Time, its scales and part in satellite navigation systems. Czas, jego skale i udział w Nawigacyjnych Systemach Satelitarnych


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1 Scientific Journals Maritime University of Szczecin Zeszyty Naukowe Akademia Morska w Szczecinie 2010, 20(92) pp , 20(92) s Time, its scales and part in satellite navigation systems Czas, jego skale i udział w Nawigacyjnych Systemach Satelitarnych Jacek Januszewski Gdynia Maritime University, Faculty of Navigation, Ship Operation Department Akademia Morska w Gdyni, Wydział Nawigacyjny, Katedra Nawigacji Gdynia, al. Jana Pawła II 3, Key words: timescales, time dilution of coefficient (TDOP), timesystems Abstract There are different scales related to time; actually two the most important timescales are the TAI (Time Atomic International) and the UTC (Universal Time Coordinated). In addition to these times Satellite Navigation Systems (SNS) have developed their own system time: GPS Time (GPST), the GLONASS System Time (GLONASSST) and the Galileo System Time (GST). The sources, the generation and the relation between all these times and timescales are described in this paper. Additionally the time dilution of precision (TDOP) coefficient and the data concerning the time transmitted in navigation messages by satellites of different SNS will be presented. Słowa kluczowe: skale czasu, współczynnik dokładności pozycji użytkownika (TDOP), systemy czasu Abstrakt Z czasem związane są różne skale, ale dwie najważniejsze z nich to TAI (Międzynarodowa Skala Atomowa) i UTC (Czas Uniwersalny Skoordynowany). Nawigacyjne Systemy Satelitarne (NSS) stworzyły jednak własne skale czasu: GPST czas systemu GPS, GLONASSST czas systemu GLONASS i GST czas systemu Galileo. W artykule omówiono źródła, pochodzenie i relacje zachodzące między wszystkimi ww. czasami i skalami. Dodatkowo opisano współczynnik dokładności pozycji użytkownika TDOP oraz te parametry dotyczące czasu, które są przekazywane w depeszach nawigacyjnych satelitów poszczególnych systemów. Introduction Time is a component of the measuring system (e.g. satellite navigation system) used to sequence events, to compare the events and the intervals between them (e.g. time of signal propagation between satellite and terrestrial receiver), and to quantify the motions of objects. The use of atomic properties for time measurements was born in 1955 when the first cesium beam frequency standard began regular operation in the United Kingdom [1]. As nowadays the satellite position fix is based on pseudorange measurements (apparent transit time of the signal from a satellite to the receiver), the knowledge of all used universal and atomic time scales and the relation between them is very important for all users of Satellite Navigation Systems (SNS). This transit time is defined as the difference between signal reception time, as determined by the receiver clock, and the transmission time at the satellite, as market on the signal. SNS is also a timing system, that is, it can be used for time synchronization. Universal and Atomic Time scales Two basic groups of time scales are of importance in satellite navigation systems: Universal Time, connected with the diurnal rotation of Earth. The timedependent orientation of Earth with respect to the inertial space is required in order to relate the Earthbased observations to a spacefixed reference frame. UT is a modern continuation of Greenwich Mean Time (GMT); 52 Scientific Journals 20(92)
2 Time, its scales and part in satellite navigation systems Atomic Time, related to phenomena in nuclear physics. The precise measurement of signal travel times, e.g. pseudorange in satellite navigation systems, requires a uniform and easily accessible time scale with high resolution. The third basic groups of time scales, Ephemeris (Terrestrial) Time, important in satellite geodesy, in particular, is derived from the orbital motion of celestial bodies around the Sun. All these time scales are based on the observation of uniform and repetitive astronomical or physical phenomena. Universal Time (UT) family Before the acceptance of atomic scales astronomical time scales were used for everyday timekeeping. Although astronomical times are no longer the best measure of time, they continue to play a role in current research. These time scales are still used today, but mostly for applications related to astronomy. UT is witness to the Earth s rotation, whilst serving also to establish Coordinated Universal Time (UTC). They are based on mean solar time. The mean solar second provides the basis for Universal Time (UT). We can distinct three principal variations of UT [2, 3]: UT0, the original mean solar time scale, based on the rotation of the Earth on its axis; UT1, the principal form of UT, the most widely used astronomical time scale, it is an improved version of UT0 with corrections added for polar motion. UT1 is the same everywhere on Earth. The correction from UT0 to UT1 is at most about s. The current version of UT1 (since 2003, namely sometimes UT1R) is exactly what is needed for geophysical investigations. It permits evaluation of the length of the day with a precision that revels changes due to storm systems and changes in ocean currents. UT1 drifts with respect to atomic time. This is on the order of several milliseconds per day and can accumulate to 1 second in a 1 year period; UT2, a smoothed version of UT1 by adding an empirical formula to remove the effect of the annual seasonal variations in the rotation of the Earth. It is mostly of historic interest and rarely used anymore. Atomic Time family Atomic time scales are derived from groups of commercial and laboratory cesium standards which generate time intervals, based on the definition of the International System of Units (SI). The definition of the second atomic time scale, related to Cesium 133 atom, has been worked by the 13 th Conference of the International Committee of Weights and Measures BIPM (Bureau International des Poids et Mesures) in Paris, We can put the question why in this definition the number of the periods of the radiation is equal 9,192,631,770? Because it corresponded exactly with the previous definition of the second, the ephemeris second. In practice, atomic time scale are derived from groups of commercial and laboratory cesium standards which generate time intervals, based on the definition of the SI second. The time scale based on atomic standards is called International Atomic Time (TAI). TAI is a uniform time scale based on the atomic second, which is defined as the fundamental unit of time in the International System of Units. TAI is the continuation of time scales which began with the first cesium atomic clock in 1955 which is not tied to the earth s rotation on its axis or its revolution around the Sun. TAI is computed as the weighted mean of individual clocks. Therefore TAI is a statistically formed common time scale for international use. TAI is referred to as a paper time scale since it is not kept by a physical clock. The value all existing atomic time scales was equal to that of UT2 on January 1, 1958, but that date was before highprecision international coordination of time had begun. The name TAI was officially proposed in 1970 and adopted in Due to the deceleration of Earth s rotation the difference between TAI and UT scales is increasing. The difference between TAI and UT1, for some selected dates, is presented in the table 1. We must say that large size of these differences stems from the fact that the unit of the SI second was adopted from the length of the ephemeris second. The latter was derived from the mean duration of the solar day between 1756 and 1895, when Earth s rotation was faster than today [4]. Nowadays there are two different time scales and two seconds definitions, universal and atomic, while one time scale is required only. This new scale must provide both a highly uniform time unit and the best possible adaptation to UT1, and hence to Earth rotation. Table 1. The difference TAI UT1 for selected dates [4] Tabela 1. Różnica między TAI i UT1 w wybranych dniach [4] Difference [s] Date +6.1 January 1, January 1, January 1, January 1, January 1, January 1, 2003 Zeszyty Naukowe 20(92) 53
3 Jacek Januszewski That s why, in January 1, 1972, a compromise time scale, Universal Time Coordinated (UTC), was introduced. UTC has been run according to the guidelines in Recommendation ITU R TF of the International Telecommunication Union (ITU) [1]. The definition of the UTC second is the same as that for atomic time, and is based on the cesium atom. UTC is now the scale for public time throughout the world. We can say that this is the new GMT. The acronym UTC is an EnglishFrench mixture for Coordinated Universal Time (CUT) in English or Temps Universal Coordonne (TUC) in French. It was internationally agreed to write Universal Coordinated Time as UTC, rather than CUT or TUC, making it language independent. UTC was set to agree with UT1 at 00 hours on January 1, At first the two time scales were kept close by introducing 0.1 second steps in UTC, as needed. Since 1972, changes in the Earth s spin rate have been accommodated by introducing leap second (p. 1.3) in UTC. This time is thus obtained by periodically adding or subtracting one second from TAI in order to build up a reference time that follows the Earth s rotation. That s why nowadays UTC and TAI differ by an integer number n of seconds: UTC = TAI n (1 s) (1) On 1 January 1972, TAI UTC was equal to 10 s. At the time of this writing (February 2010) the difference between TAI and UTC was: TAI UTC = +34 s (2) UTC is generated after the fact on the basis of the times kept by about 250 cesium clocks and hydrogen masers located at about 65 different laboratories located around the world. In the United States, UTC estimates are generated by the National Institute of Standards & Technology (NIST), Boulder, Colorado, and the United States Naval Observatory (USNO), Washington, D.C. Both institutions are charged with supplying time and frequency to the U.S. government and BIPM. Their UTC estimates are referred as UTC (USNO) and UTC (NIST). Other countries have similar institutional arrangement to their national time standards, which serve as the basis for realtime estimates of UTC. It takes BIPM about a month to collect and process the data to generate TAI and UTC. A monthly bulletin from BIPM reports the time difference that existed between each of the contributing clocks and UTC [5]. Differences between TAI and UTC since 1 January, 1972 (from the beginning of UTC) to the time of this writing is given in the table 2. Table 2. Difference Δt between TAI and UTC in years (in seconds) Tabela 2. Różnica Δt między TAI a UTC w latach (w sekundach) From to Δt From to Δt The USNO determines and distributes the timing and astronomical data required for accurate navigation and fundamental astronomy, and maintains a UTC time scale that is (by mutual agreement) within 100 ns of UTC(NIST) [3, 5]. In different countries around the world, local time is attached to UTC corrected by a whole number of hours. This is sometimes stipulated by written law (e.g. in France). Legal institutions sometimes prefer to use the national approximation to UTC, e.g. in Germany. There are countries where UTC is not legally recognised, although it is actually used, since no other time scale is readily available [1]. The still widespread use of the acronym GMT is not correct when it is intended to refer to UTC, as it is the case when expressing the time in general usage. After steering corrections, TAI is known from the values of TAI UTC(k) at standard dates. Each laboratory k has a master clock which supplies an approximation UTC(k) to UTC. This clock serves as a reference for all local dating procedures. BIPM publishes the values of UTC UTC(k) every month in its Circular T, available by electronic mail. Apart from this, by tracking GPS and GLONASS satellites for time comparisons, values of UTC GPS time and UTC GLONASS time are provided with similar uncertainties to those in UTC UTC(k). Time signal emissions conform as closely as possible to UTC. An ITU recommendation fixes a tolerance of 1 ms. In reality, the discrepancy is much smaller than this. It is also recommended 54 Scientific Journals 20(92)
4 Time, its scales and part in satellite navigation systems that the carrier frequency be tuned to the TAI frequency, with relative frequency offset less than [1]. Leap seconds A leap second is a second added to UTC time scale to keep the difference between UT1 and UTC to within ± 0.9 second. The introduction of one positive or negative leap second must be made at the end of a UTC month, preferably at the end of December or June, otherwise at the end of March or September. The first leap second was inserted on June 30 th, Since then, they have occurred at an average rate of less than one per year. All 24 leap seconds were positive, 9 were inserted on June 30 th, 15 on December 31 st. In February 2010 the 5 last leap seconds were added on December 31 st, 1995, June 30 th, 1997, December 31 st, 1998, December 31 st, 2005 and December 31 st, Dates for leap seconds are fixed by the International Earth Rotation Service (IERS) and announced at least 8 weeks beforehand. The announcement appears in IERS s Bulletin C. This bulletin is updated every six months, either to announce a time steep in UTC, or to confirm that there will be no time step at the next possible date. The probability that negative leap second will be needed is almost zero. Leap seconds are primarily for the benefit of astronomers: they keep UTC synchronized with the orbits of the stars and planets. If there were no leap seconds, then in about years from now, the sun would seem to be rising an hour late [6]. Information about the leap seconds can be found at the U.S. Naval Observatory Web site, usno.navy.mil. The current value of UT1 UTC is called the DUT1 correction (DUT1 = ± N 0.1 seconds, where N is a digit between 1 and 8) and is obtained from Time Section of the BIPM. The resolution of the DUT1 correction is 0.1 s, and represents an average value for an extended range of dates. Values of DUT1 and their application date are provided one month beforehand by the IERS and they are the same for all emissions. DUT1 corrections are broadcast among other things by the stations of NIST, as WWV, WWVH, and WWVB. The corrections values of DUT1 at 0000UTC of the selected days can be found in the vol. 2 of ALRS [7], e.g. on Mars 15, 2007 DUT1 was 0.1 s, on June 14, 2007 it was 0.2 s. The knowledge of these corrections allows the user to correct the value of disseminated UTC. Satellite navigation systems time scales While most clocks in the world are synchronized to UTC, the atomic clocks on the satellites are set to own SNS time. GPS System Time (GPST) GPS uses its own particular, continuous time scale GPS System Time (GPST). It differs from UTC by a nearly integer number of seconds: GPS time UTC = n s C t (3) where: n is an integer number, and the correction term C t is in the order of several nanoseconds. GPS system is not corrected to match the rotation of the Earth, so it does not contain leap seconds or other corrections which are periodically added to UTC. GPST is specified to be maintained to within one microsecond modulo integral seconds, and for the past ten years it has been maintained to within ( 25 ns) of this goal [8]. GPST is steered to UTC(USNO) on a daily basis. Over last several years GPST was kept within a few tens of ns from UTC(USNO) and TAI (modulo 1 second) [9]. GPST and UTC(USNO) were coincident at 0 h January 6, As at this moment the difference between TAI and UTC was 19 seconds, GPST remains at a constant offset with TAI: TAI GPS time = 19 seconds (4) At the time of this writing (February 2010) the difference between GPST and UTC was 15 seconds. Therefore the reception of GPS signals provides realtime access to TAI and UTC with uncertainties below 1 microsecond [4]. The GPST is also a paper time scale; it is based on statistically processed readings from the atomic clocks in the satellites and at various ground control segment components. This time, defined by the Control Segment, is generated from all the atomic clocks of the system, including those in the satellites. The GPS satellites have rubidium (Rb) and cesium (Cs) atomic clocks onboard (today s satellites block IIa have 2 Cs + 2 Rb, blocks IIR and IIR M have 3 Rb). These are kept within a millisecond of the master clocks at the GPS master control station. The largest unit used in stating GPS time is one week, defined as seconds where seconds is at Saturday / Sunday midnight GPS Time. Each week at this time, the week number increments by one, and the seconds into week resets to 0. Zeszyty Naukowe 20(92) 55
5 Jacek Januszewski Therefore as opposed to the year, month, and day format of the Gregorian calendar, the GPS date is expressed as a week number (WN) and a day of week number. The WN is transmitted as a tenbit field in the C/A and P(Y) navigation messages, and so it becomes zero again every 1024 weeks (2 10 = 1024). GPS week zero started at 00:00:00 UTC (00:00:19 TAI) on January 6, 1980, and WN became zero again for the first time at 23:59:47 UTC on August 21, 1999 (00:00:19 TAI on August 22, 1999). At this moment the difference between TAI and UTC was 32 seconds. The number of days passed since August 21, 1999, divided by 7 gives the WN, e.g. week 512 is from 15th to 21st June. In navigation message the data concerning time are transmitted in the first two and the last two subframes. Ephemeris parameters in subframe 1 contain estimated group delay differential (eightbit information about clock correction term) and four additional satellite clock correction parameters. Ephemeris parameters in subframe 2 contain reference time ephemeris. The almanac data provided in subframes 4 and 5 contain data time also, reference time almanac (time of applicability) and two satellite clock correction parameters. The 8 parameters providing the translation of GPST to UTC time are in page 18 of subframe 4 [10]. All these parameters time permit to calculate the GPST of transmission from the satellite, which will be used for calculation of its position and time of signal propagation from satellite to the user. The problem of keeping precise time and synchronizing clocks that are separated by considerable distances is an old one. The Transit, the first SNS, as terrestrial radionavigation systems (e.g. Loran C) were capable of time transfer with an accuracy level of about 1 milisecond. With the current techniques, GPS can distribute time with an accuracy of about 30 ns, and can compare remote clocks with an accuracy of about 5 ns [5]. GLONASS System Time (GLONASSST) GLONASS time, base on an atomic time scale similar to GPS, is strongly liked to the National time scale of Russian Federation UTC(SU) which is maintained by the Main Metrological Center of the Russian Time and Frequency service at Mendeleevo in the Moscow region. On other hand GLONASS system itself is the most powerful and accurate mean of UTC(SU) dissemination through out Russia and the world. That s why one of requirements of GLONASS updates is to keep UTC UTC(SU) difference within 10 ns [11]. Unlike the GPS time scale, GLONASS system time currently implements leap seconds, like UTC, and it has a constant offset of three hours (difference Moscow time to Greenwich time). This time is generated and controlled by the GLONASS Central Synchronizer, based on a set of hydrogen masers. The relation between UTC and GLONASSSTS is: UTC = GLONASS time + τ c 3 h (5) The discrepancy, τ c, comes from the different clock ensembles used and is communicated to the GLONASS users in frame 5 of the GLONASS navigation message [4]. GLONASS time is maintained within 1 ms, and typically better than 1 microsecond (μs) of UTC(SU) by the control segment with the remaining portion of the offset broadcast in the navigation message [12]. All GLONASS satellites use cesium atomic clocks. In navigation message the data concerning time are transmitted in the immediate data which include time marks and synchronization difference between satellite clock and GLONASS time, and in the nonimmediate data which include raw clock corrections to the GLONASS time and the GLONASS time correction relative to UTC(SU). Galileo System Time (GST) Galileo System Time (GST), modulo 1 second, is planned to be steered to a prediction taken from a number of UTC laboratories obtained through an external Galileo time service provider. GST is specified to be kept to within 50 ns (95%) of TAI over any 1 year time interval. The offset between TAI and GST will be known with a maximum uncertainty of 28% (2 sigma), assuming the estimation of TAI six weeks in advance. Users equipped with a Galileo timing receiver will be able to predict UTC to 30 ns for 95% of any 24 hours operation [13]. The GST is produced only with terrestrial clocks available in the two redundant Precise Time Facilities (PTF) of Galileo. PTF will host an active H maser (with necessary hotspares) and an ensemble of Cesium clocks, and steer the maser output to TAI. This steered time scale will serve as a physical representation of GST. Galileo will use a continuous reference time, like GPS. The first test Galileo satellite GIOVE A has on board rubidium atomic clock, the second satellite GIOVE B operates on hydrogen maser atomic clock, for the first time in history. The GST is optimized in order to achieve a very good shortterm stability required for the functions 56 Scientific Journals 20(92)
6 Time, its scales and part in satellite navigation systems associated with navigation. The use of satellite clocks, as in GPST, has two important aspects: the internal satellite clock s frequency drift and the inherent measurement error associated with satellite clocks. Both aspects would have had the effect of decreasing GST accuracy. Therefore, for meteorological aspects, comparisons with clocks external to Galileo will be used [14]. In Galileo navigation message the data concerning time are transmitted in each subframe, clock correction and GST status in the page 1, GST in the pages 2 and 3, GST UTC conversion, GST GPS conversion and Time of Week (TOW) in the page 4. Translation of SNS time to UTC/TAI UTC is obtained from GPS receiver, and in the future from Galileo receiver, by adding the integral number of leap seconds and fine UTC / TAI correction information contained in the navigation data. In order to provide an estimate of UTC from GPS, the navigation message broadcast by each GPS satellite includes estimates of the time difference between GPST and UTC(USNO) modulo one second, and its rate. The navigation message also includes the wholesecond difference between the two time scales due to leap seconds. These parameters allow a receiver clock to calculate an accurate estimate UTC(USNO). We know the time kept by a user s receiver clock, t u, and we want to generate UTC, t UTC. The latter can be defined from the following equation: t UTC = t u Δt u Δt UTC (6) where: Δt u is the receiver clock bias relative to GPST, and Δt UTC is the bias between GPST, t GPS, and UTC(USNO), t UTC. A GPS navigation receiver computes Δt u in order to schedule measurements, to time tag position estimates, and to timealign the measurements for precise relative positioning. The bias Δt UTC is equal: Δt UTC = t GPS t UTC (7) The USNO monitors Δt UTC and provides this information to the Control Segment. Its value can be computed at any instant (defined in GPST) from: Δt UTC = A 0 + A 1 (t GPS t 0U ) + Δt LS (8) where: A 0 and A 1 are constant and first order terms of polynomial, t 0U is reference time for UTC data, and Δt LS is the number of leap seconds added to UTC since 1980 (15 seconds as of 1 January 2009). The values of all these four parameters (A 0, A 1, t 0U and Δt LS ) are broadcast by each GPS satellite in its navigation message (page 18 of subframe 4). The time t GPS is equal: t GPS = t S Δt S (9) where t S is the time kept by a satellite clock, and Δt S is the satellite clock offset defined by: Δt S = α f0 + α f1 (t t 0c ) + α f2 (t t 0c ) 2 + Δt r (10) where: t 0c is the reference epoch, α f0 is the clock offset, α f1 is the fractional frequency offset, and α f2 is the fractional frequency drift. All these four parameters are broadcast by each GPS satellite in its navigation message (subframe 10), Δt r is the relativistic term calculated from other data. The rms error in estimation of Δt S and Δt UTC is currently estimated to be about respectively, 5 and 10 ns. As navigation receiver can estimate the receiver clock bias with a rms error of about 25 ns, the total error in direct time distribution from GPS is about 25 ns. Telecommunications applications typically require synchronization of multiple nodes with an accuracy of 100 ns, or better. Such synchronization can be achieved by setting up a GPS antenna at a fixed, surveyed location at each node, and determining time independently. With antenna position known, a GPS receiver can determine precise time by tracking one satellite only [5]. Time Dilution of Precision (TDOP) coefficient Dilution of Precision (DOP) terms represent the impact of the geometric scattering of the satellites, with respect to the receiver s position, on the position error, and hence on the accuracy of the positioning. There is a linear relation between DOP values and the resulting position accuracy for a given pseudorange error value σ UERE. We can distinct five DOP coefficients in common use which are useful to characterize the accuracy of various components of the position / time solution. One of these coefficients is TDOP (Time DOP) which value is defined by the quotient of the square root of the element of the covariance matrix and the speed of the radio wave. In some treatments, DOP is equal to the mentioned above square root only. In this case the variable c t b represents a range equivalent of the time bias error and σ ctb defined by the product TDOP σ UERE is its standard deviation [5, 8]. Zeszyty Naukowe 20(92) 57
7 Jacek Januszewski From among all DOP coefficients which depends on user s latitude, the least value has TDOP at equator. For a nominal GPS constellation (24 satellites fully operational), if all satellites are in view, TDOP coefficient can be less than 0.8 [15]. Satellite navigation system receivers time Satellite navigation systems receivers display the time in 12 hour or 24 hour notation, and the default setting is 24 hour notation. AM or PM is shown when 12 hour notation is selected. The time and date are in UTC or in Local Time (LT). The first time signalized by the receiver is UTC, but this receiver can also display LT. That s why the hour and minute, unlike second, can be changed by the user by entering a time difference from UTC. Some SNS receivers can show the time depending on season of the year, as summer time or winter time. Time synchronization related errors As any pseudo range error leads to user s position error we can also take into account synchronization errors. The problem of synchronization has to be clearly distinguished from those of precision or stability. Synchronization is related to the fact that all the SNS components deal with a common timescale. This is of primary importance when carrying out time measurements in the GNSS fields. We must remember the fact that 1 ns is equivalent to 30 cm. The synchronization of satellites clocks to GPS time is obtained from the navigation message. The problem of receiver synchronization must be carried out on a frequent time base [14]. Interoperability Interoperability of satellite navigation systems, as GPS, GLONASS and Galileo, and satellite based augmentation systems, as EGNOS and WASS can be defined as ability of each of these systems having independent control loop to operate jointly with other systems without interfering each other on condition that signal frequency ranges, coordinate reference frames and time reference frame coincide as much possible. Both GPST and GST are real time versions of the various UTC(k) laboratories they reflect. If the offset between these times is made available to user, interoperability is ensured. The GPS Galileo time offset will be easily determined or received by the user receiver. The U.S. and EU have agreed to have their satellites broadcast the GPS Galileo time offset in the future. The accuracy of this time offset modulo 1 second is specified to be less than 5 ns with 2sigma confidence interval over any 24 hour period. Once Galileo is operational (2015 or later), it is anticipated by many that most users will use a combined GPS and Galileo PNT (positioning, navigation, timing) service. There are two options for obtaining the GPS Galileo time offset [13]: the user is able to determine this offset in the position and navigation processing at the cost of one additional satellite tracked (fifth satellite when determining a three dimensional position); the offset could be measured by transitional time transfer techniques (e.g. two way, common way) or precisely estimated in near real time at the monitor station of both systems using a integrated GPS / Galileo receiver. Nowadays the difference between GPS time and GLONASS time is known with accuracy 30 ns, in the future 2 6 ns [7, 16]. When using GPS and GLONASS systems jointly, the difference in system time depends on the clocks from both systems and has to be taken into account. GPS Galileo Time Offset GPS Time and GST will be generated independently from each other. The residual offset between GST and GPS Time will be probably in the order of tens of nanoseconds. This GPS Galileo time offset (GGTO) will cause a bias between GPS and Galileo measurements taken by integrated receivers of these two systems. This will lead to an additional error in the user s navigation solution. A similar effect will appear when users correct pseudorange measurements to UTC using the broadcast offsets between GPS and Galileo reference time scales and UTC. At user level, GGTO can be estimated from GPS and Galileo measurements as an additional unknown in the user navigation solution. This would increase the dimension of the estimation problem, requiring at least five, and no four, measurements (pseudoranges) to be available to calculate user 3D position, time offset, and GGTO. At system level, GGTO can be determined by the GPS and Galileo ground segments, then predicted for the near future, and finally broadcast in the navigation messages to all users. Therefore the users can correct their observations with the received GGTO value and proceed with the classical navigation solution with four parameters; i.e. 3D position and time offset [9]. 58 Scientific Journals 20(92)
8 Time, its scales and part in satellite navigation systems Conclusions All time systems of GPS, GLONASS, and Galileo are based on UTC, but using individual realizations of UTC. Spending one satellite s observations enables a SNS receiver itself to solve for the time offset between two different satellite systems; typically the internal navigation system time (e.g. GPST, GLONASS System Time) is only used as a part of the navigation solution and is not considered as standard time product; with the current techniques, GPS system can distribute time with an accuracy of about 30 ns, and can compare remote clocks with an accuracy of about 5 ns; the GPS time is a paper time scale (computations performed at the Master Control Station), while Galileo System time is physically produced at Galileo Precise Timing Facility (PTF); the tendency is that most of modern navigation professional GPS equipment uses GPS time as the time base. Therefore, the translation from GPS time to UTC time may no longer be needed in modern receiver; GPS Galileo time offset (GGTO) can be determined at user level in the user receivers (at least five measurements are required) and at system level by GPS and Galileo systems and broadcast in the navigation message of both systems. Reference 1. AUDIN C., GUINOT B.: The Measurements of TimeTime, Frequency and the Atomic Clock, Cambridge University Press, Cambridge SEEBER G.: Satellite Geodesy, de Gruyter, Berlin / New York MISRA P., ENGE P.: Global Positioning System Signals, Measurements, and Performances, Ganga Jamuna Press, Lincoln VAN DIGGELEN F.: A GPS: Assisted GPS, GNSS, and SBAS, Artech House, Boston / London Admiralty List of Radio Signals. The United Kingdom Hydrographic Office, 2009, 10, vol KAPLAN E.D., HEGARTY C.J.: Understanding GPS Principles and Applications, Artech House, Boston / London MOUDRAK A. et al.: Interoperability on Time GPS Galileo Offset Will Bias Position, GPS World, 2005, Vol. 16, No BAOYEN TSUI J.: Fundamentals of Global Positioning System Receivers, John Wiley & Son Inc. New Jersey HAHN J., POWERS E.: GPS and Galileo Timing Operability, Global Navigation Satellite System Conference, Rotterdam SAMANA N.: Global Positioning, Technologies and Performance, John Wiley & Son Inc. New Jersey GROVES P.D.: Principles of GNSS, Inertial, and Multisensor integrated navigation systems, Artech House, Boston / London HEIN G.W. et al.: Envisioning a Future GNSS System of Systems, Part 2 Inside GNSS, 2007, Vol. 2, No. 2. Zeszyty Naukowe 20(92) 59
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