Relative comparisons of Loran-C frequency transmissions between the master station of Catanzaro (Simeri Crichi) and the X, Z slave stations of Estartit (Spain) and Lampedusa (Italy) are carrying out by the GG LORSTA monitor station of the Mediterranean Sea Loran-C chain. These comparisons are able to emphasize the relative and, under certain conditions, the absolute rate of the emitting standard frequencies of the slave stations and some relevant statistical properties of the Loran-C Method for frequency transmission and time synchronization. The stability of each Loran-C frequency standard transmission is subject to perturbations, more or less known, due to the propagation medium and other causes. Following the Allan (1966) method for data processing, the performance of the relative rate of frequency of the transmissions of the X, Z slave stations are described calculating the standard deviation of a set of N frequency measurements from its mean averaged during sampling times. This standard deviation is designated as the measure of the stability of the Loran-C frequency transmission

Proverbio, E.

Quesada, V.

Simoncini, A.

English

NASA Technical Reports Server

STABILXTY AND NOISE SPECTRA O F  RELATEE IDRAN-C 
FREQUENCY COMPARISONS 
E. Proverbio 
V. Quesada 
A. Simoncini 
International Astronomical Latitude Station, Cagliari, Italy 
ABSTRACT 
Relative comparisons of Iloran-C frequency transmissions between the master 
station of Catanzaro (Simeri Crichi) and the X, Z slave stations of Estartit 
(Spain) and Lampedusa (Italy) are carrying out by the GG WRSTA Monitor 
Station of the Mediterranean Sea b ran -C  chain. These comparisons are able 
to emphasize the relative and, under certain conditions, the absolute rate of the 
emitting standard frequencies of the slave stations and some relevant statistical 
properties of the b r a n - C  Methad for frequency transmission and time synchron- 
ization. In fact the stability of each b r a n - C  frequency standard transmission 
is subject to perturbations, more o r  less known, due to the propagation medium 
and other causes. Following the Allan (1966) method for data processing, the 
performance of the relative rate  of frequency of the transmissions of the X, Z 
slave stations are described calculating the standard deviation 0 (N, r) of a set 
of N frequency measurements from its mean averaged during sampling times r. 
We designate this standard deviation a s  the measure of the stability of the hran- 
C frequency transmission. 
Typical performance of h r a n - C  transmissions has been successively studied 
by determining the Spectral density of the relative frequency variations between 
the X, Z slave stations a s  regards master station. 
One of the parameters addressed by this Interoperability Committee was timing 
and synchronization. The recommendations, and supporting rationale for these 
recommendations, will be provided. 
INTRODUCTION 
In order  to study the stability of the b r a n - C  radio-navigation system in the 
Mediterranean chain and to determine i ts  typical performance, relative com- 
parisons of b r a n - C  frequency transissions between the master station of 
Catanzaro (Simeri Crichi) and the X, Z slave stations of Estartit (Spain) ?nd 
Lampedusa (Italy) a r e  carrying out by the CG LORSTA Monitor Station of the 
Mediterranean Sea b r a n - C  chain. All b r a n - C  station transmit on 100 kHz 
https://ntrs.nasa.gov/search.jsp?R=19750003222 2020-03-23T03:04:19+00:00Z
and are controlled by cesium-beam atomic clodss. The analyzed data are re- 
ferred to the period January-December 1972 for the Estartit s tatbn and to the 
period Ckptember-December 1972 for the LampeQlsa station as this last station 
is entered upon office only from September 1972. The phase differences A # 
@I - X) and A - 2) between the frequency of the master and slave stations 
X and Z as received at the Cagliari Monitor Station has been reconstructed 
taking in account the corrections produced at the emitting station in order to 
closely synchronize each slave stztion to a common reference. The Table 1 
gives us a statistical distribution of the phase and time steps carried out at the 
emitting slave stations. These data show that phase variations due to steps in 
time a r e  generally smaller than 0.1 mec this means that the virtual o r  relative 
synchronism of the bran-C time scale is maintained to about 0.1 psec. 
Table 1 
Statistical Distributian in Rrcen t  of Man Made Time Steps Carried Out 
in the Emitting X and Z hm-C Statians of the Mediterranean Chain 
Denoting by A # (M - S) = B (M - S) the daily phase difference of the slave sta- 
tions X and Z with respect to the primary frequency of the master station as 
received at the Monitor Station and by d# (M - S) the phase steps brought into 
the emission, the daily calculated phase difference between slave and master 
station will be 
The quantities A O  (M - S),,, = B (M - S),,, correspond to the theoretical 
relative ohase difLerences between the master station and the X, Z slave sta- 
tion . Figure 1 and Figure 2 a re  plotted the real (full points) and theoretical 
@la. @ints) integrated time scales defined a s  Z B (M - S) and L: B (M - S),,, . 
Range h microsecood 
0.00 - 0.03 
0.03 - 0.06 
0.06 - 0.39 
0.09 - 5.12 
0.12 - 0.15 
0.15 - 0.18 
0.18 - 0.21 
@ f - z ) %  
0.0 
15.5 
31.0 
45.7 
3.1 
0.8 
3.9 
( M - X I %  
0.0 
16.0 
35.8 
42.0 
4.9 
1.0 
0.3 
1 
DE;T ERMINISTIC INSTABILTTIES 
The theoretical time scales Z B (M - X),,, and Z B (M - Z),,, represent the 
relative performance of the master time scale with respect to the X 2nd Z time 
scales. The instabilities of each time scale are due to deterministic process 
such as, for  instance, frequency drift o r  systematic changes (real o r  apparent) 
in the path and to m n  deterministic processes (random fluctuations). From the 
date given in Figure 1 and Figure 2 we can dedcce that the relative rate of the 
Master with respect to X and Z stations was +29.2 nsec/day and +35.6nsec/ 
day respectively o r  about +3.4 x lo-' ' and 4.1 x lo-' ' . These data show the 
excellent s'ability of each time scale and of the cesium beam clocks. The pro- 
gressive phase differences C B (M - S) observed a t  intervals of fiftees miautes 
was analysed for  emphasizes, the performance of this time scale upon periods 
included in the intervals of 0.5 - 24 hours and 1 - 45 days. The spectral densi- 
ties of the time scale Z1 B (M - Z) plotted in Figure 3 a r e  the trimensual average 
of the values calculated on periods of thirty days. It is interesting to point out 
the existence of peaks common to each curve which could be associated to syste- 
matic fluctuations in time scale. On the contrary the spectral density plots of 
time variation referred to the same scale Z B (M - Z) for period between 1 and 
45 days is given in Figure 4. 
The theoretical daily rate  of time scales C B (M - S), represent a significant 
parameter for  the study of frequencl drift in cesium standards (Winkler et al., 
1970). The values of the relative daily frequency rate  B for the frequency com- 
parison (M - X ) and (A1 - 2) are plotted in Figure 5. No noticeable drift appears 
for the relative rate R (M - X); as regards the rate  3 (M - X) the available data 
are too little to be *ble to draw a conclusion, because these frequency shifts can 
only be determined reliably over very long periods 01 time. It is interesting how- 
ever to point out a certain similarity in the trend and in the peaks of the common 
part  to the curves. The spectral analysis of the quantities B (M - Z) shows the 
probable existence of periodical irregularities of about 40 and 120 days with 
amplitudes of 3 - 4 x lo-' '. If these fluctuations would result rea l  a their cause 
could be looking for in thecesium beam standardsor in the relative path hariations. 
NON DET E "MINISTIC FLUCTUATIONS 
Non random phase fluctuations of the cesium beam introduced along a propagation 
path may be studied by using suitable statistical techniques. A useful measure in 
time and frequency domain has been shown to be the value of the standard devi- 
ation. Following D. Allan (1966) we have described the performance of the rela- 
tive rate  of frequency of the h r a n - C  transmission for the X and Z slave stations 
with respect to master station, calculating the standard deviation 6 (N, 7 )  of a 
se t  of N frequency measurement from i ts  mean versus sampling time. We 
designate this standard deviation as  the measure of the stability of the hran-C 
frequency transmission. The Figure 7 and Figure 8 shows the trend of the 
standard deviation o ( r )  (black points) of the relative frequency fluctuations Y 
versus measurement interval r in the frequency comparisons between the master 
stations M and the slaves X and Z. The results obtained in both cases a re  very 
similar but more interesting are the rcsults obtained from the B (M - 2) data 
owing to the very long measurement interval available. 
We can see (Fig. 8) that for sampling time r < 1 day and r > 30 days about the 
hran-C comparisons exhibit white phase noise. For these ranges the stability 
results 
about 100 ns for r < 1 day 
about 250 ns for r > 30 days 
On the contrary hran-C relative comparisons exhibits "perturbing" noise (white 
F M  noise?) for sample time ranging from 1 day to 30 days abouh the existence of 
these noise could be associated to the existence of long-term drift with period of 
about 5 - 10 and 40 days (see Fig. 6). 
CONCLUSION 
The phase fluctuations analyzed are  composed of the following components: 
A Q) (measured) = A 9 (propagation) + A t# (cesium) + A t# (transmitter) 
+ A t# (receiver) + A Q) (residual) 
If we assume that the phase noise in the receiver and transmitter is negligible 
with respect to the cesium and propagation fluctuations (Allan & Barnes, 1967) 
we can write 
Assuming, following Winkler et al., (1970). for the daily standard deviations of 
a cesium clock about 1 - 2 x lo-' q we can point out from the observed values 
of om given in Figure 7 and Figure 8 that fluctuations due to the influence of the 
medium on the propagation delay result of the same order of the random fluctu- 
ation of cesium beam, that is about lo-' * . 
ACKNOWLEDGEMENTS 
The authors express their appreciation and thanks to Mr. C. Y. Potts and to Com- 
manding Officer of the USAC Uran-C Station, Sardinia, for their kind cooperation. 
REFERENCES 
Winkler, G. M. R, Hall, R. G., Percival, D. B., 1970, Metrologia, Vol. 6, 
No. 4, 126. 
-
Allan, D. W., 1966, Pmc. of the IEEE, Vol. 54, No. 2, - 221 
- 5 : .' .I F E 3  MAR APR Y AV Jut JUL AUO SLP OCT KOV DTC 
Figure 1. Theoretical relative time scale (blank points) between the Master Station (Sirneri Crichi) 
and Z slave station (Lampedusa)of the bran-C Mediterranean sea chain during 1972. Blank points 
represent the real relative time scale after adjustments steps in phase carried out at the emission. 
2 B (M-X) 
J SEP OCT NOV DEC 
-5 
Figure 2. Theoretical and real relative time scales between the Master Station 
(Simeri Crichi) and X slave station (Lampedusa) as received at the Cagliari 
Monitor Station. 
SPECTRAL ANALYSIS OF S B  (M-Z) 
JAN-FEB-MAR 
3- 
0 
I T T  I " " l " " 1 " ' ~  
5 10 15 20 24 HOURS 
Figure 3. Spectral density plot of relative time scale C R (M - 2) 
determined with a sampling period of 0.25 h. 


SPECTRAL ANALYSIS B(ht1-Z) 
Figure 6. Spectral Analysis of the daily relative frequency 
rates B (M - Z) versus period in days. 
Figure 7. mectra cayabilities of bran-C relative compari.sons between Master Station and X slave station 
(Lampedusa). Plot of the square root of the variance of a,, ( r )  of the frequency variations. The dashed lines 
indicate the noise limits for theoretical time stabilities of -100 and 200 nsec based on the assumption of "white 
phase noise". 
Figure 8. Spectral capabilities of Uran-C relative mmparimns between Master Station and Z slave station 
(Estartit). Plot of the square root of the variance a, ( r )  of the frequency fluctuations. The dashed lines in- 
dicate the noise limits for theoretical time stabilities of 100 and 200 nsec based on the assumption of ''white 
phase misen. 


Stability and noise spectra of relative Loran-C frequency comparisons

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