IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-15, NO. 4, DECEMBER, 1966

A Dual Frequency VLF Timing System

L. FEY AND C. H. LOONEY, JR., SENIOR MEMBER, IEEE

Abstract-The use of high precision portable clocks and radiosignals is discussed in relation to synchronization of remotely locatedclocks. The demonstrated inherent phase stability, approximatelyten uAs rms, of very-low-frequency (VLF) propagation and its lowattenuation rate with distance, have led to various approaches toexploit these virtues in timing applications. The system consideredhere employs two carrier frequencies with timing information con-tained in their difference frequency to permit identification of aspecific cycle of one of the carrier frequencies. Such a system makesstringent demands on phase stabilities of the transmitted signals andof the receiving system as well as that of the propagation mediumitself.

The present system, whose development has been supportedjointly by NBS and NASA, makes use of NBS radio station WWVLat Fort Collins, Colo. Receivers are of the standard VLF phase track-ing servo type. A special signal generator is used in conjunction withthe local clock to simulate the transmitted signal in order to relatethe local time scale to that at the transmitter.

One of the carrier frequencies is maintained at 20 kHz. With asecond frequency (500 Hz removed from this frequency), carriercycle identification was achieved on about 90 percent of the daysfor over a month on the path from Fort Collins, Colo., to Greenbelt,Md. Since January 4, 1966, the difference frequency has been 100Hz, with somewhat more fluctuation in results. However, lowerprecision is required for the initial synchronization. The results ofaveraging to improve this performance will be discussed.

r WO BASIC methods are used for synchronizingremotely located high precision clocks. One istransportation of operating clocks between loca-

tions where clocks are to be synchronized; the other ispropagation of radio signals which contain timing in-formation.

Until recently, high-frequency (HF) propagationsuch as from radio station WWV, rather than theportable clock method, offered the higher practical pre-cision of synchronization, with modest investment inreceiving equipment. This system employs amplitudemodulation of an HF carrier with time ticks once persecond. The bandwidth used is limited by considera-tions of spectrum availability rather than any inherentequipment limitations. Propagation is by means of theE and F ionospheric layers, whose inherent instabilitieslimit precisions of synchronization to around one milli-second from day to day so that no additional advantageaccrues from increasing the present bandwidth. On theother hand, improvements in the uniformity with whichtime scales can be kept, and the development of portable

Manuscript received June 23, 1966. This work was partially sup-ported by NASA under Contract S-49285 (G), and was presented atthe 1966 Conference on Precision Electromagnetic Measurements,Boulder, Colo.

L. Fey is with the National Bureau of Standards, Boulder, Colo.C. H. Looney, Jr., is with the Goddard Space Flight Center,

Greenbelt, Md.

quartz crystal clocks and atomic oscillator clocks, nowpermit synchronization with precisions of the order ofone microsecond using portable clocks [1], [2]. Sincemany of the demands in such areas as satellite and mis-sile tracking, geodesy, seismology, and sophisticatedcommunications systems are in the range which canonly be satisfied by portable clocks, increasing use isnow being made of these devices. The difficulty withthis approach is that extreme reliability is required ofclocks to maintain synchronization for long periods afterthey have been synchronized. Furthermore, even with-out clock failures it has been shown [3] that time keptby clocks driven by crystal oscillators may be expectedto depart from that of a uniform standard in a randonwalk fashion, necessitating periodic resynchronization.One obvious approach in solving this problem is to

make use of the extreme stability of very-low-frequency(VLF) propagation compared to that of HF propaga-tion. This stability is that of the ionospheric D layerby which VLF signals propagate and is such that day-to-day repeatabilities of better than 10 nmicroseconds arepossible. A further advantage is the reliability of thismode of propagation and its extremely low attenuationrate, permitting worldwide reception from a single sta-tion [4], [5]. The simplest way to make use of theseadvantages is to synchronize a remote clock by use of aportable clock, then maintain the remote clock's syn-chronization by manual adjustment of its oscillator fre-quency, obtaining the necessary corrections from VLFreception. For direct time synchronization, however, theVLF approach has serious limitations when carried outin the same way as the high-frequency case -that is,using pulse modulated timing information. This limita-tion is due to the combination of low carrier frequencyand high transmitting antenna Q which severely re-stricts the useful bandwidth and prevents the broadcastof fast rise time pulses by VLF.

Essentially, then, the difference between HF methodsand VLF methods arises from the comparatively narrowbandwidth capability but high propagation stabilityavailable at VLF which make new techniques necessaryif the potential synchronization stability is to be reached.An early description of a VLF system having such a po-tential was given by Casselman and Tibbals at the 1958IRE Conference on Military Electronics [6]. The orig-inal suggestion for this system, which is known asOmega, was attributed to J. A. Pierce of Harvard, whoalso first established that VLF transmissions possessedextremely good phase stability [7].

190

FEY AND LOONEY: VLF TIMING SYSTEM

The Omega system was proposed for and is currentlyunder active study as a worldwide navigation system[8]. Here it is the position on the earth's surface whichis to be determined, but the necessary measurement is atime comparison between CW signals received frompairs of transmitting stations. However, a single CWsignal is insufficient, since time measurements on a CWsignal would have ambiguities equal to the period of thesignal (betw-een about 30 ,us to 100 .ts for the VLF band)resulting in position ambiguities spaced by a few miles.In order to resolve these ambiguities, the navigatorwould require independent knowledge of his position tobetter than one-half the spacing of the ambiguities,which corresponds to previous synchronization uncer-tainty of less than one-half of a carrier period. Omegaemploys coherent, closely spaced, multiple frequencyCW broadcasts to overcome this difficulty. In essence,the difference frequency between a pair of closely spacedcarrier frequencies, having a longer period than eithercarrier frequency, is used to resolve ambiguities of thecarrier phase. The difference frequency period fluctua-tions need only be less than one-half the carrier periodto permit a particular carrier cycle to be unambiguouslyassociated with a zero crossover of the difference fre-quency for this resolution. The Omega system carriesout these resolutions in several steps, starting with arelatively small difference frequency period to resolvecarrier ambiguities, and then resolving difference fre-quency ambiguities in turn with longer difference fre-quency periods. This process continues until positionambiguities are too widely spaced for the navigator tobe uncertain as to which location he is nearest. Thismulti-step procedure is necessary in a navigation sys-tem where only a short averaging time is allowed foreach determination of position, and where the measure-ment must be made at any time of day or night ratherthan at the time propagation conditions are best. TheNBS-NASA timing system requirements are less strin-gent in that receiving locations are fixed and synchro-nization informnation is not needed so often as navigationposition information. For example, at NASA trackingstations [9], employing atomic oscillators or ultra-stablecrystal oscillators and the resultant highly uniform timescales, it is now thought sufficient to make a time syn-chronization determination once a day during the timeof most stable propagation conditions.

NBS-NASA SYSTEM DESCRIPTION

The NBS-NASA system, while using the same tech-niques as Omega, is simpler in that only one transmitterlocation is used, making transmission time sharingamong stations unnecessary. Ultimately the system mayemploy more than one difference frequency, but testshave been made using only one at a time for a period ofseveral months each. The frequencies used in the NBS-NASA tests are the 20.0 kHz standard frequency carrier,offset from the United States Frequency Standard

(USFS) to conform to the coordinated Universal Timescale, with either 20.5 kHz or 19.9 kHz as the single aux-iliary frequency for a given test period. These frequenciesare all synthesized from a common source which is phaselocked to the offset USFS. Carrier period ambiguitiesare thus 50 As; difference frequency period ambiguitiesare either 2 ms or 10 ms. Frequency shift keying is emn-ployed to utilize the single transmitter and antenna atFort Collins, Colo., allowing 10 seconds transimissionitime alternately for each frequency. In order to relatethese transmissions to Universal Time (UTC) thephases of the two frequencies being broadcast areadjusted at the transmitter to go through zero simul-taneously in a positive direction coincident with aseconds tick of UTC. These phase relations are main-tained, upon reception, with the time of simultaneousphase agreement delayed by an amount depending onthe phase velocity of the signals and on the distance ofreceiver from transnlitter. Since there is a slight de-pendence of phase velocity on frequency, an additionalsmall phase shift of the difference frequency will occur.In order to extract ticning information from the signals,one or, with a little more convenience, two conventionalphase tracking VLF receivers may be used.

It is necessary to relate the phases of the receivedsignals to the time scale operating at the receiving sitein order to perform a time synchronization. This is doneby making use of an auxiliary device, referred to as acalibrator, to generate from the local time scale the sametwo frequencies as transmitted, with the same simul-taneous phase relationship conditions. The calibratoractually consists of a sawtooth waveform generator,which is synchronized by a 100 pulse-per-second ratetaken from the local time scale divider chain. Thiswaveform has the desired properties that all harmonicsof the fundamental fr-equency exist, (in particular, 19.9kHz, 20.0 kHz, and 20.5 kHz) and all go through zeroin a positive directionl coincident with each pulse of the100 pps clock output which is in turn synchronized withthe 1 pps clock outp at. An interchange of signals fromthe receiving antenna with the calibrator output permitsa measurement to be made of the pair of phase differ-ences. From these two measured quantities, the relationbetween transmitter time scale and receiver time scalemay be calculated, provided only that the carrier propa-gation phase delays are known. In order to study propa-gation fluctuations on the path from Fort Collins, Colo.,to the Goddard Space Flight Center at Greenbelt, Md.,however, the clocks at the two locations have been keptsynchronized by the uise of portable clocks and propaga-tion delay' treated as the unknown quantity. If Atldenotes the measured time difference between the phase

1 For purposes of simplicity, the treatment of this paper assumesthat propagation is dispersionless so that no distinction betweenphase velocity and group velocity is made. The term propagationdelay will thus be used throughout in referring to either phase orgroup delay; effects of dispersion will be treated later as a correction.

191

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT

DIFFERENTIAL PHASE20.0KHz vs. 20.5KHZ

tFORT COLLINS, COLO. TO GREENBELT, MD.

C],

z-Li.0z0

(9

0LE

LiH

0

z

8150

8100- ---a

8050 ---

--- DAILY VALUES J- 5 DAY AVERAGE

8000 -

a0CEw

QE

0

w20

I

-

Lia

0

z0

0~0-

00z

LL I1WL L J

5 15 25 5 15 25NOV DEC

1965

Fig. 1.

of the received signal and locally genlerated signal of thelower frequency fi, and At2 denotes measured time dif-ference similarly for the higher frequency f2, then it isshown in the Appendix that when the transmitter andreceiver clocks are synchronized, the propagation delaytd, as determined from the difference frequency, is

td = (At2 - tAl) [1 i f] + At2.

Using this formula with measurements made aroundnoon each day at Greenbelt, Md., propagation delayhas been calculated for data taken from late October1965 to June 1, 1966. From October to January 4, thetwo frequencies broadcast were 20.0 kHz and 20.5 kHz.From January 4 to June the frequencies were 20.0 kHzand 19.9 kHz. Results are shown in Figs. 1 and 2, whichdisplay a plot of indicated propagation delay as derivedfrom the difference frequency measurements. The datawere obtained from the ,us-counter dial of a pair of com-mercial VLF receivers which have a resolution of 0.1 ,us.This accounts for the steps in indicated propagationdelay, and also points out the severe requirement onrelative phase stability of the two carrier frequencies.Even though each transmitted frequency is nominallyphase-locked to a common reference, there has beensome long term differential phase fluctuation. This madedaily local measurement of differential phase, as trans-mitted, necessary. The data in Figs. 1 and 2 have beencorrected for this fluctuation. On M\Iay 24 an improvedAGC circuit was installed in the transmitter phase con-trol servos, resulting in considerable improvement inthe transmitted phase stability as shown in Fig. 2. Inorder to gain a knowledge of longer term propagationfluctuation, the data has been smoothed by making five-day averages. These results are also shown in Figs. 1and 2. The value for (Wt2-Atl) for the months of Febru-

8000

8050

8100

8150

8200

DIFFERENTIAL PHASE19.9 KHz vs. 20.0 KHz

FORT COLLINS, COLO. TO GREENBELT, MD.JAN.-JUNE, 1966

1-

0

A,~ ~ I I I

ii I-r -4

DAILY VALUES5 DAY AVERAGE

5 IS 25 5 15 25 5 15 25 5 15 25 5 IS 25 5 15 25JAN FEB MAR APR MAY JUNE

1966Fig. 2.

ary through early June 1966 approximates -9.5 ,us,which corresponds to a propagation delay of approxi-mately 8100,s. Portable clock measurements indicatea value for propagation delay of approximately 8050 As.This difference of 50 As between VLF and portable clockmeasurements is equivalent to a 0.25 ,us bias in (At2 -Atl)which may be due to the variation of phase velocity withfrequency.

According to mode theory calculations of Wait andSpies [10], propagation phase velocity decreases withincreasing frequency in the neighborhood of 20.0 kHz,resulting in about 0.2 Mus delay of the 20.0 kHz signalover that of 19.9 kHz and about 0.7 Mus delay of the 20.5kHz signal over that of 20.0 kHz signal. These values of0.2 ,us and 0.7 ps, when applied to the measured datashown in Figs. 1 and 2, do indicate a value of approxi-mately 8050 ,us for propagation time, thus bringing theVLF and portable clock data into close agreement. Thiscorrection is of theoretical interest, and arises from thedispersive properties of the earth ionosphere waveguidewhich cause the phase and group velocities to be dif-ferent. It is necessary in making predictions of propaga-tion delay to receiving points for which portable clockmeasurement is not readily accessible. At present, themeasured values of propagation delays must also beextrapolated with care for another reason. Measure-ments made using portable receiving equipment indicatethat as much as one microsecond bias error in the phaseof the difference frequency may occur as a result of closeproximity of the receiving antenna to long metallicstructures, such as power lines, pipes, or buildings. Thiserror in phase could cause an indicated propagationdelay error of as much as 200 /is and makes evidentthat, where precise synchronization is required, propa-

192 DECEMBER

FEY AND LOONEY: VLF TIMING SYSTEM

I

LL

zLLu

cxLLIL

LuJ

R

30282624222018

161412108642U .*

5 15 25 5 15 25 5 15 25 5 15 25 5 15 25 5 15 25JAN FEB I MAR APR I MAY JUNE

1966

Fig. 3. Residual daily VLF time fluctuations assuming correctcarrier cycle identification each day.

gation delay should be determined with a portable clock.As can be seen in Fig. 2, phase stability of the re-

ceived 100 Hz difference frequency was not sufficient topermit identification of the same carrier cycle every daymeasurements were made. For this to have occurred,the measurements would have to all be between two ofthe indicated dashed horizontal lines. If the systemwere being used for timing, an error of 50 us would haveoccurred in indicated time each day the measurementsshifted from one band into an adjacent band. Takingfive-day averages improves the synchronization at theexpense of a delay in making a determination. The de-gree of objection to such delay depends on the uni-formity which can be ascribed to the local time scale.Catastrophic failures would, of course, make a com-plete resynchronization necessary.

In order to evaluate the maximum stability of syn-chronization of the system over the path under discus-sion, the day-to-day time variation of the received car-rier is plotted in Fig. 3. This would be the systemsynchronization capability if the same carrier cycle hadbeen identified each day. The capability of VLF incomparing frequencies to better than 1 part in 1012 isreadily apparent from this figure. Between January andM\Iarch the mean slope is about 2 parts in 1012.

In order to permit positive carrier cycle identificationcontinuously during day and night, it is apparent thatseveral difference frequencies must be transmitted si-multaneouslv. MIore effort is needed to determine theoptimum frequencies; but it appears that if both 500and 100 cycle frequencies had been used simultaneously,cycle identification could have been accomplished nearlyevery day in twxo steps, with an initial synchronizationcertainty of + 5 milliseconds from WWV transmis-sions. A completely self-sufficient VLF system is clearlypreferable; possibly this system would provide the con-

venient frequencies of 1 Hz, 100 Hz, and 1000 Hz in amultiple transmission from an NBS VLF station, andwe believe would permit time synchronization of betterthan 10 us throughout most of the wrorld.

APPENDIX

In deriving an expression for the propagation phasedelay of the differenlce frequency, it is convenient torefer to Fig. 4, which displays phase relationships of thetwo carrier frequencies at significant times at transmit-ter and receiver. The dotted line represents the travelingwave of the signal from the transmitter as it progressesin distance, on the vertical axis, and in time, on thehorizontal axis. The slope of the dotted line then indi-cates phase velocity. The time origin is t=to, the timeof occurrence of a seconds tick. This time is synchro-nized at transmitter and receiver locations using aportable clock.The phases of fi and f2, the lower and upper frequency

carriers, are identically zero at t = to from both thetransmitter, represernted by (4it, and 42tx, and from thecalibrator at the receiver, represented by 4lcal andcI2cal. Assume that the phase relationships of two signalsemitted from the traLnsmitter at time t 0 may be ob-served during propagation to the receiver. If propaga-tion phase velocity is the same for each frequency, theirphases will remain at zero and they will arrive at thereceiver with that relationship as represented by 41rx andI2rx-. 1leanwhile, the phase of each signal emitted fromthe calibrator will have advanced. The observed phasedifference between received signal and calibrator signalof fi will be

cIlrx clcal = 1 (1)and of f2 will be

b,2rx - 4I2ca1 02.- (2)

We denote the total phase advance of calibrator phaseof fi during propagat;ion of the signal from transmitterto receiver by 01 and, similarly, the total phase advanceof f2 by 02. Now 02 will advance more rapidly as a func-tion of distance than 01, since f2>fl. Let the distance dof the receiver from the transmitter be sufficiently smallso that during propagation timne td from transmitter toreceiver 02 has advanced over 01, by less than one com-

plete cycle. The consequences of removing this restric-tion will be considered later. Therefore, let the numberof complete cycles advance by either 01 or 02 fromn thecalibrator during t1 be denoted by N. Thlen

0L = 2wN±+ 0 (3)

and

= 2irN + 2,

where 42> 01. From (3) and (4),

(4)

02-01-4 2--4 1- (5)

N

RELATIVE TIME DIFFERENCE -NBS USFS vs. GODDARD Cs OSCILLATOR

VIA 20.0 KHz WWVLCARRIER PHASE COMPARISON _

FORT COLLINS, COLO. TO GREENBELT, MD.

fl III

1931966

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT

At202 2wr-, (Ila)

RECEIVER ID2aDiaLOCATION O , Z12sr,^ 442rx,(Dirx

Z~<WQ.) 45fxI

TRANSMITTER!LOCATION TIME, t-

Fig. 4. Phase relationships of calibrator signaland propagated signal.

The propagation time td is equal to calibrator phase ad-vance in cycles at either frequency multiplied by theperiod Ti or T2 of that frequency; hence,

td = 012 (6)27r

- Nr1 + 41i (6a)2r

are often obtained in the following way.VLF receivers are commonly equipped with counters

which totalize in steps of 0.1tis changes in time betweenthe phase of the received carrier and the local oscillatorreference. This is a useful form of presentation when thereceivers are used to measure time accumulation be-tween local clock and transmitter clock, since thisquantity does not depend on carrier frequency whilephase accumulation does.

Using a receiver so equipped in order to make a timemeasurement, the time readings corresponding toreceived phases (DI, and 12rx are noted. Interchangingreceiver VLF input from antenna to calibrator, the timereadings corresponding to calibrator phases 4lCaI and4)2cal are noted. Only the differences At, and At2 betweenthese sets of readings are meaningful, since the measure-ments themselves depend on unknown receiver phaseshifts which are assumed constant throughout themeasurement and therefore cancel out.

Substituting (11) and (lta) into (10) and rearranging,

from (3), or

T2td 602

2r

= Nr2 + 02T227r

(7)

(7a)

from (4). ThenTi

62 =-01

from (6) and (7).for 61,

(8)

Substituting for 62 in (5) and solving

0)2 - 41

Ti

-- 1T2

(9)

td = (At2 - Atl) [ -T2 + AWI.-Tl - 72-

Using the definitions

1T1 -

fiand

IT2 = J

f2

(12) becomes

Id = (At2 - AtW) [1 -1 ] + At,A

or

Substituting 01 into (6),

(42 - 02) T1la-

r1 27r- 1

T2

td = (AtW2 Atl)[ fi] + At2.

(10)

02-401 1

f2-fl 2r

which is seen to be group delay [11]. The quantities O2and 41 are generally not measured directly by VLFreceivers. Instead, the corresponding time changes At,and At2, where

At1

¢1 = 27r-'r

(11)

and

(14a)

This is the time corresponding to propagation delay as

determined from the difference frequency. Once deter-mined, it is used to resolve carrier cycle ambiguities inthe following way.

First, round the first term in (14a) to the nearestintegral multiple of the carrier period T2, 50 As. That isthe coarse time determination and follows recognitionthat, from (6a), (lla), and (14a),

N-T2 -(A/12 - Atl)_ _

Jn - fl-(15)

If the errors in determination of Atl2 and At, produce an

error of less than 2r2, this roundoff procedure will pro-

(12)

(13)

(13a)

(14)

194 DECEMBER

o1 =

FEY AND LOONEY: VLF TIMING SYSTEM

duce the correct value for Nr2 and avoid error due tothe magnification term [f/(f2-f) ]. Then the time Wt2,the second term of (14a), is added to this integral num-ber of periods to give the final answer or the fine timedetermination.The case where the phase of f2 advances by more than

one cvcle over that of fi will be considered. This evi-dently occurs when distance d is so large that propaga-tion delay td is greater than the period Tdiff of the differ-ence frequency. This period corresponds to a distance ofone wavelength Xdiff of the difference frequency, whereapproxiimately

.LL.I

ZU)g z

2Xdiff

Xdiff

TRANSM ITTERLOCATI ON

(2) (3)--Dotx .D2tX(4) (5) Tdiff, 2 Tdi ff

6'Pi$>cal, 2cal ,

- ..(3) (4) t5

Xdiff = CTdiff

with c -velocity of light. In this case, when calculatedby (14a), td is too small by one or more periods of thedifference frequency. This situation causes no problemfor difference periods under discussion here. For in-stance, the two ms periods correspond to one completewavelength of difference frequency, being somewhat lessthan 400 miles. If d is uncertain by less than half thisamount, then the correct value of td can be readilydetermined by observing which value of n, for n=0,1, 2, 3, . . . results in (td-+tnTdiff) being nearest thevalue of propagation delay calculated from d and thevelocity of light. This situation is illustrated in Fig. 5.where the distance and time scales have been lengthenedto include twvo periods of the difference frequency.Ambiguities of distance occur at n = 1 and n = 2 whereall phases retuLrn to their values at t=to. When td is

2 Tdif f values of td calculated from (14a) may benegative. This merely means that they are to be sub-tracted from (n+l)Tdiff, rather than added to n Tdiff,and illustrates again that distance must be known tobetter than half a wavelength of the difference frequency.A sample set of data taken at Goddard Space Flight

Center is given in Table I to illustrate the above pro-cedure.From these data Att1=22.3 gs; At2= 12.8 As; At2-Atl

=-9.5 us; and fil/(f2-fs) = 199; so that, from (14a)first term, td- - 1890.5 ,us. With a difference frequencyof 100 Hz, Tdiff=10 000 Ms. The distance from FortCollins, Colo., to Greenbelt, Md., is about 2400 km sothat nTddiff is closest to a calculated propagation delayof about 8000 ,us when n =1. Subtracting the measuredvalue of 1890.5 Mes from 10 000 As results in a measuredvalue for propagation delay of 8109.5 ,us which roundsto 8100us as the time corresponding to the nearestintegral number of 20.0 kHz carrier periods. To this isadded time At2, 12.8 gs so that measured propagationdelay, finally, is 8112.8 As for this example.

It remains to point out how this system could be usedfor time synchronization if propagation delay td wereknown. In that case

AT = (t-2At) [f

] + At2 - td, (16)

TIME, t-O

Fig. 5. Phase repetition relationships of calibrator signial andpropagated ,ignal showing amiibiguities.

TABLE I

Receiver Counter Reading

FrequencyPropagated SignalCalibrator Signal

19.9 kHz1306.7 ,uss1284.3 ,us

20 kHz1302.4 ,us1289.6 ,s

where AT is time delay of the receiver clock comparedto the transmitter clock. Ambiguities would now appearas before but would be in time, rather than distance,as illustrated by ideiltical phases at times Tdiff whennn=1 and 2Tdiff when n= 2. In order to make a correctsynchronization, the receiver clock would need to besynchronized independently to better than Tdif f. Forthe case of Tdiff = 1C ms this could be achieved withWWV when it can be received. For 7¾,jiff = 2 ms use ofWWV is questionable.

REFERENCES[1] J. A. Barnes and R. L. Fey, "Synchronization of two remote

atomic time scales," Proc. IEEE (Correspondence), vol. 51, p.1665, November 1963.

[21 L. N. Bodily, "Correlating time from Europe to Asia with flyingclocks," Hewlett-Packard J., vol. 16, pp. 1-8, April 1965.

[31 J. A. Barnes, "Atomic: timekeeping and the statistics of precisiolnsignal generators," PIroc. IEEE, vol. 54, pp. 207-220, February1966.

[4] A. D. Watt and R. VWi. Plush, "Power requirements and choiceof an optimum frequency for a worldwide standard-frequencybroadcasting station," J. Res. NBS (Radio Science), vol. 63D,pp. 35-44, July-August 1959.

[51 A. D. Watt, R. W. l'lush, V. XV. Brown, and A. H. Morgani,"Worldwide standard frequency and time signal broadcasting,"J. Res. NBS, vol. 65L), pp. 617-627, November-December 1961.

[61 C. J. Casselman and M. L. Tibbals, "The Radix-Omega longrange navigation system," 1958 Proc. Second Nat'l Conv. onMilitary Electronics, pp. 385-389.

[7] J. A. Pierce, "The diurnal carrier-phase variation of a 16-kilocycle transatlantic signal," Proc. IRE, vol. 43, pp. 584-588,May 1955.

[81 J. A. Pierce, "Omega," IEEE Trans. on Aerospace and Elec-tronic Systems, vol. AES-1, pp. 206-215, December 1965.

[91 C. H. Looney, Jr., "VLF utilization at WASA satellite trackingstations," J. Res. NB3S (Radio Science), vol. 66D, pp. 43-45,January 1964.

[10] J. R. Wait and K. P. Spies, "Characteristics of the earth-ionospheric waveguide for VLF radio waves," NBS, Washington,D. C., Technical Note 300 (Supplement) February 1965.

[11] C. A. Coulson, Waves. New York: Interscience, 1947, pp. 128-133.

"T I 0 *l t." 40,Is &

1966 195