TWO-WAY SEQUENTIAL TIME SYNCHRONIZATION:PRELIMINARY RESULTS FROM THE SIRIO-1 EXPERIMENT**)

E. Detoma, S. LeschiuttaIstituto Elettrotecnico Nazionale "Galileo Ferraris"

Torino - Italy

ABSTRACT

A two-way time synchronization experiment was per-formed in the spring of 1979 and 1980 via the Ital-ian SIRIO-1 experimental telecommunications satel-lite.

The experiment was designed and implemented by theIstituto Elettrotecnico Nazionale, Torino (Italy),to precisely monitor the satellite motion and toevaluate the possibility of performing a high-preci-sion, two-way time synchronization using a singlecommunication channel, time-shared between the par-ticipating sites.

The results of the experiment show that the preci-sion of the time synchronization is between 1 and5 ns, while the evaluation and correction of thesatellite motion effect has been performed with anaccuracy of a few nanoseconds or better over a timeinterval from 1 up to 20 seconds

INTRODUCTION

The principal features of the SIRIO-1 time synchronizationexperiment can be briefly summarized as follows:- the experiment was designed to precisely monitor the satel-lite motion and the effects of this motion on the time syn-chronization accuracy;

(*) Work supported by the Italian National Research Council.

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https://ntrs.nasa.gov/search.jsp?R=19810018945 2020-07-16T16:49:10+00:00Z

- the time synchronization is performed using the two-waytime synchronization technique and a single communicationchannel, time-shared between the two sites;

- the experiment tests a new technique that has been proposedto correct for the satellite motion effect while performingthe time synchronization;

- by using a single communication channel, no effects affect-ing the accuracy of the time*" synchronization at the 1 nslevel are due to the space segment (from one ground anten-na to the other), thanks to the high frequencies used forthe RF carriers;

- the time signals used allow the independent determinationof the uncertainties of the time-of-arrival measurementsat the two stations, to separate the contribution of eachstation to the total precision.

This last feature can be important .to understand the contri-bution of local phenomena (ground equipment, atmospheric con-ditions affecting the signal attenuation, especially rain,etc.) to the synchronization precision.

ORGANIZATION OF THE EXPERIMENT

A detailed description is given in ref. 1. Only a few remarksare given here, mainly for reference purposes.

Two ground stations, Fucino and Lario (fig. 1), participateto the experiment. Both sites are in Italy, in the north-ern (Lario) and in the central part (Fucino) of the country;one IEN Cesium clock was installed at each site.

Fucino (fig. 2) transmits its time signal at 0 seconds of thesynchronization frame (Fucino time), acting as station 'A',while Lario transmits its own signal at 0.5 s (Lario time),acting as station 'B1.

Two times-of-reception are then measured at each site; withreference to fig. 3, these are T^ and T-, at Fucino and T-,and Tc at Lario (we have no need to measure TQ and T? sincethese aresknown).

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To simplify the notation and for a better understanding, wemay note that T4 - T0 is the time of propagation of the timesignal from Fucino to Fucino, T-| - TQ is (neglecting for nowE) the time of propagation from Fucino to Lario, etc., so wecan write:

T(FF) = T4- T-, = T4m T(FL) * T-, -T0*^ T!U; T(LF) * T3-T2*c* T.-0.5

T(LL) = T5-T2 = T^-O.^

(*) local time reference

T(FF), T(FL), T(LF) and T(LL) are the actual results of thetime measurements at the two sites [except for the subtrac-tion of 0.1 s, resulting from the hardware implementation,see ref. 1 ] and will be used in any following computation.

Two data types are considered: pseudo-range data, such asT(FF) and T(LL), that are the time intervals measured againstthe same time reference, and synchronization data, such asT(LF) and -T(FL); the starting and ending times of the latterintervals are measured with reference to different clocks.

Data format

Actually, each one of the values listed in (1) results fromthe measurement process as the mean over ten independentmeasurements: a rough data file is shown in fig. 5. Eachtime of arrival is then evaluated as the arithmetic mean ofthe measured data. The data is rejected if the associatedstandard deviation is larger than 100 ns; however, less than0.5y£ of the data was rejected because their standard devia-tion was exceedingly large. On the average, the standard de-viation for each of the time-of-arrival evaluations, basedon ten data values, is in the range 10 to 50 ns.

The basic synchronization frame lasts 1 s and is repeatedevery 10 s; during the 1979 series of measurements, smallgroups of data (10 to 15 measurement frames) were recordedsequentially, to characterize the performance of this tech-nique over time intervals of 100 to 150 seconds: this wasactually performed also to verify the assumption of a linearmotion of the satellite and the validity of the correctionused (see eq. (7) to (15), ref. 1) over this time interval.

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During 1980 a second series of measurements were per-formed over longer time intervals (up to 16 minutes); thecomparison between the results obtained via the satellite,the TV method and portable clock trips are shown in fig. 6,where c . is the difference between the two atomic clockslocated at the ground sites. An expanded view over four con-secutive days of satellite measurements is given in fig. 7.

The overall accuracy of the clocks comparison was estimatedto be between 50 and 100 ns, with reference to some portableclock comparisons.

Synchronization estimate (T = 1 s)

The clocks difference £•£ at the time t, defined as:

(2) E. = t(B) - t(A) = t(LAR) - t(PUC)"C

is given (see ref. 3), over the basic synchronization frametime intervalT (T = 1 s), by the equation:

T (PL) - T (LF)(3) E.(T = 1 s) = —2 * + (0.5)-C

* 2since (t2-t1) is 0.5 s (see fig. 3).

The range-rate correction C to E., as defined in ref. 1, iscomputed as:

1

(4) C = + —20

The magnitude of C was usually found to be in the range2*4 ns/s, yielding a range rate correction of 1 to 2 ns overthe basic frame.

An estimate of E is obtained by taking the arithmetic meanof a number of successive data (from 100 s up to 16 minutes).If e would be constant over this measurement interval, thenthe standard deviation <T(E ) of the data would be related tothe precision of the method.

The evaluation of £ and <T(E ) is carried on by applying a3-sigma width filter; that is, the £ value is rejected ifthe residual | E-E.|> 3<r ; if anys has been rejected, a new

T» t

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e and<r(e) are evaluated using the remaining data.This procedure is repeated until no more data are rejected;usually this filter rejects less than the 5$ of the availabledata.

Assuming a normal distribution of the data, the one-sidedestimated error|6c| in the determination of £ is given, withthe 99.5$ confidence, as:

<r-t ™c(n-1)(5) |6£l= ^

The magnitude of 6E , when £ is computed over 50 to 100 dataranges usually between 1 and 5 ns (see fig. 7 and fig. 8).

The capability to look at the precision of the method overshort time intervals is demonstrated by fig. 8 and fig. 9,where two-hours data are plotted, together with an unweightedleast- squares fit of the available data.

As it can be seen, the average error of the fit is quite small,less than 1 .5 ns.

Expanded time synchronization frame (t = 10 s and T = 20 s)

As explained in ref . 1 , the time synchronization frame canbe lenghtened by simply rearranging the data.

This shows the capability of the method to synchronize twoclocks by using a single communication channel even if a fastswitching of the RF carrier at the two sites is not possibleand a large effect due to the satellite motion is then expect-ed; however, the amount of the correction due to this motioncan be computed very accurately by using the pseudo-rangedata available.

In this case, the clocks difference E can be computed as:

T (PL) - T (LF)(6) e.(t = 10 s) = — - - i±12 - + (10.5)-C

* 2

(since now (t2-t-| ) 10 .5 s) where C is given by eq . (4).

This is equivalent to have a station transmitting its timesignal at to and the other site transmitting at (t.o+10.5)s.

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Accordingly, to simulate a longer time interval (T = 20 s) wecan write:

T (PL) - T (LF)(7) et(x = 20 s) = — * - -^^ - + (20.5)-C

where now C is computed as:

1 r(3) C = + -

A comparison of single measurements of e , evaluated by usingeq. (3), (6) and (7) is presented in fig. 10, over a 200 stime interval. The agreement between the values of e^. for dif-ferent T's is remarkable, if we note that the correction tobe applied to eq. (6) and (7) amounts respectively to about48 and 95 ns in most cases.

Further analysis on the experimental data

Instead of using the differences between the measurement dataT(FL) and T(LF) to compute e ., it is possible to use a poly-nomial fit of the data and then evaluate et over the coef-ficients of the fitted polynomial.

This procedure has the advantage that less data are exchangedbetween the two sites (the fit coefficients only) and thatalso missing data points at one site can be recovered fromthe fitted curve.

By writing:n

T(FF) = rt ai(t-t0)1

T(LL) = I- b.(t-t0)x

(9) 2 1 iT(FL) = I± c.(t-tQ)

T(LF) = I\ di(t-t0)1

eq. (3) can be written as:

1 n

where:

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(11)20

n .

20

If e^. is constant over the measurement interval, then et=E.and eq. (10) becomes: °

If only the linear (velocity) terms are significant and anyhigher order term (acceleration) of the satellite motion isneglected, then C is given by

a. -i- b.(13) C .+ X

4 x

This procedure was actually carried on over measurements in-tervals up to 600 s; over time intervals up to 200 s it wasfound that a linear (first order) fit (as given by eq. (12)and (13)) was usually good anough to evaluate E, and anyfurther increase in the degree of the polynomial does notimprove the fit; obviously this result depends mainly on theclocks and the synchronization process behaviour.

This was also a further check of the correctness of the lin-ear motion assumption as given by eq. (4).

The test of statistical significance (see ref. 2) of the com-puted coefficients of the polynomials (9) was carried on bycomputing the standard deviation of the estimated coeffi-cients.

This was done in the following way: the least squares fit isexpressed by the normal equations that, in matrix form, are:

(14) (X'X) = (X'Y)

where: ( X ' X ) is the normal equations matrix (or x-productsmatrix);

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(X'Y) is the cross-products matrix;4> is the vector of the coefficients.

An estimated value of the standard deviation of the fit iscomputed as:

where n is the number of data, k is the number of estimatedcoefficients and r.^ is the i-th residual. The estimated standard deviation (ref. 2) of the k-th coefficient is given by:

(16) <r = ff-1C

where c i,. is the k-th diagonal element of the matrix (X'X)~.Actually the computation of the (X'X)~1 matrix was performedwith Gauss-Jordan reduction and pivot search to minimize thenumerical computation errors. Then an estimated confidenceinterval for the coefficient can be computed, by using theStudent t-distribution at (n-k) degrees of freedom.

Ground-equipment delays measurements

Two types of measurements were performed: test-loop-translator(TLT) measurements and transmitting-chain delay measurements(LARIO site only).

Test-loop-translator measurements

The experimental set-up is shown in fig. 11. The measurementsperformed showed a precision around 1 ns and a long term (1month) stability of the delay in the order of 1 to 3 ns, ifthe ground equipment is operated at the same power level. Themeasurements were performed in the same operating conditionsas during the synchronization sessions.

The loop-delay was found to be 3.776 us (LARIO) and 4.618 us(FUCINO) on the average.

Transmitter delay measurements (LARIO site only)

The proposed use of a microwave cavity as a frequency discrim-inator was tested. The cavity was characterized by a Q of150.0 at the transmission frequency. Unfortunately, the only

336

way to couple the cavity near the TLT was via an existingdirectional coupler, that attenuates the signal more than40 dB.

The rectified signal consequently was very small, since thecavity contributed an additional attenuation of about 12 dB,and, under these conditions, the measurement was impossible.

In order to increase the rectified signal, it was necessaryto increase the frequency deviation: in these conditions thecommunication equipment was working outside the range of nor-mal operation and the overall system response degraded no-ticeably. The measurement jitter, for instance, increased upto 50 ns (1 sigma), as compared to the 1 ns found in the TLTmeasurements; this was verified by performing the same TLT.measurement, but with the larger frequency deviation.

The reproducibility of the measurements, mainly related tothe critical setting of the microwave cavity (the cavity res-onance was adjusted at the RP carrier frequency when no mod-ulation was applied), was better than 100 ns, even whenworking in these very critical conditions.

ACKNOWLEDGMENTS

The authors would like to thank the Telespazio personnel atthe two ground stations for their assistance in performingthe experiment.

We wish also to acknowledge the work of the IEN personnelthat actually carried on the measurements; we are especiallygrateful to V. Pettiti, E. Angelotti, L. Canarelli, P. Corda-ra, V. Marchisio, G. Moro and L. Pietrelli, to Mr. G. Gallop-pa for the drawings and to Mrs. M. Castello for the typewrit-ing.

One of the authors (E. Detoma) wishes to dedicate his workto Mrs. Marina Castello, for her constant cooperation, en-couragement and sincere friendship: to acknowledge thatfriendship and loyalty towards the friends are always moreimportant than scientific and personal achievements.

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REFERENCES AND NOTES

1. E. Detoma, S. Leschiutta - The SIRIO-1 timing experiment,Proc. of the 11th Precise Time and Time Interval Meeting(PTTI), Nov. 1979 (Washington, B.C.)

2. M.Or. Natrella - Experimental statistics, NBS Handbook 91(1963). '

3. The actual computations were carried on by computing £ as:

£ = t(FUC) - t(IAR)

However, while the. data plotted result from these compu-tations, in the text of this paper the same notationis used as in ref. 1.

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QUESTIONS AND ANSWERS

MR. DAVID ALLEN, National Bureau of Standards

Two questions; one what is the size of the antenna involved?

PROFESSOR LESCHICUTTA:

Yes, please. In the ground station the size is 17 meters with atrue bandwidth — RF bandwidth of 34 megahertz. Also, in the re-peater satellite in the real bandwidth of base band bandwidth of6 megahertz.

As regards the experiment on the ship, the diameter of thedish is on the order of 2 1/2 meters but the bandwidth is just1.5 megahertz. So, obviosuly the precision should be deteriorated.

MR. ALLEN:

I thought it was a very excellent result that you received. I haveone question in regard to the equation. Because the stations arebasically north/south you would not see any effect due to the SANYACcorrection.

PROFESSOR LESCHIUTTA:

Yes, the SANYAC correction is 13.5 nanoseconds, in our case becausethe area of the path is very small in the equitorial plan.

MR. ALLEN:

The correction was not in the equation?

PROFESSOR LESCHIUTTA:

No, no, it was not included but is in the order of 14 nanoseconds.

MR. ALLEN:

Thank you.

PROFESSOR LESCHIUTTA:

13 foot.

MR. ALLEN:

Very good.

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CHAIRMAN BUISSON:

Any other questions?

MR. LAUREN RUEGER, The Johns Hopkins University/Applied Physics Laboratory

Do you ever take advantage of planning your experiments on the satel-lite motion when the relative changes to the stations are minimized?

PROFESSOR LESCKIUTTA:

There, again, we are not in a position to do so. We just receivefor some hours during the day, but we are planning periods of ex-periments to make all day measurements in order to follow the satel-lite. .

In previous experiments we have seen the maximum relativespeed of the satellite is of the order of 3.5, 4 meter per second.

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