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the International Journal Volume 11 on Marine Number 2 http://www.transnav.eu and Safety of Transportation June 2017

DOI: 10.12716/1001.11.02.01

The Concept of in Navigation

A. Weintrit Maritime University, Gdynia,

ABSTRACT: The article discusses the concept of time in navigation, especially in marine navigation, as well as selected time measures, among others: Mean Time (GMT), Coordinated (UTC), International Atomic Time TAI (Temps Atomique International), GPST (Global Positioning ) eLoran Time and interrelation between these measures. Understanding how time is involved in navigation, and using it, is one of the navigatorʹs most important duties. Nowadays we have navigation to us know where we are. These contain several very precise and accurate , because time and location are completely and totally inter‐related in . There is growing interest internationally concerning the vulnerability Global Navigation Satellite Systems (GNSS) to natural and man‐made interference, plus the jamming and spoofing of their transmissions. These vulnerabilities have led to a demand for sources of resilient PNT (Positioning, Navigation and Timing) [16], including a robust means of distributing precise time nationally and internationally.

1 INTRODUCTION In the 20s and 30s of the twentieth , that is, during the initial period of the maritime Time is the indefinite continued progress of existence radionavigation, the problem of time knowledge did and events that occur in apparently irreversible not really matter to the user, as the position was succession from the through the to the measured by the only one radiolocation device, i.e. [9]. Time is a component quantity of various direction finder (RDF), where measured used to sequence events, to compare parameter was angle. The situation radically the of events or the intervals between them, changed with the emergence of new methods, based and to quantify rates of change of quantities in on distance measurements or distance differences, material reality or in the conscious experience. Time is and when there was a need to synchronize broadcast often referred to as the fourth dimension, along with time transmissions. If in classical navigation and the three spatial dimensions [2]. astronavigation the accuracy of 0.5 s, even 1 s both and knowledge of time was sufficient, The of the origins of time measurement is unfortunately in radionavigation became very distant and closely associated with the unacceptable. The problem of creating one, common development of astronomical research. The count of to all, time scales, became of particular importance time is of great importance in everyday life and has the launch of new terrestrial radionavigation systems also played an important role in navigation [14]. and satellite navigation systems covering the entire surface of the .

209 For several now, especially in long‐ 3 UNDERSTANDING TIME IN NAVIGATION measurements of and time signals have been used mainly the radio signals emitted by Time understand as a point in duration can use many navigation systems. This is possible because different reference points. When we talk about local navigational systems are based on the measurement time, for our location is quite different from of the delay of radio signals emitted by several remote noon to someone in or America. If we want transmitting stations, and the of the operation to reference time to some common point so that of these systems indicates that all stations must emit everyone in the knows what that time is, then synchronous signals based on one common time we must all agree on the point. scale. These valuable properties of signals emitted by (GMT) is the primary time used for official events and navigation systems have made them used to measure is measured at the zero in Greenwich, which the frequency and time of signals used in has been agreed upon by all nations of the world synchronous systems. Some than hundred years ago. Time and are operators also use these signals to directly control the so intertwined in navigation that it is difficult to of telecommunication devices. discuss of one without understanding the other. But The first global radionavigation system was the before we get into this relationship, let go first to Omega system, which has long since been cover some history in the search for time, its decommissioned [12]. The practical application for measurement, and the inventions used to measure it of telecommunication networks has [11],[15]. found the Loran‐ system, whose some individual For most of history, ordinary people did not have chains are still interwoven with some marine areas. access to any kind of time‐measuring device, other However, the widespread use of navigation system than to glance at the sky on a sunny and see signals for the synchronization of where the was. For them, time as we understand networks has only brought the GPS system. it today did not really exist. The measurement of time began with the invention of in ancient Babylon and about 16th century BC. The need for a way to measure time independently of the sun 2 CONCEPT OF TIME eventually gave rise to various devices, such as sandglasses, waterclocks, and glowing candles. Time is the physical size, characterizing events by the Sandglasses and waterclocks utilized the flow of sand order in which they occur. Usually, time is used in and water to measure time, while candles used their three completely different meanings [14]: decreased height. All three provided a metaphor for  as the (point of duration) at which the time as something that flows continuously, and thus took place; in practice, this means that the began to shape the way we usually think of time [11]. exact of the selected time point is given, e.g. when the position of the ship is determined; in Though their accuracy was not great, these devices satellite systems this refers, for example, to the provided a way to measure time without the need for time the satellite transmits the signal; the sun to be visible. Each of these time‐measuring  as a period or interval between two border events, devices carried markings designed to give e.g. time between two observed positions; in time. In addition to a lack of accuracy, sandglasses, satellite systems, this refers, for example, to the waterclocks, and candles had to be reset frequently. It time of propagation of the signal on the from did not collide with great discoveries; Bartolomeo satellite (the moment of sending the signal) to the Dias, Christopher Columbus and Vasco da Gama had terrestrial user (the time of signal reception by to use to measure time. receiver); After the discovery of the of the , a  as a duration or continuance, a measure of the more accurate clock was invented that could not only length of the past time, such as duration, count the , but eventually and . duration of counting, life; in satellite systems, The idea of measuring time by splitting it into equal, this refers, for example, to the effective life time of discrete intervals and counting them was at odds with an orbiting satellite. the concept of time as something that flows. The Time as a duration means the past, present, and division of a day into 24 equal hours, of each future of all existence. Time as an interval covers the into 60 minutes, and of each into 60 seconds period between two events. As a point in duration, are all human inventions required by the need for a time means the precise instance, , minute, more accurate measurement of time [15]. hour, day, , and as determined by a clock Despite the various improvements, most early or . clocks were highly unreliable. However, this was of The is the second (s). Over the little consequence, since they could be checked and past several , the definition of a second has adjusted regularly by reference to the sun. Thus, changed several as units of time, and new time despite the technology and the mechanical nature of scales have been established. These changes were due the time clocks produced, time was still ultimately to the introduction of ever more accurate time dependent on the sun. patterns, from mechanical through quartz to atomic, By the middle of the seventeenth century, and in the not so distant future also hydrogen. pendulum clocks that were accurate to within 10 seconds per day were being manufactured. This was far more precise than the sundial. But, for the vast majority of the worldʹs population, the sun would continue to provide the principal means of telling the

210 local time. However, the definitive time was provided rotation of the Earth around its axis, which was then by a clock. From then on, clocks were used to set and considered to be even. Improving the accuracy of calibrate sundials, rather than the other way around clocks, especially after introducing of William H. as previously had been the case [11]. and the quartz clocks, in the 1920s and 1930s enabled the first to detect and then measure the Of course, any system that used the sundial as a annual changes in the rotation of the Earth. In order primary reference point was using local time. To to eliminate these irregularities in 1956, the definition bring order to this temporal chaos, regional time of a second was changed, referring now to the period zones started to develop. By the late nineteenth of Earthʹs circulation around the Sun, more precisely century, many had adopted uniform time to the in 1900 (the year of the tropics, the systems within their borders but there was hardly any time between successive passages of the Sun through coordination between nations. In particular, there was the point of Aries, where crosses the the fundamental issue of where to locate the base line , and also the cycle of repetition of the for measuring longitude. ). Because of the earlier Simon Newcomb’s Time and navigation are inextricably linked theory of the motion of Earth it was apparent that the together. For example, if some people lived on one of tropical year was 31556925,9747... seconds, the new the Pacific Islands, they learned about the currents in definition said that the second is 1/31556925,9747 part the sea and the in the sky. With the stars in the of the tropical year. In 1960, such a definition entered sky they could figure out where they were when the SI, although not for long [14],[15]. sailing from one island to another. There is plenty of In the meantime, works at the National Bureau of available information on the early methods of Standards (USA) have shown that it is possible to navigation, even ancient. In the Middle Ages there phase‐conjugate a quartz oscillator to the resonant was a great desire to improve navigation and there frequency of a quantum transition in certain was a great push to advance the technology between molecules or . In such a , strong quartz 1500‐1800 as we realized that if we knew what time it oscillations are tuned into the feedback loop so that was we could determine our longitude. We also they are accurate replicas of the weak quantum shifted from using the quadrant and astrolabe to the signal. Soon the frequency standard based on atomic . It was in the 1700s that cesium ‐ prototype of modern atomic clocks was invented the , a long‐sought made. The precision of this of device, surpassing timekeeping device to solve the problem of several orders of magnitude, the conventional quartz establishing one’s East/West position (longitude) at oscillator, finally led to a second re‐definition: the SI sea. This is really important because if your clock is second is the duration of 9,192,631,770 periods of the off that means your longitude will be off too. radiation corresponding to the transition between the The establishment of a worldwide system to two hyperfine levels of the ground state of the measure longitude brought with it a notion of cesium‐133 (1967). worldwide time. Since there are 24 hours in a day and This SI second, referred to atomic time, was later 360 degrees in a circle, each 15 degrees of longitude verified to be in agreement, within 1 part in 1010, with represented one hour. Thus, by wrapping a 360‐ the second of time as determined from longitudinal grid around the earth, the lunar observations. Nevertheless, this SI second was was divided into 24 time zones, each one hour already, when adopted, a little shorter than the then‐ different from its neighbours. current value of the second of mean Though largely hidden from our view, the fine‐ Where did such number of periods in this grained notion of time in use today, based on the definition come from? The first cesium frequency movement of and measured by the tiny bands had the accuracy of one part per 109 ‐ 1010, quantum energy states of the atom, quite literally while the universal time seconds, even after affects the very fabric of our daily lives and the way smoothing seasonal fluctuations and Earth‐bound we view ourselves and the world we live in. We live (UT2) fluctuations, could have varied at several levels by the clock, and in many ways we are slaves to the in 108 over a . It was necessary to determine the clock. The use of Greenwich Mean Time for celestial frequency of cesium transition with a better unit, navigation is required since all the Nautical ephemeris seconds. Between 1955 and 1958, special tables are referenced to GMT and it is the official time observations of the were made (the ephemeris for all maritime navigation. Accurate time is very time is best determined on this object), receiving at important to celestial because any clock errors will the frequency of 9192631770 ± 20 Hz. The inaccuracy throw the fix off by many . of this result is mainly due to the error of ephemeris. Further follow‐up to 1967 confirmed this result. To this day, the compatibility of ephemeris seconds with atomic seconds is satisfactory, although the future 4 DEFINITION OF TIME UNIT will settle for how long. Any recurrent physical phenomenon can be used to We can guess that the already mentioned atomic determine the time unit pattern. Initially, the second time is the scale by which the atomic second is was related to the rotation of the Earth. In 1832, discussed here. In fact, time signals distributed by Charles F. Gauss defined a second as 1/86400 part of radio and available on a daily basis are synchronized the mean solar day, i.e. the period between the lower to atomic frequency patterns. There are many such of the mean Sun. This approach patterns, and each one works independently of each remained until 1956. From this definition it was other. Consequently, there is a need to continually evident that the time unit was derived from the compare their practices and develop a certain average

211 scale; it is the Temps Atomique International, or TAI. day, defined to be as uniform as possible despite In this situation, it will be very important how long is variations in the rotation of the Earth; the TAI second. It turns out that since 1987  UT1 is the principal form of Universal Time; while (previously, it was different), the TAI second is conceptually it is mean solar time at 0° longitude, systematically longer than the definite SI second from precise measurements of the Sun are difficult; the sea level. In 1995, the difference was specifically hence, it is computed from observations of distant one part for 1014. Who cared about such a small quasars using long baseline , laser deviation? However, there are more serious reasons ranging of the Moon and artificial satellites, as for efforts to improve this scale. They provide the well as the determination of GPS satellite ; pulsars ‐ fast‐rotating neutron stars. It seems very UT1 is the same everywhere on Earth, and is likely that some of the pulsars rotate proportional to the rotation angle of the Earth with more stable than the best atomic scales in averaging respect to distant quasars, specifically, the periods of the order of a year or more. At such International Celestial Reference Frame (ICRF), intervals, the instability of atomic patterns may neglecting some small adjustments; the therefore limit the accuracy of certain parameters observations allow the determination of a measure obtained from observation [14]. of the Earthʹs angle with respect to the ICRF, called the Earth Rotation Angle (, which serves as a Good example of the use of atomic clocks is modern replacement for Greenwich Mean Sidereal provided by the Global Positioning System. GPS Time); UT1 is computed by correcting UT0 for the depends on a network of 24 satellites orbiting the effect of polar motion on the longitude of the earth. Each satellite continually beams down a signal observing site; it varies from uniformity because of giving its position and the mean‐time determined by the irregularities in the Earthʹs rotation; the four atomic clocks it carries on board. By picking  UT0 ‐ is the rotational time of a particular place of up and comparing the time signals from three observation; local approximation of universal time satellites, a ground receiver can compute its without taking into account polar motion; it is and longitude with an accuracy of a few meters with observed as the of stars or selective availability turned off. The clocks on the extraterrestrial radio sources., and also from satellites have to be extremely accurate. The ranging observations of the Moon and artificial determination of the position of the ground receiver Earth satellites. The location of the observatory is depends on the tiny intervals of time it takes an considered to have fixed coordinates in a electromagnetic signal to travel from each of the terrestrial reference frame (such as the satellites to the receiver. Since the signal travels at International Terrestrial Reference Frame) but the 186,000 miles per second, a timing error of one‐ position of the rotational axis of the Earth wanders billionth of a second will produce a position error of over the surface of the Earth; the difference about one foot. The onboard clocks are accurate to between UT0 and UT1 is on the order of a few tens one second in 30,000 years [11]. of ; the designation UT0 is no longer in common use;  UTC (GMT) ‐ Coordinated Universal Time; it differs from TAI by an integral number of seconds; 5 TIME SCALES it is the international standard on which is based; it ticks SI seconds, in step with TAI; it The most important observation of covering the stars usually has 86,400 SI seconds per day but is kept by the Moon is the moment in time when the within 0.9 seconds of UT1 by the introduction of phenomenon occurred. An observer should have one‐second steps to UTC, the ʺleap secondʺ; as of access to a time service, that is, a clock operating 2017, these leaps have always been positive (the according to a certain scale. Time information was days which contained a were 86,401 obtained over the ages from different sources, seconds long); whenever a level of accuracy better including shuttle clocks. For marine users, these than one second is not required, UTC can be used , however, were not useful due to rolling and as an approximation of UT1; the difference pitching. The situation changed radically only in 1759 between UT1 and UTC is known as DUT1; when English John Harrison ʺLongitudeʺ  TAI is the International Atomic Time scale, a replaced the pendulum with a metal and statistical timescale based on a large number of constructed the first mechanical chronometer. Until atomic clocks; the unit of this time is SI second; the appearance on the market the first receivers of the  TDT (Terrestrial Dynamical Time) or TT satellite system, the chronometers were the () ‐ Earth dynamic time, used for main sources of time information on sea‐based observation from the surface of the Earth; with vessels. unit of duration 86400 SI seconds on the geoid, is In order to establish a time scale, you should not the independent argument of apparent geocentric only measure, calibrate, but also determine the ephemerides. TDT = TAI + 32.184 seconds; beginning of the time scale. Earthʹs rotation is  TDB (Barycentric Dynamical Time) ‐ Barycentric associated with three time scales: star time, mean dynamic time, used for ephemeris related to the solar time, and the most known universal time UT, solar barycentric system; is the independent based on averaged over a year of Earth rotation. argument of ephemerides and dynamical theories that are referred to the solar system barycentre; The most famous international time scales include TDB varies from TT only by periodic variations; the following scales:  GMT (Greenwich Mean Time) is the mean solar  UT ‐ Universal Time ‐ is counted from 0 hours at time at the Royal Observatory in Greenwich, , with unit of duration the mean solar . GMT was formerly used as the

212 international civil , now superseded Coordinated Universal Time UTC ‐ in that function by Coordinated Universal Time based on TAI taking into account the irregular (UTC). Today GMT is considered equivalent to rotation of the Earth and coordinated with solar time. UTC for UK civil purposes (but this is not To ensure that the mean Sun over a year passes over formalised) and for navigation is considered Greenwich meridian at 12:00 UTC, with an accuracy equivalent to UT1 (the modern form of mean solar of not less than 0.9 s, from time to time to UTC is time at 0° longitude); these two meanings can added so‐called transient second. This operation is differ by up to 0.9 s. Consequently, the term GMT carried out by IERS (International Earth Rotation should not be used for precise purposes; Service). Coordinated Universal Time is expressed  GAST (Greenwich Apparent Sideral Time) ‐ using a 24‐hour clock and uses the Gregorian associated with the true date; is calendar. It is used in air and maritime navigation, Greenwich Mean (GMST) corrected where it is known under the military name Zulu time for the shift in the position of the vernal equinox (ʺZuluʺ in the phonetic alphabet corresponds to the due to nutation. Nutation is the mathematically letter ʺzʺ, which denotes the Greenwich meridian 0). predictable change in the direction of the earthʹs axis of rotation due to changing external torques In October 1971, the atomic scale of TAI (Inter‐ from the sun, moon and . The smoothly national Atomic Time) was introduced officially, varying part of the change in the earthʹs based on atomic patterns in which the unit is said SI orientation (precession) is already accounted for in second. The difference between TAI and UT1 on the GMST. The component of nutation beginning of selected years is shown in Table 1. The is called the ʺequation of the equinoxesʺ; difference is growing steadily, exceeding the 34  GMST (Greenwich Mean Sideral Time) ‐ average seconds in 2010 and 37 seconds in 2017. time of the star for the Greenwich meridian; it is the measure of the earthʹs rotation with respect to Table 1. Difference between TAI and UT1 on 1st Jan. in distant celestial objects; linked to the average selected______years equinox for a given date. Compare this to UT1, Year TAI ‐ UT1 [s] which is the rotation of the earth with respect to ______the mean position of the sun. One sidereal second 1558 0 1968 6,1 is approximately 365.25/366.25 of a UT1 second. In 1978 16,4 other words, there is one more day in a sidereal 1988 23,6 year than in a solar year. 1998 30,8 Currently, GMT can be considered as a general ______2003 32,3 equivalent of universal time UT. The ET, which today only has historical significance, is Earthʹs is not uniform. Quasi‐periodic associated with the Kepler movement, or central changes as well as decline are observed. Because gravity‐based movement. Ephemeris time ET was a of this, time scales based on Earthʹs rotation are dynamic scale used in the period 1960‐1983. Later it changing relative to atomic time and dynamic scales. was replaced by the TDT and TDB scales. The Delta T is the difference between Terrestrial Time (TT) difference between earthly and barycentric dynamic and Universal Time (UT1) i.e. time scale is due to the change of gravitational potential along the Earthʹs . Delta T = TT – UT1. After the introduction of atomic time models into the market in the 1960s, a new term emerged ‐ atomic It is a measure of the difference between a time time, the unit of which is the atomic second. The scale based on the rotation of the Earth (UT1) and an beginning of the atomic time scale was set at idealised uniform timescale at the surface of the Earth 1 January 1958 00h 00m 00s UT2. At this time the time (TT). TT is realised in practice by TAI, International in both scales was identical. Since then there have Atomic Time, where TT (TDT) = TAI + 32.184 seconds. been two time scales, one based on rotational motion In order to predict the circumstances of an event on of the Earth, and the other on atomic patterns. Earthʹs the surface of the Earth such as a , a rotation is associated with day and phenomena prediction of Delta T must be made for that instant of that are associated with the biological cycle of all TT. living organisms living there. Therefore, on the one hand, it was necessary to measure time with increasing accuracy, and on the other hand to Delta T = TDT – UT continue using universal time. Due to the fact that one second in atomic time is shorter by about 2.6 ∙ 10‐8 s, The value of Delta T changes quite irregularly and the number of past atomic seconds increases faster is difficult to predict. The length of the day varies than the universal ones. That means that after a year throughout the year by 0.002 seconds. The speed of the atomic scale reading will be about 0.82 s larger rotation of the Earth is highest in July and August and than the universal scale. For this reason, a the smallest in March. 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. This solution has introduced a new time scale called Coordinated Universal Time ‐ Universal Time Coordinated (UTC).

213 purposes. The daily Delta T data and predictions are 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 plotted for the period 2006 April 1 to 2027 October 1 along with their uncertainties (vertical error bars). The current trend of observed Delta T data lies between the two sets of predictions. This diagram illustrates the problem faced by almanac producers when trying to estimate suitable values of Delta T for future . Figure 1. Annual irregularities in vortex movement [1]

Tidal forces in the Earth‐Moon system cause energy dissipation and synchronization of the Moonʹs spin motion relative to its orbital motion. The speed of rotation of the Earth also depends on tidal forces. For example, the difference T in 1999 was about 64 s (Fig.2).

Figure 4. Current values and longer term predictions of Delta T (2000 to 2050) [1]

6 GPS TIME (GPST) Figure 2. Irregularities in vortex movement in recent years (based on data from The Astronomical Almanac [1]) Over the last twenty years, the Global Positioning System (GPS) has become the primary tool for The diagram (Fig.3) displays the values of Delta T national and international atomic clocks. This for the telescopic era (1620 to the present) as tabulated technique gives ten times better accuracy than using on pages K8 and K9 of the current edition of The the Loran‐C navigation system (also used for most Astronomical Almanac [1]. Data are given for the time station services in many Western countries). This beginning of each year. A simple parabolic function is why for the first time the best world frequency used to estimate Delta T is also plotted for standards can be compared in a way that is accurate comparison purposes. It takes the form Delta T = – 20 to their accuracy. So far, technology has + 32∙T2 [8], where T is the number of since always been ahead of time. Time accuracy of GPS 1820. This function is based on the assumption that satellites is 10‐20 ns (1 ns = 10‐9 s) at intercontinental the length of the mean solar day has been increasing distances and 2‐3 ns within one . With by about 1.7 milliseconds per century. average averaging of 10 days, the difference in pattern frequencies is measured at one part level at 1014. There are further studies counting on achieving clock accuracy of 0.3 ns or better. GPS is a satellite navigation system based on measurements of distances to satellites. Atomic clocks (cesium or ). It allows you to instantly and continuously determine position and time anywhere in the world. Nearly all of the time service labs are equipped with well‐performing, fully automated GPS receivers. The system has its own time, the so‐called GPST (GPS Time). GPS time is a continuous scale (GPS time counting started midnight from 5 to 6 January 1980 00h 00m 00s UTC) synchronized to one Figure 3. Telescopic era values of Delta T (1620 to 2017) accuracy with UTC (USNO) time, i.e., UTC time in the [1],[8] Naval Observatory (in turn this implementation differs from UTC in general less than The diagram (Fig. 4) shows the values of Delta T 1 ms). As far as GPS is concerned, no leap seconds are derived from Bulletin B of the IERS. Two sets of introduced, so far (first half of 2017), the difference predictions are also provided for comparison between UTC has risen to 18 seconds (GPST ‐ UTC);

214 the TAI ‐ GPST difference is approximately 19 appropriate corrections (called DUT1 and dUT1 with seconds. GPS satellite signals carry encoded accuracy of 0.1 and 0.02 s respectively) also read from information about the current satellite clock radio signals: UT1 = UTC + DUT1 + dUT1. correction relative to GPS time and UTC (USNO) time with accuracy 100 ns. To set up a telescope for a particular star, we need a local real star time. We can calculate it for a specific time UT from the Greenwich Mean Sidereal Time Table 2. Difference between local time LT, UTC, GPS time, (GMST), adding a correction to the score (it is also Loran time and TAI: for 17‐03‐2007 at 12:14:36 UTC [6] read from the almanac) adding the longitude of the observation location:

ST = GMST + (nutation) + λ.

In the opposite case, we want to know when the selected object is in a certain position relative to the for 12‐12‐2010 at 20:32:10 UTC . We must then know or calculate its angle in this place. If the object culminates, then we know immediately that its q is 0h (12h). In other situations, it is generally necessary to use simple spherical trigonometric formulas. From an , 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 for 01‐06‐2011 at 20:21:36 UTC Greenwich Mean Sidereal Time GMST. Now to the Greenwich time GMST to UT, we need to calculate or look up the almanac and read the GMST0, i.e. the Greenwich Mean Sidereal Time at midnight UT in Greenwich. If GMST0 is numerically larger than GMST, it means that the last one is for the next star daily, so for continuity it should be returned (add to GMST) one day, i.e. 24 hours. We now safely calculate for 13‐05‐2017 at 22:21:43 UTC the final:

UT = (GMST ‐ GMST0) ∙ 0.997269566329,

always receiving a non‐negative value less than 24h. If the UT falls less than 4 minutes, then our object probably (if there is no significant motion in the right angle) will again appear on the same hour angle (24 hours after the star, i.e. after 23h 56m 04.09s of mean 7 PRACTICAL USE OF THE TIME SCALES solar time). We should use time as uniformly as possible in the Which of the many time scales should we use in observation results. On very long stretches, the best practice? It depends on the situation, on our needs, approximation is the ephemeris time we get from abilities and on specific applications. A sailor, an universal time by adding the DT parameter (we read amateur of astronavigation for observation, should, in it from the tables or, for dates before 1620, we principle, have sufficient time in the Baltic Sea region, calculate according to one of the analytical CET or EET (Central or ), expressions available in the literature). Dates are obtained by synchronizing the local clock to the radio expressed in ephemeris Julian days (JED), i.e. we use time signals of one of the many stations. When a simple algorithm to calculate the JED for the compiling observations, it should convert this time calendar year, month and day, but the UT time is into a universal time coordinated UTC by subtracting replaced by the calculated ET hour. The measure of 1 or 2 hours from the . Sun observers should the distance of two events in time is the difference of have the ability to calculate the real sun time, because the respective Julian days: JED2‐ JED1. it governs the position of the sun relative to the horizon; e.g. at 12:00 oʹclock that time, the sun is on Since 1955 there is also an equivalent ephemeris the local meridian, i.e. in the highest point on the nuclear scale, but more accurate than the ET scale horizon. Real time is obtained from the universal by related to TAI we have from , 1961 (since adding the longitude of the place (λ, positively East of 1972 they are full seconds time differences TAI ‐ Greenwich) and adding the time equation (read from UTC). By moving from ET to TAI, however, the astronomical almanac). If we are interested in the remember that these scales are shifted in relation to accuracy of one second, then we do not have to worry each other by 32,184 seconds. Even more uniform is about the differences between UTC, UT0, UT1 and the TT scale in BIPM (Bureau International des Poids UT2 identifying them with just universal time, UT et Mesures) implementation. Unfortunately, it is only [14]. available since 1976. TT scales can be treated exactly the same as ET, because they are intended as Professional may need rotational continuators of it. time, so they should convert UTC to UT1 by adding

215 Complete information on the UTC scale and its LST (Local Sidereal Time) ‐ The definition of Local related problems can be found in, inter alia, . 2, Sidereal Time given in the glossary of the Explanatory Admiralty List of Radio Signals in the chapter titled Supplement to the Astronomical Almanac is ʺthe local Radio Time Signals [13]. hour angle of a catalog equinox.ʺ This fits the common text book definition Since the early 1990s, all radio signals are UTC. Also, the broadcasting of terrestrial broadcasting systems and satellite navigation systems is directly or Hour Angle = LST ‐ Right Ascension indirectly related to UTC. In practice, LST is used more loosely to mean either LMST or ʺLocal Apparent Sidereal Timeʺ = GAST + (observerʹs East longitude). The operational 7.1 Astronomical Times Definitions definition probably varies from one observatory to the Several important time scales still follow the rotation next. of the earth, most notably civil and sidereal time, but of these are now derived from atomic time through a combination of earth rotation theory and actual 7.2 TAI, UTC and Leap Seconds measurements of the earthʹs rotation and orientation. The global reference for time is International Atomic GMST (Greenwich Mean Sidereal Time) ‐ Sidereal Time (TAI), a time scale calculated at the BIPM, using time is the measure of the earthʹs rotation with respect data from some 400 atomic clocks in over 70 national to distant celestial objects. Compare this to UT1, laboratories. The BIPM organizes clock comparisons which is the rotation of the earth with respect to the for the determination of TAI through an international mean position of the sun. One sidereal second is network of time links. Corrections to local national approximately 365.25/366.25 of a UT1 second. In other timing laboratory clocks are generally applied words, there is one more day in a than in monthly or weekly and typically will be a few a solar year. (ns). By convention, the reference points for Greenwich TAI long‐term stability is set by weighting Sidereal Time are the Greenwich Meridian and the participating clocks. The scale unit of TAI is kept as vernal equinox (the intersection of the planes of the close as possible to the SI second by using data from earthʹs equator and the earthʹs orbit, the ecliptic). The those national laboratories which maintain the best Greenwich sidereal day begins when the vernal primary standards. These will generally be Hydrogen equinox is on the Greenwich Meridian. Greenwich or high performance Cesium standards. Mean Sidereal Time (GMST) is the hour angle of the average position of the vernal equinox, neglecting UTC is identical to TAI except that from time to short term motions of the equinox due to nutation. time a leap second is added to ensure that, when averaged over a year, the Sun crosses the Greenwich It might seem strange that UT1, a solar time, is meridian at noon UTC to within 0.9 s. The dates of determined by measuring the earthʹs rotation with application of the leap second are decided by the respect to distant celestial objects, and GMST, a International Earth Rotation Service (IERS) [3]. sidereal time, is derived from it. This oddity is mainly due our of solar time in defining the atomic time second. Hence, small variations of the earthʹs rotation are more easily published as (UT1 ‐ Atomic 7.3 PNT (Positioning, Navigation and Timing) Time) differences. In practice, of course, some form of Global Navigation Satellite Systems (GNSS) provide sidereal time is involved in measuring UT1. positioning, navigation, and timing information. GAST (Greenwich Apparent Sidereal Time) ‐ These satellite systems are augmented by ground Greenwich Apparent Sidereal Time (GAST) is stations which can be used as reference points to Greenwich Mean Sidereal Time (GMST) corrected for increase the accuracy of information derived from the the shift in the position of the vernal equinox due to satellite signals. nutation. Nutation is the mathematically predictable All three: positioning (determining location), change in the direction of the earthʹs axis of rotation navigation (finding your way from one to another), due to changing external torques from the sun, Moon and timing (supplying highly accurate time to and planets. The smoothly varying part of the change synchronize complex systems) are used together with in the earthʹs orientation (precession) is already map data and other information ( or traffic accounted for in GMST. The right ascension data, for instance) in modern navigation systems [16]. component of nutation is called the ʺequation of the equinoxesʺ [5]. We need a broad range of smart, low‐cost, high‐ performance GPS/GNSS timing clock and test products for next generation navigational systems. It GAST = GMST + (equation of the ) should be well suited for some of the following applications: LMST (Local Mean Sidereal Time) ‐ Local Mean  GPS/GNSS timing for mobile locations, Sidereal time is GMST plus the observerʹs longitude  navigational timing measurement & analysis measured positive to the East of Greenwich. This is instruments, the time commonly displayed on an observatoryʹs  ground pseudo GPS timing systems, sidereal clock. LMST = GMST + (observerʹs East  guidance & telemetry reference clocks, longitude)  radar & sensor timing systems,  submarine navigational timing systems,

216  high‐performance clock stability analysers. A number of countries are actively reconsidering their dependence on GNSS across multiple critical infrastructure applications and some are planning the 7.4 Enhanced Loran as a National Time Standard implementation of eLoran networks. Within this context falls the question of how to deliver Enhanced Loran eLoran is an internationally their national time service to those clients who have standardized positioning, navigation, and timing come to recognize their own vulnerability to the (PNT) service for use by many modes of disruption of GNSS. The paper [4] discusses the and in other applications. It is the latest in the long‐ concept of delivering such national time services by standing and proven series of low‐frequency, Long‐ means of eLoran signals. It was proposed the use of Range Navigation (Loran) systems, one that takes full eLoran to disseminate precise time, timing and phase advantage of 21st century technology [3]. traceable to UTC for both indoor and outdoor applications. Continuous accuracies of better than 100 eLoran meets the accuracy, availability, integrity, ns with respect to UTC are being achieved in current stability and continuity performance requirements for proof‐of‐concept and technology‐readiness trials. The aviation non‐precision instrument approaches, paper [4] proposes and illustrates a method of maritime port and harbour entrance and approach establishing national time standard services using manoeuvres, land‐mobile vehicle navigation, and eLoran. These would be traceable to sovereign location‐based services, and is a precise source of time national UTC. They would be of great benefit to a and frequency for applications such as wide range of users, notably telecommunications telecommunications. It is an independent, dissimilar, providers and financial sector organisations for whom complement to Global Navigation Satellite Systems. It precise time synchronisation will be required by allows GNSS users to retain the safety, security, and future services. These organisations are also becoming economic benefits of GNSS, even when their satellite concerned about their dependence on GNSS timing, services are disrupted. given its vulnerability to jamming and interference What is important, eLoran meets a set of and the complexity and expense of deploying it, worldwide standards and operates wholly especially when required indoors. independently of GPS, Glonass, Galileo, BeiDou or The paper [4] explores the ability of eLoran to any future GNSS. Each user’s eLoran receiver will be distribute UTC traceable time to applications in operable in all regions where an eLoran service is GNSS‐denied environments, including indoors. It sets provided. eLoran receivers work automatically, with the foundation for further research into the minimal user input. eLoran transmissions are application and dissemination of UTC using eLoran synchronized to an identifiable, publicly‐certified, signals in geographical regions where they are source of Co‐ordinated Universal Time (UTC) by a available. Research into this topic has been conducted method wholly independent of GNSS. This allows the by Chronos Technology in collaboration with eLoran Service Provider to operate on a time scale UrsaNav [3]. This has shown that UTC‐traceable time that is synchronized with, but operates independently of an accuracy better than 100 ns and with a quality of, GNSS time scales. Synchronizing to a common comparable to that provided by GPS can be received time source will also allow receivers to employ a even indoors at ranges of more than 800 km (500 mixture of eLoran and satellite signals [4]. miles) from eLoran transmitting stations. This new The principal difference between eLoran and time service meets the latest ITU performance traditional Loran‐C is the addition of a data channel standards in respect of telecommunications phase on the transmitted signal [3]. This conveys stability. application‐specific corrections, warnings, and signal 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 8 THE BENEFITS AND RISKS OF USING non‐precision instrument approaches and bringing TELECOMMUNICATION SIGNALS IN ships safely into harbour in low‐visibility conditions. NAVIGATION SYSTEMS eLoran is also capable of providing the exceedingly precise time and frequency references needed by the Until advances in the late twentieth century, telecommunications systems that carry voice and navigation depended on the ability to measure communications. latitude and longitude. Latitude can be determined Each that contributes to Universal through ; the measurement of Coordinated Time (UTC) operates a national time longitude requires accurate knowledge of time. This standard that is independent of GNSS. Its technology need was a major motivation for the development of will generally be based on a Hydrogen . This accurate mechanical clocks, including marine will be adjusted using monthly corrections supplied chronometers. While satellite navigation systems such by the BIPM in [4]. as the Global Positioning System (GPS) require unprecedentedly accurate knowledge of time, this is Low‐frequency eLoran is now emerging as the supplied by equipment on the satellites; vessels no preferred advanced source of positioning, navigation longer need timekeeping equipment. and timing (PNT) signals alternative or complementary to global navigation satellite systems The basic requirement for proper operation of the (GNSS). eLoran is globally‐standardized and does not GPS system is to maintain a uniform time scale within share the vulnerability of GNSS to incidental or it, and this property is used for telecommunications. deliberate jamming, intentional spoofing, radio‐ Most stationary GPS receivers have the ability to frequency interference or weather events.

217 output a one‐second signal (1 pps) closely related to the use of lower class quartz or rubidium generators the GPS time scale. and thus lower their price. The benefits of using GPS and in the future Galileo In telecommunications applications, the difference (possibly also Glonass) are significant. ‐ between the UTC time scale and the GPS time scale is produced non‐military GPS receivers are cheap, omitted. So using the GPS signals allows you to play which is conducive to a wide range of GPS all the quality nodes with the UTC time scale in all capabilities [14]. nodes of the telecommunications network, which is an undoubted advantage of the solution. The GPS signals allow you to reproduce with exactly disadvantages of the solution include the dependence equal accuracy the unambiguously expressed seconds of the correct operation of the operator network from pulses representing the GPS time scale in almost the the access to GPS signals, which the operator has no entire globe. A one‐second signal can be used as a influence. reference and as a reference frequency signal. Precise time signal can be the basis of effective and common encryption methods, including in areas such Standard time signals are used to maintain as finance, banking, insurance, electronic document accurate time uniformity in different areas of the certification, etc. economy, such as [14]:  telecommunications (charging, identification of Telecommunication providers should ask: what places of failure), would happen to existing networks if GPS were no  telematics, ITS, ICT (data flow control), longer available? This discussion has shown that  power engineering (charging, synchronization of Loran can provide telecommunication providers with power generators), a redundant synchronization source to GPS that  banking (transaction date, time stamps), satisfies some technical requirements. Legacy Loran  state administration (documentation of events ‐ has historically demonstrated the ability to easily police, rescue services, customs), meet the frequency performance requirements of a  transport (trains, buses, ships, aircraft), PRS in a wired telephone network and the basic  road transport (tolls, tolls, synchronized traffic requirements of the wireless CDMA (Code Division ). Multiple Access) network. eLoran adds the timing capabilities that allow it to better meet the time 1 pps signal is used as the reference frequency synchronization requirements of CDMA and to signal mainly for synchronizing telecommunication potentially support future networks with sub‐ networks and to stabilize radio frequencies where the microsecond synchronization requirements. With its needs exceed the standard level. Use of GPS signals large coverage area and its of performance, can be done in two ways. eLoran can provide telecommunications providers In the first, passive, 1 pps signal acts as a reference with the synchronization redundancy they need to frequency when measuring the clock frequencies keep their networks fully operational in the absence produced by telecommunication clocks and possibly of GPS. initiating alerts in case of anomaly. In the second mode, the active 1 pps signal is used to generate clock signals in telecommunication devices controlled automatically and corrected based on GPS signals. In 9 CONCLUSIONS this case, mediation of the quartz or rubidium generator affected by the digital phase loop is There are a of time definitions. Time is the required. indefinite continued progress of existence and events that occur in apparently irreversible succession from In the first solution the use of a GPS signal allows the past through the present to the future. Time is a the placement of two instead of three cesium clocks in component quantity of various measurements used to that clock, which at a substantial price and for several sequence events, to compare the duration of events or years only implies the importance of the pattern. the intervals between them, and to quantify rates of Economic benefits. Despite the reduction in the change of quantities in material reality or in the number of cesium patterns, it will be possible to conscious experience. Time is often referred to as the indicate which of the two cesium patterns have been fourth dimension, along with the three spatial damaged or that the GPS receiver has been damaged dimensions [7],[10],[17]. (disassembled). In addition, with the use of uncomplicated measuring instruments, data can be In this paper, the Author presents the ability of obtained for manual correction of the frequency of using eLoran as a national time standard and particular cesium standards to approximate the proposes further research to assess spatial and coherence requirements of clock signals with UTC temporal variations in the reception of UTC traceable time scale. time distributed by using eLoran. It proposes this new means of disseminating national sovereign UTC for The second solution applies to automatically use at times and in places where GNSS is denied. It controlling and correcting frequencies in lower clock will serve critical infrastructure applications, notably hierarchically. These are SSU clocks for transit and telecommunications networks and financial services, local nodes (a solution especially used on the in which sub‐microsecond UTC‐traceable time is American continent), and even digital or cellular base essential to the continuity of operations. In particular stations. Some operators under normal operating it will serve these applications without the need for conditions do not use GPS signals, but this capability expensive roof mounted GNSS antenna deployments is used in emergency situations. Generally this allows or managing complex fibre connectivity.

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