~ng time$ have been found to be quite reasonable. Convergentsolutions have requiredl 20 to I40 ainutee on the Ballistic ResearchlAboratories. O-RDVAC vhlt:h requires the coding to include floating decimalsub-routines. Mom modern nOlsIes, such as the DNLEM, -nov under con-structiOn at the Ballistic Research laboratories, will perfom the Samcomputation In 2 to J4 minutes. Bence, It Is realistic to claim that thesystem potentially has the capabiity of orbit deterninatioU Within, fivem:!zutes of the observation time. in conclusion, the method In general=d, therefore, need be confined to neither Doppler fequazneies norKePlee-Aa orbits, In partlcuALr, if the limitatton of Keplerlmn motionmay be retained, onay minor modificatIon is required to use the method14h all.oer types of satellite observatins

143

ICIOSPREC MMAsR MD.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 Nf 2 (13)

0

where N is the electron density in electrons per cubic meter an& f is• 0

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

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

: u-Il

a.w~~EJjHJj~J i:J II a U

*~ :.- aa4 0

a -~

1- .39- ~ I'ma ~a- * 2

agZ ---a- I-

I t-~ I m0 gj ~Z .3 -

4

1:3 3; :~- 3 a, * II 3~ - e

-- * 0[iJI~ mm - gS

I4~I g1mb.. -z

3 mm 0liii-a- m~ 2

a: I

:3 ~:i1 --

ma-a

S.

L

"LIP

N dr (15)(I- F 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 3.24 x 108 " 6.9 x 1013 electrons (16)324 .......... x lo-8 square meter ":

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

*. w..

A4

~L..-.4

&SER IV D2P4Z CYLEI1.

4=U iVRiiDO0E /yLS* t -49

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 raytracing 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

WAL it:mv ON .k 13 No. fme

~J ±." E 4. ...... ..

75

... ~~~if .. .. ......

WW--

It L

*~~ LA23P/OUJ3*

U.2.

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

REmFCES

1. Richard, Victor W. DOPIOC Trackirs .'ilter, BRL Me.-orandum Report1173, October 1958, Ballistic Resea srch Laboratories, de -nProving Ground, Maryland.

Dean, William A. Precision Frequeney easurement of Noicy DopplerSignal, BRL Memorandum Report 1.10, June 1960, Ballistic Researchlaboratories, Aberdeen Proving Ground, Yryland.

Patton, Robison B., Jr. Orbit Determination from Single Pas-3Doppler 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 Mixerfor Dispersive Doppler Measurements, BRL Memorandum Report 1343, March1961, Ballistic Research laboratories, Aberdeen Provi" Ground,Mar-land

5. Crulckehank, William J. Instruwntatior Used for Ionosphere ElectronD.nsity Meaurements, BRL Technical Note 1317, May 1960, BallisticReseerch laboratories, Aberdeen Proving Ground, Maryland.

6. Bowhill, S. A. The Paraday Rotation Rate of a Satellite RadioSignal, Journal of Atmospheric and Terrestrial Physics, 13 (1 and2), 175, 1958.

7. Garriott, 0. K. The Determination of Ionospheric Electron Contentand 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 Fadingof Satellite Signals to Study Electron Content and Irregularltle3in the Ionosphere, National Bureau of Standards JournlI of Research,v64D, No. 4, July - August 1960.

5,4

DIST RI=BjION LIST

No. of No. or

Chief of Ordnance CosmanderATTN: ORDIB - Bal See Electronic Systems DivisioaDepartment of the Army A-'M: CCSIN (Spicetrack)Washington 25, D.C. L.G. Hanscom Field

Bedford, MassachusettsComanding OfficerDiamond Ordnance Fuze Laboratories 2 Cmmsanding GeneralATM: Technical Information Office, Army Ballistic Missile Agency

Branch 041 ATTN: Dr. C.A. LundquistWashington 25, D.C. Dr. F.A. Speer

Redstone Arsenal, Alabama10 Cosander

Armed rervices Technical 2 Director

SiLformation Agency National Aeronautics andATTN: TIPCR Space AdministrationArlington Hall Station ATE: Dr. Robert JastrowArlington 12, Virginia Mr. John T. Mengel

1520 H.Str-et, N.W.10 Ccoander Washington 25, D.C.

British Army StaffBritish Defence Staff (W) 1 Chief of Staff, U.S. ArmyATTN: Reports Officer Research and Development3100 Massachusetts Avenue, N.W. ATM: Director/Special WeaponsWashington 8, O.C. Missilee & Space Division

Washington 25, D.C.4 Defence Research Member

Canadian Joint Staff 1 Electrac Space Electronics laboratory2450 Massachusetts Avenue, N.W. 53T B West ValenciaWashington 8, D.C. Fuller )n, California

Coimander 1 Tnternational Duiness Machine Corp.Naval Missile Center Federal Systems DivisionATTN: Mr. Lloyd 0. Ritland, Code 3143 ATTm: Mr. D.C. Sising -Point Mugu, California Systems Development Library

7230 Wisconsin AvenueComander Pethesda, V*,-'iwndAir Force Systems CowndATTX: CRS 1 Philco CorporationAndrews Air Force Base Western rxDvelopment LaboratoryWashington 25, D. C. PTfI7: Mr. Peter L. . ,t

3871 Fabian WayPalo Alto, CJlV" .i%

55

DI" IBWEYC, LIST

No. of 1o. ofConies Organization Copes Organization

Space Technology Laboratories, 1 Mr. Arthur EcksteinIncorporated U.S. Army Signal Research and

Informatlon Services Acquisition Dey-lopment LaboratoryAirport Office Building Astro-Electronics Division83029 Sepulveda Boulevard Fort Monmouth, New JerseyLos Angeles 45, California

1 Dr. Roger Gallet1 Westinghouse Electric Corporation National Bureau of Standards

Friendship International Airport Central Radio Propagation Lab.ATTN: Mr. F.L. Rees - Mai! Stop 649 Boulder, ColoradoP.O. Box 169rBaltimore 3, Mryiand 1 Dr. Wa. H. Guier

Howard County LaboratoryMr. Edvir C. Admas Applied Physics LaboratoryCook L-.ectric Company Silver Spring, MarylandCook Technological Center.6401 Oakton Str-t 1 Professor Robert A. HelliwellMorton Grove, Illinois Stanford University

Electronics FildingDr. O.J. Baltzer, Stanford, California

Tec nical DirectorTextron Corporation 1 Dr. Paul HergetBox 907 University of CincinnatiAustin 17, Texas Cincinnati, Ohio

Mr. W.J. Botha 1 Mr. L. Lambertc/o N. I. T. R. Columbia UniversityP.O. Box 10319 632 W. 125th StreetJohannesburg, South Afrtca New York 27, New York

Dr. R.N. Buland 1 Dr. A.J. MalLinekrodtFord Motor Company 1.4141 Stratton AvenueAercnutroic Division Santa Ana, CaliforniaSystem Analysis DepartmentFora Road 1 Mr. D.J. MudgvsyNewport Beach, California Electronic Techulques Group

Weapsn Beseur, --.- 4blisbeentMr. David M. Chase P.O. Box 1424 HTGR Incorporated Salisbury, South Australia2 Aer.al WaySyosset, Long Island, New York 1 Mr. .W. O'Bzien

Radio Corporation o AericaDr. G.M. 17'.7r- . Servo Su.-UnitU.S. Naval Observatory "'oatton 101-203Washington 25, D. C. Moorestown, New Jerocy

56

DISTRIBUTION LIST

No. of No. orOrganization CopieA Organization

Mr. B It. Rhodes Professor George W. Swensun, Jr.Midwest Research Institute UhiYersity of Illinois4?Ks Vityr 1liesri Department of ElectricalKansas City 10, Missouri Engineering

Dr. Thomas p. Rona Urbana, IllinoisBoeing AlrPlane Compny Dr. V. G. SzebehelyAero-S~ace Division

GnrlEeti opnOrg. 2-5410, Ml1 Stop 22-99 General Electric CcSytP. 0. Box 3707 Missile and Ordnance Systeeattle 24, Washingtonepartment3198 Chestnut Street

Prfessor Willlam j. Ross Philadelphlia, Pennsylvania

Associate Professor of1 Dr. James . WarwickElectrica. Enineerg University of ColoradoThe Pennsylvania State University High Altitude O trvatoryUniversity Park, Pennsylvmnla Boulder. olorado

Mr. William Scharfman Dr. Fred L. WhippleStanford Research Institute Sitsonlan InstituteAntenna Labratorny Astrophysical ObservatoryMenlo Park, California 60 Garden Street

Mr. E. H. Sheftelman Cambridge 38, MassachusettsAVCO Manufacturing CorporationR:3earch and AdvancedDevelopment Division

201 Lowell StreetWilmington, Massachusetts

57

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