209
1 INTRODUCTION
Timeistheindefinitecontinuedprogressofexistence
and events that occur in apparently irreversible
succession from the past through the present to the
future [9]. Time is a component quantity of various
measurements used to sequence events, to compare
thedurationofeventsortheintervalsbetweenthem,
and to quant
ify rates of change of quantities in
materialrealityorintheconsciousexperience.Timeis
oftenreferredtoasthefourthdimension,alongwith
thethreespatialdimensions[2].
Thehistoryoftheoriginsoftimemeasurementis
very distant and closely associated with the
development of astronomical research. The count of
ti
meisofgreatimportanceineverydaylifeand has
alsoplayedanimportantroleinnavigation[14].
Inthe20sand30softhetwentiethcentury,thatis,
during the initial period of the maritime
radionavigation,theproblemoftimeknowledgedid
not really ma
tter to the user, as the position was
measured by the only one radiolocation device, i.e.
radio direction finder (RDF), where measured
parameter was angle. The situation has radically
changedwiththeemergenceof newmethods,based
on distance measurements or distance differences,
andwhentherewasaneedtosynchronizebroa
dcast
time transmissions. If in classical navigation and
astronavigation the accuracy of 0.5 s, even 1 s both
measurementand knowledge of time was sufficient,
unfortunately in radionavigation became
unacceptable.The problem of creatingone, common
toall,timescales,becameofparticularimportanceat
thelaunchofnewterrestrialradionav
igationsystems
and satellite navigation systems covering the entire
surfaceoftheEarth.
The Concept of Time in Navigation
A.Weintrit
GdyniaMaritimeUniversity,Gdynia,Poland
ABSTRACT:Thearticlediscussestheconceptoftimeinnavigation,especiallyinmarinenavigation,aswellas
selected time measures, among others: Greenwich Mean Time (GMT), Universal Time Coordinated (UTC),
International Atomic Time TAI (Temps Atomique International), GPST (Global Positioning System Time)
eLoranTimeandinterrelationbetweenthesemeasures.Understandinghowti
meisinvolvedinnavigation,and
usingit, is one ofthe navigatorʹs mostimportantduties. Nowadays we havesatellitenavigation to help us
knowwhereweare.Thesesatellitescontainseveralverypreciseandaccurateclocks,becausetimeandlocation
are completely and totally int
er‐related in satellite navigation. There is growing interest internationally
concerningthevulnerabilityGlobalNavigationSatelliteSystems(GNSS)tonaturalandman‐madeinterference,
plusthejammingandspoofingoftheirtransmissions.Thesevulnerabilitieshaveledtoademandforsourcesof
resilientPNT(Positioning,NavigationandTiming)[16],includingarobustmea
nsofdistributingprecisetime
nationallyandinternationally.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 11
Number 2
June 2017
DOI:10.12716/1001.11.02.01
210
For several years now, especially in long‐term
measurements of radio frequency and time signals
have been used mainly the radio signals emitted by
navigation systems. This is possible because
navigational systems are based on the measurement
ofthedelayofradiosignalsemittedbyseveralremote
transmittingstations,and
thenatureoftheoperation
ofthesesystemsindicatesthatallstationsmustemit
synchronous signals based on one common time
scale.Thesevaluablepropertiesofsignalsemittedby
navigationsystemshavemadethemusedtomeasure
the frequency and time of signals used in
synchronous telecommunication systems. Some
operators
alsousethesesignalstodirectlycontrolthe
clockoftelecommunicationdevices.
The first global radionavigation system was the
Omega system, which has long since been
decommissioned [12]. The practical application for
synchronization of telecommunication networks has
found the Loran‐C system, whose some individual
chains are still interwoven with some
marine areas.
However, the widespread use of navigation system
signalsforthesynchronizationoftelecommunications
networkshasonlybroughttheGPSsystem.
2 CONCEPTOFTIME
Timeisthephysicalsize,characterizingeventsbythe
order in which they occur. Usually, time is used in
threecompletelydifferentmeanings[14]:
as the moment (point of duration) at which the
event took place; in practice, this means that the
exactdateoftheselectedtimepointisgiven,e.g.
when the position of the ship is determined; in
satellite systems this refers, for example, to the
timethesatellitetransmitsthe
signal;
asaperiodorintervalbetweentwoborderevents,
e.g. time between two observed positions; in
satellite systems, this refers, for example, to the
timeofpropagationofthesignalontheroutefrom
satellite(themomentofsendingthesignal)tothe
terrestrial user (the time of
signal reception by
receiver);
as a duration or continuance, a mea sure of the
length of the past time, such as watch duration,
durationofcounting,starlife;insatellitesystems,
thisrefers,forexample,totheeffectivelifetimeof
anorbitingsatellite.
Time as a duration means the past,
present, and
futureofallexistence.Timeasanintervalcoversthe
period between two events. As a point in duration,
time means the precise instance, second, minute,
hour,day,month,andyearasdeterminedbyaclock
orcalendar.
Thebasicunitoftime is the second(s).Over
the
past several decades, the definition of a second has
changedseveraltimesasunitsoftime,andnewtime
scaleshavebeenestablished.Thesechangesweredue
to the introduction of ever more accurate time
patterns, from mechanical throughquartz to atomic,
andinthenotsodistantfuturealso
hydrogen.
3 UNDERSTANDINGTIMEINNAVIGATION
Timeunderstandasapointindurationcanusemany
different reference points. When we talk aboutlocal
time, noon for our location is quite different from
noontosomeoneinAustraliaorAmerica.Ifwewant
to reference time to some common point
so that
everyoneintheworldknowswhatthattimeis,then
wemustallagreeonthepoint.GreenwichMeanTime
(GMT)istheprimarytimeusedforofficialeventsand
ismeasuredatthezeromeridianinGreenwich,which
has been agreed upon by all nations of the world
morethanhundredyearsago.Timeandlongitudeare
so intertwined in navigation that it is difficult to
discussof one without understanding theother. But
before we get into this relationship, let go first to
cover some history in the search for time, its
measurement,andtheinventionsused
tomeasureit
[11],[15].
Formostofhistory,ordinarypeopledidnothave
access to any kind of time‐measuring device, other
than to glance at the sky on a sunny day and see
wherethesunwas.Forthem,timeasweunderstand
ittodaydidnotreallyexist.The
measurementoftime
began with the invention of sundials in ancient
BabylonandEgyptabout16thcenturyBC.Theneed
forawaytomeasuretimeindependentlyof the sun
eventually gave rise to various devices, such as
sandglasses, waterclocks, and glowing candles.
Sandglassesandwaterclocksutilizedtheflowof
sand
andwatertomeasuretime,whilecandlesusedtheir
decreasedheight.Allthreeprovideda metaphor for
timeassomethingthatflowscontinuously,andthus
begantoshapethewayweusuallythinkoftime[11].
Thoughtheiraccuracywasnotgreat,thesedevices
providedawaytomeas uretime
withouttheneedfor
the sun to be visible. Each of these time‐measuring
devices carried markings designed to give sundial
time. In addition to a lack of accuracy, sandglasses,
waterclocks,andcandleshadtoberesetfrequently.It
did not collide with great discoveries; Bartolomeo
Dias,ChristopherColumbusand
VascodaGamahad
tousehourglassestomeasuretime.
Afterthediscoveryofthelawsofthependulum,a
moreaccurateclockwasinventedthatcouldnotonly
countthehours,buteventuallyminutesandseconds.
Theideaofmeasuringtimebysplittingitintoequal,
discreteintervalsandcounting
themwasatoddswith
the concept of time as something that flows. The
division of a day into 24 equal hours, of each hour
into60minutes,andofeachminuteinto60 seconds
areallhumaninventionsrequiredbytheneed for a
moreaccuratemeasurementoftime
[15].
Despite the various improvements, most early
clocks were highly unreliable. However, this was of
little consequence, since they could be checked and
adjusted regularly by reference to the sun. Thus,
despitethetechnology andthemechanicalnatureof
the time clocks produced, time was still ultimately
dependentonthesun.
By the middle of the seventeenth century,
pendulum clocks that were accurate to within 10
secondsperdaywerebeingmanufactured.Thiswas
far more precise than the sundial. But, for the vast
majority of the worldʹs population, the sun would
continuetoprovidetheprincipalmeansoftelling
the
211
localtime.However, thedefinitivetimewasprovided
byaclock.Fromthenon,clockswereusedtosetand
calibratesundials,ratherthan the other wayaround
aspreviouslyhadbeenthecase[11].
Of course, any system that used the sundialas a
primary reference point was using
local time. To
bring order to this temporal chaos, regional time
zones started to develop. By the late nineteenth
century, many countries had adopted uniform time
systemswithintheirbordersbuttherewashardlyany
coordinationbetweennations.Inparticular,therewas
thefundamentalissueofwheretolocatethe
baseline
formeasuringlongitude.
Time and navigation are inextricably linked
together.Forexample,ifsomepeoplelivedononeof
thePacificIslands,theylearnedaboutthecurrentsin
thesea andthestarsinthesky.Withthestarsinthe
sky they could figure out where they were
when
sailingfromoneislandtoanother.Thereisplentyof
available information on the early methods of
navigation, even ancient. In the Middle Ages there
was a great desire to improve navigation and there
wasagreatpushtoadvancethetechnologybetween
1500‐1800aswerealizedthat
ifweknewwhattimeit
was we could determine our longitude. We also
shiftedfromusingthequadrantandastrolabetothe
sextant. It was in the 1700s that John Harrison
invented the marine chronometer, a long‐sought
timekeeping device to solve the problem of
establishing one’s East/West position (longitude)
at
sea.Thisisreally importantbecause if yourclockis
offthatmeansyourlongitudewillbeofftoo.
The establishment of a worldwide system to
measure longitude brought with it a notion of
worldwidetime.Sincethereare24hoursinadayand
360degreesina
circle,each15degrees of longitude
represented one hour. Thus, by wrapping a 360‐
degreelongitudinalgridaroundtheearth,theplanet
was divided into 24 time zones, each one hour
differentfromitsneighbours.
Though largely hidden from our view, the fine‐
grained notion of time in use today, based
on the
movement of pulsars and measured by the tiny
quantum energy states of the atom, quite literally
affectstheveryfabricofourdailylivesandtheway
weviewourselvesandtheworldwelivein.Welive
bytheclock,andinmanywaysweareslaves
tothe
clock.TheuseofGreenwichMeanTimeforcelestial
navigationisrequiredsincealltheNauticalAlmanac
tablesarereferencedtoGMTanditistheofficialtime
for all maritime navigation. Accurate time is very
important to celestial because any clock errors will
throwthefixoffby
manymiles.
4 DEFINITIONOFTIMEUNIT
Any recurrent physical phenomenon can be used to
determinethetimeunitpattern.Initially,thesecond
was related to the rotation of the Earth. In 1832,
CharlesF.Gaussdefinedasecondas1/86400partof
themeansolarday,i.e.theperiod
betweenthelower
culmination of the mean Sun. This approach
remained until 1956. From this definition it was
evident that the time unit was derived from the
rotationoftheEartharounditsaxis,whichwasthen
considered to be even. Improving the accuracy of
clocks, especially after introducing of William
H.
Short and the quartz clocks, in the 1920s and 1930s
enabled the first to detect and then measure the
annualchangesintherotationoftheEarth.Inorder
toeliminatetheseirregularitiesin1956,thedefinition
ofasecondwaschanged,referringnowtotheperiod
ofEarthʹ
scirculationaroundtheSun,moreprecisely
tothetropicalyearin1900(theyearofthetropics,the
timebetweensuccessivepassagesoftheSunthrough
thepointofAries,wherecelestialequatorcrossesthe
ecliptic, and also the cycle of repetition of the
seasons). Because of the earlier Simon
Newcomb’s
theoryofthemotionofEarthitwasapparentthatthe
tropical year was 31556925,9747... seconds, the new
definitionsaidthatthesecondis1/31556925,9747part
ofthetropicalyear.In1960,suchadefinitionentered
theSI,althoughnotforlong[14],[15].
Inthemeantime,worksatthe
NationalBureauof
Standards (USA) have shown that it is possible to
phase‐conjugate a quartz oscillator to the resonant
frequency of a quantum transition in certain
moleculesoratoms.Insuchaprocess,strongquartz
oscillations are tuned into the feedback loop so that
they are accurate replicas of the
weak quantum
signal.Soonthefrequencystandardbasedonatomic
cesium‐prototype of modern atomic clocks was
made.Theprecisionofthistypeofdevice,surpassing
severalordersofmagnitude,theconventionalquartz
oscillator,finallyledtoasecondre‐definition:theSI
secondisthedurationof9,192,631,770periods
ofthe
radiationcorrespondingtothetransitionbetweenthe
two hyperfine levels of the ground state of the
cesium‐133atom(1967).
ThisSIsecond, referred to atomictime, was later
verifiedtobeinagreement,within1partin10
10
,with
the second of ephemeris time as determined from
lunar observations. Nevertheless, this SIsecond was
already,whenadopted,alittleshorterthanthethen‐
currentvalueofthesecondofmeansolartime
Where did such number of periods in this
definition come from? The first cesium frequency
bands
had the accuracy of one part per 10
9
‐10
10
,
while the universal time seconds, even after
smoothing seasonal fluctuations and Earth‐bound
(UT2)fluctuations,couldhavevariedatseverallevels
in10
8
overadecade.Itwasnecessarytodeterminethe
frequency of cesium transition with a better unit,
ephemeris seconds. Between 1955 and 1958, special
observationsoftheMoonweremade(theephemeris
time is best determined on this object), receiving at
thefrequencyof9192631770±20Hz.Theinaccuracy
ofthisresultismainlyduetotheerrorofephemeris.
Further follow‐up to 1967 confirmed this result. To
thisday,thecompatibilityofephemerissecondswith
atomic seconds is satisfactory, although the future
willsettleforhowlong.
We can guess that the already mentioned atomic
time is the
scale by which the atomic second is
discussed here. In fact, time signals distributed by
radioandavailableonadailybasisaresynchronized
to atomic frequency patterns. There are many such
patterns,andeachoneworksindependently of each
other. Consequently, there is a need to continually
comparetheir
practicesanddevelopacertainaverage
212
scale;itistheTempsAtomiqueInternational,orTAI.
Inthissituation,itwillbeveryimportanthowlongis
the TAI second. It turns out that since 1987
(previously, it was different), the TAI second is
systematicallylongerthanthedefiniteSIsecondfrom
thesea level. In 1995,
the difference was specifically
one part for 10
14
. Who cared about such a small
deviation? However, there are more serious reasons
for efforts to improve this scale. They provide the
pulsars‐fast‐rotating neutron stars. It seems very
likely that some of the millisecond pulsars rotate
morestablethanthe best atomicscales in averaging
periods of the
order of a year or more. At such
intervals, the instability of atomic patterns may
therefore limit the accuracy of certain parameters
obtainedfromobservation[14].
Good example of the use of atomic clocks is
provided by the Global Positioning System. GPS
depends on a network of 24 satellites orbiting
the
earth.Eachsatellitecontinuallybeamsdownasignal
givingitspositionandthemean‐timedeterminedby
thefouratomicclocksitcarriesonboard.Bypicking
up and comparing the time signals from three
satellites,agroundreceivercancompute its latitude
andlongitudewithanaccuracyofa
fewmeterswith
selective availability turned off. The clocks on the
satellites have to be extremely accurate. The
determinationofthe position ofthe ground receiver
depends on the tiny intervals of time it takes an
electromagnetic signal to travel from each of the
satellites to the receiver. Since the
signal travels at
186,000 miles per second, a timing error of one‐
billionthofasecondwillproduceapositionerrorof
about one foot. The onboard clocks are accurate to
onesecondin30,000years[11].
5 TIMESCALES
Themostimportantobservationofcoveringthestars
by the Moon
is the moment in time when the
phenomenon occurred. An observer should have
access to a time service, that is, a clock operating
according to a certain scale. Time information was
obtained over the ages from different sources,
including shuttle clocks. For marine users, these
timers, however, were not useful
due to rolling and
pitching.Thesituationchangedradicallyonlyin1759
whenEnglishwatchmakerJohnHarrisonʺLongitudeʺ
replaced the pendulum with a metal spring and
constructed the first mechanical chronometer. Until
theappearanceonthemarketthefirstreceiversofthe
satellite Transit system, the chronometers were the
main sources
of time information on sea‐ba sed
vessels.
Inorderto establishatimescale,youshould not
only measure, calibrate, but also determine the
beginning of the time scale. Earthʹs rotation is
associated with three time scales: star time, mean
solar time, and the most known universal time UT,
basedonaveragedoverayearofEarthrotation.
Themostfamousinternationaltimescalesinclude
thefollowingscales:
UT‐UniversalTime‐iscountedfrom0hoursat
midnight, with unit of duration the mean solar
day,definedto be as uniform aspossibledespite
variationsintherotationof
theEarth;
UT1istheprincipalformofUniversalTime;while
conceptuallyitismeansolartimeat0°longitude,
precise measurements of the Sun are difficult;
hence,itiscomputedfromobservationsofdistant
quasars using long baseline interferometry, laser
ranging of the Moon and artificial satellites, as
well as the determination of GPS satellite orbits;
UT1 is the same everywhere on Earth, and is
proportionaltotherotationangleoftheEarthwith
respect to distant quasars, specifically, the
International Celestial Reference Frame (ICRF),
neglecting some small adjustments; the
observationsallowthedeterminationofameasure
ofthe
EarthʹsanglewithrespecttotheICRF,called
theEarthRotationAngle(ERA,whichservesasa
modernreplacementforGreenwichMeanSidereal
Time);UT1iscomputedbycorrectingUT0forthe
effect of polar motion on the longitude of the
observingsite;itvariesfromuniformitybecauseof
theirregularitiesintheEarthʹsrotation;
UT0‐istherotationaltimeofaparticularplaceof
observation;localapproximationofuniversaltime
without taking into account polar motion; it is
observed as the diurnal motion of stars or
extraterrestrial radio sources., and also from
ranging observations of the Moon
and artificial
Earthsatellites.Thelocationoftheobservatoryis
considered to have fixed coordinates in a
terrestrial reference frame (such as the
InternationalTerrestrialReferenceFrame)butthe
positionoftherotationalaxisoftheEarthwanders
over the surface of the Earth; the difference
betweenUT0andUT1
isontheorderofafewtens
ofmilliseconds; the designation UT0 isnolonger
incommonuse;
UTC (GMT)‐Coordinated Universal Time; it
differsfromTAIbyanintegralnumberofseconds;
itistheinternationalstandardonwhichciviltime
is based; it ticks SI seconds, in
step with TAI; it
usuallyhas86,400SIsecondsperdaybutiskept
within 0.9 secondsof UT1by the introduction of
one‐secondstepstoUTC,theʺleapsecondʺ;asof
2017, these leaps have always been positive (the
days which contained a leap second were 86,401
secondslong);wheneveralevelofaccuracybetter
thanonesecondisnotrequired,UTCcanbeused
as an approximation of UT1; the difference
betweenUT1andUTCisknownasDUT1;
TAI is the International Atomic Time scale, a
statistical timescale based on a large number of
atomic
clocks;theunitofthistimeisSIsecond;
TDT (Terrestrial Dynamical Time) or TT
(Terrestrial Time)‐Earth dynamic time, used for
observation from the surface of the Earth; with
unitofduration86400SIsecondsonthegeoid,is
theindependentargumentofapparentgeocentric
ephemerides.TDT=
TAI+32.184seconds;
TDB (Barycentric Dynamical Time)‐Barycentric
dynamic time, used for ephemeris related to the
solar barycentric system; is the independent
argumentofephemeridesanddynamicaltheories
that are referred to the solar system barycentre;
TDBvariesfromTTonlybyperiodicvariations;
GMT (Greenwich Mean Time)
is the mean solar
time at the Royal Observatory in Greenwich,
London. GMT was formerly used as the
213
internationalciviltimestandard,nowsuperseded
in that function by Coordinated Universal Time
(UTC). Today GMT is considered equivalent to
UTC for UK civil purposes (but this is not
formalised) and for navigation is considered
equivalenttoUT1(themodernformofmeansolar
time at 0° longitude); these two
meanings can
differbyupto0.9s.Consequently,thetermGMT
shouldnotbeusedforprecisepurposes;
GAST (Greenwich Apparent Sideral Time)‐
associated with the true equinox date; is
GreenwichMeanSiderealTime(GMST)corrected
fortheshift inthepositionofthevernal equinox
due to
nutation. Nutation is the mathematically
predictable change in the direction of the earthʹs
axis of rotation due to changing external torques
from the sun, moon and planets. The smoothly
varying part of the change in the earthʹs
orientation(precession)isalreadyaccountedforin
GMST.Therightascensioncomponent
ofnutation
iscalledtheʺequationoftheequinoxesʺ;
GMST (Greenwich Mean Sideral Time)‐average
time of thestar for the Greenwichmeridian; it is
themeasureoftheearthʹsrotationwithrespectto
distant celestial objects; linked to the average
equinox for a given date. Compare
this to UT1,
which is therotation of the earth with respect to
themeanpositionofthesun.Onesiderealsecond
isapproximately365.25/366.25ofaUT1second.In
other words, there is one more day in a sidereal
yearthaninasolaryear.
Currently, GMT can be considered
as a general
equivalentofuniversaltimeUT.Theephemeristime
ET, which today only has historical significance, is
associated with the Kepler movement, or central
gravity‐based movement. Ephemeris time ET was a
dynamicscaleusedin the period1960‐1983.Later it
was replaced by the TDT and
TDB scales. The
difference between earthly and barycentric dynamic
time scale is due to the change of gravitational
potentialalongtheEarthʹsorbit.
Aftertheintroductionofatomictimemodelsinto
themarketinthe1960s,anewtermemerged‐atomic
time, the unit of which is the atomic second.
The
beginning of the atomic time scale was set at
1January195800h00m00sUT2.Atthistimethetime
in both scales was identical. Since then there have
beentwotimescales,onebasedonrotationalmotion
oftheEarth,andtheotheronatomicpatterns.Earthʹ
s
rotationisassociatedwithdayandnightphenomena
that are associated with the biological cycle of all
living organisms living there. Therefore, on the one
hand, it was necessary to measure time with
increasing accuracy, and on the other hand to
continueusinguniversaltime.Duetothefactthat
one
secondinatomictimeisshorterbyabout2.6∙10
‐8
s,
the number of past atomic seconds increases faster
thantheuniversalones.Thatmeansthatafterayear
the atomic scale reading will be about 0.82 s larger
than the universal scale. For this reason, a
compromise solution was needed that would take
into account both the advantages of
atomic patterns
and the changes in rotation and circulation of the
Earth.Thissolutionhasintroducedanewtimescale
calledCoordinatedUniversalTime‐UniversalTime
Coordinated(UTC).
CoordinatedUniversalTimeUTC‐standardtime
based on TAI taking into account the irregular
rotationoftheEarthandcoordinatedwithsolartime.
ToensurethatthemeanSunoverayearpassesover
Greenwichmeridianat12:00 UTC, with an accuracy
of not less than 0.9 s, from time to time to UTC is
added so‐called transient second. This operation is
carried out by IERS (International Earth Rotation
Service). Coordinated Universal
Time is expressed
using a 24‐hour clock and uses the Gregorian
calendar. It is used in air and maritime navigation,
whereitisknownunderthemilitarynameZulutime
(ʺZuluʺ in the phonetic alphabet corresponds to the
letterʺzʺ,whichdenotestheGreenwichmeridia n0).
In October
1971, the atomic scale of TAI (Inter‐
national Atomic Time) was introduced officially,
basedonatomicpatternsinwhichtheunitissaidSI
second.Thedifference betweenTAIandUT1 onthe
beginningofselectedyearsisshowninTable1.The
difference is growing steadily, exceeding the 34
secondsin2010and37secondsin2017.
Table1. Difference between TAI and UT1 on 1
st
Jan. in
selectedyears
_______________________________________________
YearTAI‐UT1[s]
_______________________________________________
15580
19686,1
197816,4
198823,6
199830,8
200332,3
_______________________________________________
Earthʹs spin is not uniform. Quasi‐periodic
changesaswellasagedeclineareobserved.Because
of this, time scales based on Earthʹs rotation are
changingrelative toatomictimeanddynamicscales.
DeltaTisthedifferencebetweenTerrestrialTime(TT)
andUniversalTime(UT1)i.e.
DeltaT=TT–UT1.
It is a measure of the difference between a time
scalebasedontherotationoftheEarth(UT1)andan
idealiseduniformtimescaleatthesurfaceoftheEarth
(TT). TT is realisedin practice by TAI, International
AtomicTime,whereTT(TDT)=TAI+32.184seconds.
Inordertopredictthe circumstances of aneventon
the surface of the Earth such as a solar eclipse, a
predictionofDeltaTmustbemadeforthatinstantof
TT.
DeltaT=TDT–UT
ThevalueofDeltaTchangesquite
irregularlyand
is difficult to predict. The length of the day varies
throughout the year by 0.002 seconds. The speed of
rotationoftheEarthishighestinJulyandAugustand
thesmallestinMarch.
214
Figure1.Annualirregularitiesinvortexmovement[1]
Tidal forces in the Earth‐Moon system cause
energydissipationandsynchronizationoftheMoonʹs
spinmotionrelativetoitsorbitalmotion.Thespeedof
rotationoftheEarthalsodependsontidalforces.For
example, the difference T in 1999 was about 64 s
(Fig.2).
Figure2. Irregularitiesin vortexmovementin recentyears
(basedondatafromTheAstronomicalAlmanac[1])
Thediagram(Fig.3)displaysthevaluesofDeltaT
forthetelescopicera(1620tothepresent)astabulated
on pages K8 and K9 of the current edition of The
Astronomical Almanac [1]. Data are given for the
beginning of each year. A simple parabolic function
used to estimate Delta T
is also plotted for
comparisonpurposes.IttakestheformDeltaT=–20
+32∙T
2
[8],where Tisthenumberofcenturiessince
1820. This function is based on the assumption that
thelengthofthemeansolardayhasbeenincreasing
byabout1.7millisecondspercentury.
Figure3. Telescopic era values of Delta T (1620 to 2017)
[1],[8]
Thediagram(Fig. 4)showsthevaluesofDelta T
derived from Bulletin B of the IERS. Two sets of
predictions are also provided for comparison
purposes.ThedailyDeltaTdataandpredictionsare
plotted for the interval 2000 to 2050 from MICA
v2.2.2. The predictions derived from the IERS
Sub‐
bureau for Rapid Service and Predictions are also
plottedfortheperiod 2006April1 to2027October1
alongwiththeiruncertainties(verticalerrorbars).The
current trend of observed Delta T data lies between
the two sets of predictions. This diagram illustrates
theproblemfacedbyalmanac
producerswhentrying
to estimate suitable values of Delta T for future
almanacs.
Figure4. Current values and longer term predictions of
DeltaT(2000to2050)[1]
6 GPSTIME(GPST)
Over the last twenty years, the Global Positioning
System (GPS) has become the primary tool for
national and international atomic clocks. This
techniquegivesten times better accuracy than using
the Loran‐C navigation system (also used for most
timestationservicesinmanyWesterncountries).This
is why for the first time the best world frequency
standardscanbecomparedinawaythatisaccurate
totheiraccuracy.Sofar,atomicclocktechnologyhas
always been ahead of time. Time accuracy of GPS
satellitesis10‐20ns(1ns=10
‐9
s)atintercontinental
distances and 2‐3 ns within one continent. With
average averaging of 10 days, the difference in
pattern frequencies is measured at one part level at
10
14
.Therearefurtherstudiescountingonachieving
clockaccuracyof0.3nsorbetter.
GPS is a satellite navigation system based on
measurementsofdistancestosatellites.Atomicclocks
(cesiumorrubidium).Itallowsyoutoinstantlyand
continuously determine positionand time anywhere
intheworld.
Nearly all of
the time service labs are equipped
withwell‐performing,fullyautomatedGPSreceivers.
Thesystemhasitsowntime,theso‐calledGPST(GPS
Time). GPS time is a continuous scale (GPS time
counting started midnight from 5 to 6 January 1980
00h00m00sUTC)synchronizedtoonemicrosecond
accuracywithUTC(USNO)time,i.e.,UTCtimeinthe
United States Naval Observatory (in turn this
implementationdiffersfromUTCingenerallessthan
1ms).AsfarasGPSisconcerned,noleapsecondsare
introduced, so far (first half of 2017), the difference
betweenUTChasrisento
18seconds(GPST‐UTC);
215
the TAI‐GPST difference is approximately 19
seconds. GPS satellite signals carry encoded
information about the current satellite clock
correctionrelativetoGPStimeandUTC(USNO)time
withaccuracy100ns.
Table2.DifferencebetweenlocaltimeLT,UTC,GPStime,
LorantimeandTAI:for17‐03‐2007at12:14:36UTC[6]
for12‐12‐2010at20:32:10UTC
for01‐06‐2011at20:21:36UTC
for13‐05‐2017at22:21:43UTC
7 PRACTICALUSEOFTHETIMESCALES
Which of the many time scales should we use in
practice? It depends on the situation, on our needs,
abilities and on specific applications. A sailor, an
amateurofastronavigationforobservation,should,in
principle,havesufficienttimeintheBalticSearegion,
CET or EET (Central or Eastern European Time),
obtainedbysynchronizingthelocalclocktotheradio
time signals of one of the many stations. When
compiling observations, it should convert this time
intoauniversaltimecoordinatedUTCbysubtracting
1or2hoursfromthetimezone.Sunobservers
should
havetheabilitytocalculatetherealsuntime,because
it governs the position of the sun relative to the
horizon;e.g.at12:00 oʹclock thattime,thesunison
the local meridian, i.e. in the highest point on the
horizon.Realtimeisobtainedfromthe
universalby
addingthelongitudeoftheplace(λ,positivelyEastof
Greenwich)andaddingthetimeequation(readfrom
theastronomicalalmanac).Ifweareinterestedinthe
accuracyofonesecond,thenwedonothavetoworry
about the differences between UTC, UT0, UT1 and
UT2 identifying
them with just universal time, UT
[14].
Professional astronomers may need rotational
time,sotheyshouldconvertUTCtoUT1byadding
appropriatecorrections(calledDUT1anddUT1with
accuracyof0.1and0.02srespectively)alsoreadfrom
radiosignals:UT1=UTC+DUT1+dUT1.
Toset
upatelescopeforaparticularstar,weneed
alocalrealstartime.Wecancalculateitforaspecific
time UT from the Greenwich Mean Sidereal Time
(GMST), adding a correction to the score (it is also
read from the almanac) adding the longitude of the
observationlocation:
ST
=GMST+(nutation)+λ.
In the opposite case, we wantto know whenthe
selected object is inacertain position relative to the
horizon.Wemustthenknoworcalculateitsanglein
this place. If the object culminates, then we know
immediatelythatitsqis
0h(12h).Inothersituations,
it is generally necessary to use simple spherical
trigonometric formulas. From anhour angle, we get
instant local star time: LST = a + q, and hence the
Greenwich Apparent Sidereal Time GAST = ST‐λ.
From this result, we will subtract the time to get
Greenwich Mean Sidereal Time GMST. Now to
converttheGreenwichtimeGMSTtoUT,weneedto
calculateorlookupthealmanacandreadtheGMST0,
i.e. the Greenwich Mean Sidereal Time at midnight
UTinGreenwich.IfGMST0isnumericallylargerthan
GMST,itmeansthatthelast
oneisforthenextstar
daily,soforcontinuityitshouldbereturned(addto
GMST)oneday,i.e.24hours.Wenowsafelycalculate
thefinal:
UT=(GMST‐GMST0)∙0.997269566329,
alwaysreceivinganon‐negativevaluelessthan24h.
If the UT falls less than 4 minutes, then
our object
probably(ifthereisnosignificantmotionintheright
angle)willagainappearon thesamehourangle(24
hoursafterthestar,i.e.after23h56m04.09sofmean
solartime).
Weshouldusetimeasuniformlyaspossibleinthe
observation results. On very long
stretches, the best
approximation is the ephemeris time we get from
universaltimebyaddingtheDTparameter(weread
it from the tables or, for dates before 1620, we
calculate according to one of the analytical
expressions available in the literature). Dates are
expressedinephemerisJuliandays(JED),i.e.
weuse
a simple algorithm to calculate the JED for the
calendar year, month and day, but the UT time is
replaced by the calculated ET hour. The measure of
thedistanceoftwoeventsintimeisthedifferenceof
therespectiveJuliandays:JED2‐JED1.
Since 1955 there
is also an equivalent ephemeris
nuclear scale, but more accurate than the ET scale
related to TAI we have from January 1, 1961 (since
1972 they are full seconds time differences TAI‐
UTC). By moving from ET to TAI, however,
remember that these scales are shifted in relation to
eachother
by 32,184 seconds. Evenmore uniform is
theTTscaleinBIPM(BureauInternationaldesPoids
etMesures)implementation.Unfortunately,itisonly
availablesince1976.TTscales canbetreatedexactly
the same as ET, because they are intended as
continuatorsofit.
216
Complete information on the UTC scale and its
related problems can be found in, inter alia, Vol. 2,
AdmiraltyListof Radio Signals in the chapter titled
RadioTimeSignals[13].
Since the early 1990s, all radio signals are UTC.
Also, the broadcas ting of terrestrial broadcas ting
systemsandsatellitenavigation
systemsisdirectlyor
indirectlyrelatedtoUTC.
7.1 AstronomicalTimesDefinitions
Severalimportanttimescalesstillfollowtherotation
oftheearth,mostnotablycivilandsiderealtime,but
ofthesearenowderivedfromatomictimethrougha
combination of earth rotation theory and actual
measurementsofthe
earthʹsrotationandorientation.
GMST(GreenwichMeanSiderealTime)‐Sidereal
timeisthemeasureoftheearthʹsrotationwithrespect
to distant celestial objects. Compare this to UT1,
whichistherotationoftheearthwithrespecttothe
mean position of the sun. One sidereal second is
approximately
365.25/366.25ofaUT1second.Inother
words,thereisonemoredayinasiderealyearthanin
asolaryear.
Byconvention,thereferencepointsforGreenwich
Sidereal Time are the Greenwich Meridian and the
vernal equinox (the intersection of the planes of the
earthʹsequatorand
theearthʹsorbit,theecliptic).The
Greenwich sidereal day begins when the vernal
equinox is on the Greenwich Meridian. Greenwich
MeanSiderealTime(GMST)isthehourangleofthe
average position of the vernal equinox, neglecting
shorttermmotionsoftheequinoxduetonutation.
It might seem strange
that UT1, a solar time, is
determined by measuring the earthʹs rotation with
respect to distant celestial objects, and GMST, a
siderealtime,isderivedfromit.Thisoddityismainly
due our choice of solar time in defining the atomic
time second. Hence, small variations of the earthʹ
s
rotationaremoreeasilypublishedas(UT1‐Atomic
Time)differences.Inpractice,ofcourse,someformof
siderealtimeisinvolvedinmeasuringUT1.
GAST (Greenwich Apparent Sidereal Time)‐
Greenwich Apparent Sidereal Time (GAST) is
GreenwichMeanSiderealTime(GMST)correctedfor
theshiftinthepositionofthevernal
equinoxdueto
nutation. Nutation is the mathematically predictable
changeinthedirectionoftheearthʹsaxisofrotation
duetochangingexternaltorquesfromthesun,Moon
andpla nets.Thesmoothlyvaryingpartofthechange
in the earthʹs orientation (precession) is already
accounted for in GMST.
The right ascension
componentof nutation is calledtheʺequation ofthe
equinoxesʺ[5].
GAST=GMST+(equationoftheequinoxes)
LMST (Local Mean Sidereal Time)‐Local Mean
Sidereal time is GMST plusthe observerʹs longitude
measured positive to the East of Greenwich. This is
the time commonly displayed
on an observatoryʹs
siderealclock.LMST = GMST + (observerʹs East
longitude)
LST(LocalSiderealTime)‐ThedefinitionofLocal
SiderealTimegivenintheglossaryoftheExplanatory
SupplementtotheAstronomicalAlmanacisʺthelocal
hour angle of a catalog equinox.ʺ This fits the
commontext
bookdefinition
HourAngle=LST‐RightAscension
In practice, LST is used more loosely to mean
either LMST orʺLocal Apparent Sidereal Timeʺ =
GAST + (observerʹs East longitude). The operational
definitionprobablyvariesfromoneobservatorytothe
next.
7.2 TAI,UTCandLeapSeconds
Theglobalreference
fortimeisInternationalAtomic
Time(TAI),atimescalecalculatedattheBIPM,using
datafromsome400atomicclocksinover70national
laboratories. The BIPM organizes clock comparisons
forthedeterminationofTAIthroughaninternational
network of time links. Corrections to local national
timing laboratory clocks
are generally applied
monthly or weekly and typically will be a few
nanoseconds(ns).
TAI long‐term stability is set by weighting
participatingclocks.ThescaleunitofTAI is kept as
closeaspossibletotheSIsecondbyusingdatafrom
those national laboratories which maintain the best
primary
standards.ThesewillgenerallybeHydrogen
MasersorhighperformanceCesiumstandards.
UTC is identical to TAI except that from time to
time a leap second is added to ensure that, when
averagedoverayear,theSuncrossestheGreenwich
meridian at noon UTC to within 0.9 s. The
dates of
application of the leap second are decided by the
InternationalEarthRotationService(IERS)[3].
7.3 PNT(Positioning,NavigationandTiming)
Global Navigation Satellite Systems (GNSS) provide
positioning, navigation, and timing information.
These satellite systems are augmented by ground
stations which can be used as reference points to
increase
theaccuracyofinformationderivedfromthe
satellitesignals.
All three: positioning (determining location),
navigation (finding your way from one to another),
and timing (supplying highly accurate time to
synchronizecomplexsystems)areusedtogetherwith
map data and other information (weather or traffic
data,forinstance)inmodernnavigation
systems[16].
We need a broad range of smart, low‐cost, high‐
performance GPS/GNSS timing clock and test
productsfornextgenerationnavigationalsystems.It
should be well suited for some of the following
applications:
GPS/GNSStimingformobilevehiclelocations,
navigational timing measurement & analysis
instruments,
ground
pseudoGPStimingsystems,
guidance&telemetryreferenceclocks,
radar&sensortimingsystems,
submarinenavigationaltimingsystems,
217
high‐performanceclockstabilityanalysers.
7.4 EnhancedLoranasaNationalTimeStandard
Enhanced Loran eLoran is an internationally
standardized positioning, navigation, and timing
(PNT) service for use by many modes of transport
andinotherapplications.It isthelatestinthelong‐
standing and proven series of
low‐frequency, Long‐
RangeNavigation(Loran)systems,onethattakesfull
advantageof21stcenturytechnology[3].
eLoran meets the accuracy, availability, integrity,
stabilityandcontinuityperformancerequirementsfor
aviation non‐precision instrument approaches,
maritime port and harbour entrance and approach
manoeuvres, land‐mobile vehicle navigation, and
location‐basedservices,
andisaprecisesourceoftime
and frequency for applications such as
telecommunications.Itisanindependent,dissimilar,
complementtoGlobalNavigationSatelliteSystems.It
allowsGNSSuserstoretainthesafety,security,and
economicbenefitsofGNSS,evenwhentheirsatellite
servicesaredisrupted.
What is important, eLoran meets
a set of
worldwide standards and operates wholly
independently of GPS, Glonass, Galileo, BeiDou or
anyfutureGNSS.Eachuser’seLoranreceiverwillbe
operable in all regions where an eLoran service is
provided.eLoranreceiversworkautomatically,with
minimal user input. eLoran transmissions are
synchronized to an identifiable, publicly‐
certified,
source of Co‐ordinated Universal Time (UTC) by a
methodwhollyindependentofGNSS.Thisallowsthe
eLoran Service Provider to operate on a time scale
thatissynchronizedwith,butoperatesindependently
of, GNSS time scales. Synchronizing to a common
time source will also allow receivers to employ a
mixtureofeLoranandsatellitesignals[4].
The principal difference between eLoran and
traditionalLoran‐Cistheaddition ofadatachannel
on the transmitted signal [3]. This conveys
application‐specificcorrections, warnings,andsignal
integrity information to the user’s receiver. It is this
data channel that allows eLoran
to meet the very
demanding requirements of landing aircraft using
non‐precision instrument approaches and bringing
shipssafelyintoharbourinlow‐visibilityconditions.
eLoran is also capable of providing the exceedingly
precisetimeandfrequencyreferencesneededbythe
telecommunications systems that carry voice and
internetcommunications.
Each country that
contributes to Universal
Coordinated Time (UTC) operates a national time
standardthatisindependentofGNSS.Itstechnology
will generally be based on a Hydrogen Maser. This
will be adjusted using monthly corrections supplied
bytheBIPMinFrance[4].
Low‐frequency eLoran is now emerging as the
preferredadvanced
sourceofpositioning,navigation
and timing (PNT) signals alternative or
complementarytoglobalnavigationsatellitesystems
(GNSS).eLoranisglobally‐standardizedanddoesnot
share the vulnerability of GNSS to incidental or
deliberate jamming, intentional spoofing, radio‐
frequencyinterferenceorspaceweatherevents.
A number of countries are actively reconsidering
their
dependence on GNSS across multiple critical
infrastructureapplicationsandsomeareplanningthe
implementation of eLoran transmitter networks.
Withinthiscontextfallsthequestionofhowtodeliver
theirnationaltimeservice to those clients who have
come to recognize their own vulnerability to the
disruption of GNSS. The paper
[4] discusses the
concept of delivering such national time services by
meansofeLoransignals. Itwasproposedtheuseof
eLorantodisseminateprecisetime,timingandphase
traceable to UTC for both indoor and outdoor
applications.Continuousaccuraciesofbetterthan100
nswithrespecttoUTCarebeing
achievedincurrent
proof‐of‐conceptandtechnology‐readinesstrials.The
paper [4] proposes and illustrates a method of
establishing national time standard services using
eLoran. These would be traceable to sovereign
national UTC. They would be of great benefit to a
wide range of users, notably telecommunications
providersand
financialsectororganisationsforwhom
precise time synchronisation will be required by
futureservices.Theseorganisationsarealsobecoming
concerned about their dependence on GNSS timing,
given its vulnerability to jamming and interference
and the complexity and expense of deploying it,
especiallywhenrequiredindoors.
The paper [4] explores the ability
of eLoran to
distribute UTC traceable time to applications in
GNSS‐deniedenvironments,includingindoors.Itsets
the foundation for further research into the
application and dissemination of UTC using eLoran
signals in geographical regions where they are
available.Researchintothistopichasbeenconducted
by Chronos Technology in
collaboration with
UrsaNav[3].ThishasshownthatUTC‐traceabletime
ofanaccuracybetterthan100nsandwithaquality
comparabletothatprovidedbyGPScanbereceived
even indoors at ranges of more than 800 km (500
miles) from eLoran transmitting stations. This new
time service meets
the latest ITU performance
standards in respect of telecommunications phase
stability.
8 THEBENEFITSANDRISKSOFUSING
TELECOMMUNICATIONSIGNALSIN
NAVIGATIONSYSTEMS
Until advances in the late twentieth century,
navigation depended on the ability to measure
latitude and longitude. Latitude can be determined
through celestial navigation; the measurement of
longitude requires accurate knowledge of time. This
needwasamajormotivationforthedevelopmentof
accurate mechanical clocks, including marine
chronometers.Whilesatellitenavigationsystemssuch
as the Global Positioning System (GPS) require
unprecedentedly accurate knowledge of time, this is
supplied by equipment on the satellites; vessels no
longerneed
timekeepingequipment.
Thebasicrequirementforproperoperationofthe
GPSsystemistomaintainauniformtimescalewithin
it,and this property isusedfortelecommunications.
Most stationary GPS receivers have the ability to
218
outputaone‐second signal(1pps)closelyrelatedto
theGPStimescale.
ThebenefitsofusingGPSandinthefutureGalileo
(possibly also Glonass) are significant. Mass‐
produced non‐military GPS receivers are cheap,
which is conducive to a wide range of GPS
capabilities[14].
GPS signals
allow you to reproduce with exactly
equalaccuracytheunambiguouslyexpressedseconds
pulsesrepresentingtheGPStimescaleinalmostthe
entire globe. A one‐second signal can be used as a
reference time signal and as a reference frequency
signal.
Standard time signals are used to maintain
accurate time
uniformity in different areas of the
economy,suchas[14]:
telecommunications (charging, identification of
placesoffailure),
telematics,ITS,ICT(dataflowcontrol),
power engineering (charging, synchronization of
powergenerators),
banking(transactiondate,timestamps),
state administration (documentation of events‐
police,rescueservices,customs),
transport
(trains,buses,ships,aircraft),
road transport (tolls, tolls, synchronized traffic
lights).
1 pps signal is used as the reference frequency
signal mainly for synchronizing telecommunication
networksandtostabilizeradiofrequencieswherethe
needs exceed the standardlevel. Use of GPS signals
canbedoneintwoways.
In
thefirst,passive,1ppssignalactsasareference
frequency when measuring the clock frequencies
produced by telecommunication clocks andpossibly
initiating alerts in case of anomaly. In the second
mode,theactive1ppssignalisusedtogenerateclock
signals in telecommunication devices controlled
automaticallyandcorrectedbased
onGPSsignals.In
this case, mediation of the quartz or rubidium
generator affected by the digital phase loop is
required.
InthefirstsolutiontheuseofaGPSsignalallows
theplacementoftwoinsteadofthreecesiumclocksin
thatclock,whichatasubstantialpriceand
forseveral
years only implies the importance of the pattern.
Economic benefits. Despite the reduction in the
number of cesium patterns, it will be possible to
indicatewhichofthetwocesiumpatternshavebeen
damagedorthattheGPSreceiverhasbeendamaged
(disassembled). In addition, with the use of
uncomplicated measuring instruments, data can be
obtained for manual correction of the frequency of
particular cesium standards to approximate the
coherence requirements of clock signals with UTC
timescale.
The second solution applies to automatically
controllingandcorrectingfrequenciesinlowerclock
hierarchically. These are SSU clocks for transit and
local nodes (a solution especially used on the
Americancontinent),andevendigitalorcellularbase
stations. Some operators under normal operating
conditionsdonotuseGPSsignals,butthiscapability
isusedinemergencysituations. Generallythisallows
theuseoflowerclassquartzorrubidiumgenerators
andthuslower
theirprice.
Intelecommunicationsapplications,thedifference
betweentheUTCtimescaleandtheGPStimescaleis
omitted.SousingtheGPSsignalsallowsyoutoplay
all the quality nodes with the UTC time scale in all
nodes of the telecommunications network, which is
an undoubted advantage of
the solution. The
disadvantagesofthesolutionincludethedependence
ofthecorrectoperationoftheoperatornetworkfrom
theaccesstoGPSsignals,whichtheoperatorhasno
influence.
Precisetimesignalcanbethebasisofeffectiveand
commonencryptionmethods,includinginareassuch
as finance, banking, insurance,
electronic document
certification,etc.
Telecommunication providers should ask: what
would happen to existing networks if GPS were no
longer available? This discussion has shown that
Lorancanprovidetelecommunicationproviderswith
a redundant synchronization source to GPS that
satisfies some technical requirements. Legacy Loran
has historically demonstrated the ability to
easily
meet the frequency performance requirements of a
PRS in a wired telephone network and the basic
requirements of the wireless CDMA (Code Division
Multiple Access) network. eLoran adds the timing
capabilities that allow it to better meet the time
synchronization requirements of CDMA and to
potentially support future networks with
sub‐
microsecond synchronization requirements. With its
largecoverageareaanditshighlevelofperformance,
eLoran can provide telecommunications providers
with the synchronization redundancy they need to
keep their networksfully operational in the absence
ofGPS.
9 CONCLUSIONS
There are a lot of time definitions. Time is the
indefinite
continuedprogressofexistenceandevents
thatoccurinapparently irreversible successionfrom
thepastthrough thepresenttothefuture. Timeisa
componentquantityofvariousmeasurementsusedto
sequenceevents,tocomparethedurationofeventsor
the intervals between them,and to quantifyrates of
change of
quantities in material reality or in the
consciousexperience.Timeisoftenreferredtoasthe
fourth dimension, along with the three spatial
dimensions[7],[10],[17].
In this paper, the Author presents the ability of
using eLoran as a national time standard and
proposes further research to assess spatial and
temporal
variationsinthereceptionofUTCtraceable
timedistributedbyusingeLoran.Itproposesthisnew
means of disseminating national sovereign UTC for
useattimesandinplaceswhereGNSSisdenied.It
willserve criticalinfrastructureapplications, notably
telecommunications networks and financial services,
in which sub‐microsecond UTC‐traceable
time is
essentialtothecontinuityofoperations. Inparticular
it will serve these applications without the need for
expensiveroofmountedGNSSantennadeployments
ormanagingcomplexfibreconnectivity.
219
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