Time transfer through GPS

Transcription

1 Indian Journal of Radio & Space Physics Vol. 36, August 2007, pp Time transfer through GPS P Defraigne 1, P Banerjee 2 & W Lewandowski 3 1 Royal Observatory of Belgium, Ringlaan 3, B-1180 Brussels, Belgium 2 Time and Frequency Section, National Physical Laboratory, Dr K S Krishnan Road, New Delhi , India 3 Bureau International des Poids et Mesures, Pavillon de Breteuil, 92310, Sèvres, France Received 19 June 2007; accepted 17 July 2007 Commonly available GPS receivers have, these days, hardware outputs of 1 pps. These receivers normally have the time accuracy within 100 ns. But if these are not calibrated in advance, they cannot be recommended for precise on-line applications. However, common view mode GPS time transfer using single satellite is in use for the generation of Coordinated Universal Time (UTC) by ensembling more than 40 clocks scattered all over the world. Use of carrier phase in common view mode is being explored. The initial results are quite encouraging. The paper reviews the current status of these time transfer techniques via GPS. Keywords: Global positioning system (GPS), Coordinated universal time (UTC), International atomic time (TAI), Two-way satellite time and frequency transfer (TWSTFT) PACS No.: Wx; Ft 1 Introduction Global Positioning System (GPS) has been launched for precise positioning and navigation purposes 1 for the military and civilian communities. But GPS has also proven itself to be important and valuable for time keeping purposes. It has proved to be a versatile global tool, which can be used to both distribute time to arbitrary number of users and synchronise clocks over large distances with a high degree of precision and accuracy. The introduction of GPS has led to a major improvement of world wide time metrology in precision, accuracy and coverage. For the timekeeping community, GPS today is a significant contributor to solve the traditional problems of timekeeping; it is a reliable source of time and it is a reliable time transfer system. Over the years, the clocks by which time has been kept, have become not only more precise but also more accurate and the timekeeping community has sought more precise and more stable systems to help them with synchronisation. Time metrology began to use GPS signals about 15 years ago at the National Bureau of Standards, NBS (now National Institute of Standards and Technology, NIST). A system using common-view observations of GPS satellites for accurate time and frequency transfer was suggested 2, and receivers especially designed for this purpose were built first at the NBS and then in several commercial companies. These were single-channel one-frequency C/A-code receivers capable of tracking only one satellite at a time. To operate them it was essential to issue periodic schedules of common-view observations. The common-view method was clever and far-reaching. It not only reduced some uncertainties of physical origin, but went on to cancel the deliberate degradation of GPS time introduced in 1990 under the name of Selective Availability (SA). The introduction of GPS brought about a significant improvement in time and frequency transfer. With uncertainties ranging from 10 ns to 20 ns for time comparisons during early stages of the use of GPS, it was possible, for the first time, to compare the best atomic standards in the world at their full level of performance using integration times of about 10 days. Since then a number of improvements have been introduced, including the use of ultra-accurate antenna coordinates, precise ephemerides and measurements of the ionosphere. These led at the beginning of 1990s to time comparison uncertainties of about 3 ns, which correspond to a few parts in in frequency transfer. This paralleled improvements in atomic standards, which advanced by an order of magnitude, and made possible the comparison of the

2 304 INDIAN J RADIO & SPACE PHYS, AUGUST 2007 new clocks, e.g., HP5071A Cesium Beam Frequency Standards, at their full level of performances for averaging times of several days. Timing may, normally, be achieved by receiving minimum four GPS satellites. But if the position coordinates of the location of the GPS antenna is known precisely a-priori, then by receiving only one satellite one may get precise time. Further, these efforts are being made to utilize carrier phase coupled with C/A code to improve the timing precision. This paper reviews the potentiality of these methods and their applicability. 2 On-line application Now-a-days, most of the common GPS receivers have the hardware output of 1 pps. These receivers may be used for on-line timing applications. For the reliable use of these receivers one must take two aspects into consideration, namely, the necessity of calibration and the effect of scintillation, particularly, during peak solar activity. 3 Need of calibration The constellation of GPS being more than completely full, the requirement of visibility of minimum four satellites is neither a limitation nor a disadvantage. Further, since 2 May 2000 the selective availability of GPS has been withdrawn. This has, thus, restored the accessibility of full potentiality of GPS accuracy for civilian users. In course of time, the GPS receiver technologies have seen rapid advancement leading to their miniaturization and reduction of the cost of manufacture. All these aspects, taken together, have encouraged extensive use of GPS for on-line timing application. Foreseeing the market potentiality of GPS receivers for timing purposes, different types of GPS timing receivers have evolved and consequently available in the market. Though there are umpteen companies who are manufacturing GPS receivers for normal timing application, with minor variation of their specifications, all of them may be broadly categorized into two groups. One group may be usual GPS geodetic receivers. A simple geodetic receiver not only shows position coordinates but also has the hardware output of 1 pps. The other type is a GPS disciplined quartz/rubidium clock. The performances of these receivers have hardly 3,4 been evaluated for on-line timing applications. It is well known that GPS time is synchronized to UTC (USNO), which is closely maintained to Coordinated Universal Time (UTC). This implies that this evaluation of GPS timing receiver can only be carried by the timing laboratory, whose clock is traceable to UTC. So the National Physical Laboratory (NPL), New Delhi, India, has recently conducted an exhaustive study to evaluate the performances of these receivers in a systematic way, so that the use of these receivers may be defined application wise. For GPS disciplined rubidium clock, the frequency accuracy improves substantially in the presence of GPS signal. It has been observed that performance in pseudo-lock condition is almost as good as that in locked condition. This implies that the system is quite reliable for one or two hours, even after the GPS signal is removed. Particularly, this characteristic may be quite useful in some typical strategic applications. The short term stability of the locked rubidium is slightly poorer than that of rubidium clock in free running condition. Perhaps, this may be attributed to the noise in received GPS signals. But the long term stability will be much better than that in free running mode, as the locked condition does not allow the frequency of the rubidium clock to drift away. So, the GPS disciplined rubidium clock may serve as reliable timing system, if it is calibrated prior to its use. It has also been noted that the time produced by many GPS receivers can vary over a range of a few hundreds of nanoseconds. So, in order to carry out the most accurate time transfer, it is essential that the factory-provided calibration be measured and improved upon. It may be pointed out that for a particular GPS receiver the time might have some bias-error, but it does not affect the frequency, the phase bias being observed to be largely constant. So the improvement of the frequency accuracy is independent of the prior calibration of the receiver. However, the performance of the system may be guaranteed only after evaluation or calibration. 4 Effect of scintillation Ionospheric scintillation is prominent in midlatitude to equatorial regions. In the Indian subcontinent, scintillations are quite frequent, intense and of longer duration during peak period of 11-year solar cycle. The effect of scintillations on GPS signals operating around 1.5 GHz has only recently received some attention. The effect of scintillation on the accuracy of GPS-positioning has

3 DEFRAIGNE et al.: TIME TRANSFER THROUGH GPS 305 recently been reported 5. The year 2001 was high solar activity year as the phase of 11-year solar cycles was passing through its peak. The dates of study were within one of the equinoxes in the postsunset hours when the occurrence of scintillation was highly probable. The presence of scintillation was found to deteriorate the accuracy of the time transfer quite substantially as shown in Fig.1. So during strong scintillation, GPS time may sometimes degrade beyond the expected limit. This deteriorating effect is beyond the control of the users. So, a serious attention should be given to tackle this issue. The GPS time is quite commonly used to compare two clocks remotely located. In such a case, GPS time is normally compared in a strictly common view mode 6. Most of the errors which are independent of the locations of the respective clock get eliminated or reduced in a common view mode. Thus, better accuracy may be achieved in this mode. However, the time of occurrence and the intensity of the scintillation vary unpredictably depending on the geographical location of the user s antenna. So this effect is not cancelled out even in common view mode. 5 Use of GPS for the construction of TAI The Bureau International des Poids et Mesures (BIPM), located in Sèvres near Paris, is on charge of computing and publishing international reference time scale. Construction of International Atomic Time (TAI) and UTC relies on a network of satellite time links encircling the earth (see Fig. 2). For a quarter of a century GPS has served the principal needs of BIPM for regular comparisons of remote atomic clocks. For about 12 years, The two-way satellite time and frequency transfer (TWSTFT) through tele-communication satellites is playing an increasing role. Until now the major research work was focused on GPS time transfer. This resulted in improvement of GPS time transfer reaching an accuracy of 1 ns when using multi-channel and P3 techniques. A major part of this progress is due to the new generations of satellite receivers, often geodetic. However, the TWSTFT technique has the best performance so far, approaching a value of 0.2 ns right now and having a great potential of further improvements. 6 Evolution of clocks and time links contributing to TAI The international time scales computed at the BIPM (TAI and UTC) are based on data from some 220 atomic clocks located in about 50 timelaboratories around the world. The number of clocks fluctuates a little, but remains roughly constant. The quality of the clocks, however, has been improving dramatically. In 1992, the first HP Fig. 1 Residual time error due to scintillation

4 306 INDIAN J RADIO & SPACE PHYS, AUGUST A caesium clocks with high-performance tubes were introduced into the TAI computation, and the number of hydrogen masers has also been increasing steadily. In 1999, about 65 % of the participating clocks were HP 50701A with a highperformance tube and about 17 % were hydrogen masers. Other commercial caesium clocks (including HP 5071A clocks with a lowperformance tube, and continuously operating primary frequency standards) account for only 18 %. This progress has, of course, contributed to a significant improvement in the stability of TAI. The quality of the clocks, although an important issue, is not the only factor contributing to the stability of TAI. Another important factor is the quality of the time links used to compare the clocks. Prior to 1981, only LORAN-C and TV links were used to compare clocks contributing to TAI. In 1981, the first GPS common-view single-channel C/A-code links were introduced 7. These allowed, for the first time, comparison of the stability of remote atomic clocks within an averaging time of several days. The proportion of common-view links of GPS has Fig. 2 International time links (July 2004) Fig. 3 TAI time links increased steadily over the years and in 1999 it has reached almost 100% (see Fig. 3). A new technique was then entered into TAI: that of TWSTFT. As of September 2004, nine TWSTFT links are used for TAI, and several others are in preparation. To illustrate the impact of the improved quality of

5 DEFRAIGNE et al.: TIME TRANSFER THROUGH GPS 307 Fig. 4 Frequency stability of [EAL PTB Cs2] the time links on the frequency stability of TAI, mid period has been analysed, during which the number of GPS links steadily increased, but there was no dramatic change in the nature of the participating clocks. The frequency stability of EAL (the échelle atomic libre) against the primary frequency standard, PTB CS2, is indicated in Fig. 4 for the three time periods, namely mid-1986 to mid- 1988, and The EAL is the free atomic time scale from which TAI is derived using steering corrections. A significant improvement is observed in the frequency stability of EAL for each consecutive period for averaging times up to a few tens of days (for these averaging times the white phase noise due to the time-transfer methods by which EAL was affected is drastically reduced). The evaluation of the frequency stability of EAL here is limited by the frequency stability of PTB CS2. 7 Using geodetic receivers for time and frequency transfer Up to the year 2000, the remote clock comparisons used for the computation of TAI was mainly based on GPS common view using classical time receivers. These receivers collect only C/A code observations. They are connected to the 1 pps (pulse per second) signal delivered by UTC(k), and an internal software computes, following a given procedure as recommended by the CCTF (Consultative Committee for Time and Frequency) 8, the clock offsets between UTC(k) and GPS time as realized by each satellite for conventional tracks appearing in the international BIPM tracking schedules. When comparing clocks located at several thousands of kilometres from each other, the precision of this technique is of a few nanoseconds. Geodetic GPS receivers have the advantage of providing additionally P code and carrier phase data, on both frequencies L 1 and L 2, with a noise level significantly smaller than the noise on the C/A code. However, most of these receivers do not allow a direct link between their internal clock signal and the external clock used to steer the receiver frequency, and, moreover, resynchronize their internal clock on GPS time after each tracking interruption and this with an uncertainty of 1 µs. This induces a clock discontinuity at each tracking interruption. Some geodetic receivers, however, are now especially designed to be also suitable for time transfer. These receivers are steered by an external clock frequency and synchronize their internal clock on the 1 pps signal provided by the same external clock, so that the receiver internal clock is directly a mirror of the external clock. In this way,

6 308 INDIAN J RADIO & SPACE PHYS, AUGUST 2007 there are no clock discontinuities associated with tracking interruptions as is the case with classical geodetic receivers. In order to use the geodetic GPS receivers for time transfer to TAI, a software was developed 9 which constructs, from the RINEX observation files, the CGGTTS files needed for TAI. This software follows the procedure recommended by the CCTF for the computation of the clock offsets between UTC(k) and GPS time as realized by each satellite visible during the conventional tracks appearing in the international BIPM tracking schedules (i.e. multi-channel approach). 8 Advantage of a dual frequency receiver As the ionosphere perturbation on an electromagnetic wave is frequency-dependent, a combination of two signals with different frequencies is an efficient tool to cancel the first order ionospheric delays. This can be done in the GPS case when the receiver is designed to measure the GPS signal on both frequencies L 1 and L 2. The classical CCTF procedure was therefore modified in order to use the advantage of dual-frequency receiver able to measure the precise code P1 on L 1 and P2 on L 2. Rather than using the C/A code, the new procedure uses the socalled ionospheric-free code observable P3, corresponding to a combination of the two GPS precise codes P1 and P2. Therefore, in this P3 code, the ionospheric delay is absent, while the ionospheric correction proposed in the CCTF procedure for the C/A code is based on the Klobuchar ionospheric model, which corrects only one part of the ionospheric delay, because it cannot represent and hence correct the effects of the random part of the ionospheric activity. Note that for the computation of TAI, the BIPM improves the CGGTTS results by replacing the ionospheric corrections computed by the time receiver from the broadcast Klobuchar model, with the value computed from IGS ionex maps. However, the ionex maps allows only to correct for the long wavelength and long term variations (above 2h), while the ionosphere-free combination eliminates both the short and long wavelength behaviours of the ionosphere as well as short and long term variations. Figure 5 shows the time transfer between two hydrogen masers, the first one located at NPLD (UK) and the second one at USNO (Washington), when using the classical CCTF procedure with the IGS ionex maps and when using the modified CCTF procedure, i.e. using the P3 code 9. In both cases, the precise satellite ephemerides provided by the IGS have been used for the determination of the geometric distances satellites-station and for the satellite clock synchronization errors. This new procedure improves the Allan deviation by a factor of 2 on a trans-atlantic baseline. 9 Time/frequency transfer using GPS carrier phase measurements The second kind of measurements available with the geodetic receiver are the carrier phases of L 1 and L 2. The noise level of the carrier phase measurements is about 100 times smaller than the corresponding noise level on the code measurements. For this reason, the carrier phases have been used since 1980 Fig. 5 Comparison of the time transfer results obtained using either the C/A code or the ionosphere-free combination (P3) of the two precise codes P1 and P2

7 DEFRAIGNE et al.: TIME TRANSFER THROUGH GPS 309 for different geodetic applications requiring very high precision. During the last years, the potential of GPS carrier phases for time transfer was recognized and demonstrated by different authors The carrier phase observation (for L 1 or L 2 ) collected by a receiver (q) and a satellite (i) can be decomposed as: φ = f (τ + t t ) + iono + tropo + N (1) i i i i p p p p where τ i p is the travel time, t p and t i are the receiver and satellite clock offset, iono and tropo are the i ionospheric and tropospheric delays, and N p is the phase ambiguity, constant during one track if there is no cycle slip. The clock offset between two receivers p and q is obtained from the single difference φ φ = f (τ τ + t ) + iono(p) i i i i p q p q pq iono(q) + tropo (p) tropo(q) + N N i p i q (2) where t is the clock offset between two receivers pq p and q. Due to the phase ambiguities, it is not possible to determine the absolute value of t. The carrier phase observable can thus be used for frequency transfer, i.e. for the determination of the evolution of t. The absolute value of the clock pq offset can only be determined using the code information. A combined analysis using both carrier pq phase and code observations is necessary to get the absolute value of the clock offset, with a precision limited by the code noise level (depending on the receiver type, but smaller than 1 ns), and a very precise determination of the frequency transfer allowed by the small noise level of the carrier phases. Figure 6 shows the comparison of results obtained either with the P3 analysis, i.e. obtained from code observations only, or with a combined code and carrier phase analysis using the ionosphere-free combinations P3 and L3, obtained with the Bernese V4.2 software and the IGS precise satellite ephemerides. The Allan deviation is also shown in Fig. 7 for both the analyses; the improvement allowed by the use of carrier phases is clear, but this improvement disappears for averaging times longer than 5 days, as already pointed out by different workers. 10 IGS clock products The TAI has very good long-term stability, but is available only after several weeks. The IGS provides with a 1-day delay a time scale, named IGST (or IGRT for the rapid version) with a very good shortterm stability. The IGS time scale is realized from the IGS clock combinations, i.e. satellite and receiver clock offsets, based on time transfer between IGS receiver and/or satellite clocks, and it is computed from the combination of code and phase observations. Fig. 6 Comparison between the time transfer results obtained with precise code (ionosphere-free combination P3) or combined codecarrier phases (ionosphere-free combination L3) analysis [the two curves have been separated by 5 ns in order to improve the visibility].

8 310 INDIAN J RADIO & SPACE PHYS, AUGUST 2007 Fig. 7 Allan deviation of the time transfer results between Brussels (BRUS) and Teddington (NPLD) obtained with precise code (ionosphere-free combination P3) or carrier phases (ionosphere-free combination L3) The IGS provides, on a daily basis, the clock synchronization errors of all the station clocks with respect to the IGST. This tool can be used by the IGS stations for a short-term monitoring of their clocks. The IGS time scale is steered to TAI in order to ensure the long-term stability. 11 Limitations of carrier phase results 11.1 Day boundary jumps Due to the use of daily data batches, some jumps appear in the clock solution obtained with combined code/carrier phase data analysis. These are due to the ambiguities, characteristics of the carrier phase measurements: the absolute offset is only determined by the code information, while the carrier phases allow giving a precise signal evolution. For each data batch (each day in our case) the evolution obtained from carrier phases has to be calibrated with the absolute offset obtained with the code data, and this within the noise level of the code measurements, i.e. about 1 ns. This leads to day boundary jumps up to 500 ps in the solution. In order to avoid these jumps, several propositions have been tested, either an overlap of the data files, or using a longer data batches in order to have less jumps (one jump between two data batches); or using the ambiguities obtained in the previous data batch and extend them in the beginning of the raw data set; the recalling of the results is probably the worse solution as it can introduce some trend in the result Troposphere As the troposphere activity varies rapidly, the tropospheric delay must be corrected using either water vapour radiometer (WVR) measurements or by an estimation of the parameters of a given tropospheric model. In that case, there will be a correlation between the tropospheric parameters determined and the clock solution, because both appear in the pseudo-range equation [Eq. (1)] and must, therefore, be estimated together. As shown by Hackman and Levine 13, this can lead to differences up to 300 ps in the clock solution between the solutions obtained either using WVR data for the troposphere delay or using an estimation of the tropospheric parameters GPS analysis strategy The clock solutions can be obtained either through a network analysis or in a PPP (Precise Point Positioning) process. In the first case, all the station clocks are determined in a global solution, and these clock solutions correspond to the clock synchronization errors with respect to a reference time scale, which can be either one clock in the network, or a combination of the network clocks. In the PPP analysis, the clock solutions of one single station are determined with respect to a reference time scale (GPS time or IGS time scale). In that case, the satellite orbits and clocks are taken from some external determination, e.g. the IGS products. Using

9 DEFRAIGNE et al.: TIME TRANSFER THROUGH GPS 311 both kinds of analysis leads to differences up to 200 ps in the clock solutions, depending on the analysis software used among the existing tools Hardware considerations Among the hardware considerations, one has to account for the hardware delays, which have to be determined by calibration. These hardware delays are sensitive to the ambient temperature variations. This is the reason why it is important to have temperature stabilization in the laboratories. Some experiments have been performed to test the sensitivity of the equipment (receiver, amplifiers, etc.) to the temperature variations and the results showed the importance of keeping the temperature constant within 0.1 C. Concerning the antenna, the experiments show maximum diurnal variations of 40 ps for the carrier phases, while up to 2 ns for the code measurements; some antenna cables exist with very small sensitivity to temperature variations and should be used for precise time and frequency transfer. 12 Conclusions Today, in metrology, birth of a number of new and innovative frequency standards is being witnessed. These devices have accuracy of about and seem to have short-term instability approaching This corresponds to a clock having the capability to maintain a level of performance corresponding to 10 ps/day. Since the newest devices are not transportable and do not operate continuously, it is important to compare them in a reasonable time in order to determine the existence of systematic differences among them. A measurement with a precision of 1 ns over a 24 h period corresponds to in frequency. Therefore, at today s present levels, it would take weeks to compare two such devices. That is why it is important to develop and improve time transfer methods to allow these comparisons to be made within a reasonable amount of time. For this reason the timing community is engaged in the development of new approaches to time and frequency comparisons. Among them are GPS techniques based on multi-channel GPS C/A-code measurements, GPS carrier-phase 14, GPS 9 P3 and GLONASS P-code measurements 15, temperaturestabilized antennas and standardization of receiver software. The construction of TAI requires time-transfer techniques that allow participating clocks to be compared at their full level of performance for intervals at which TAI is computed. In the pre-gps era this was impossible, because the technology of atomic clocks was always ahead of that of time transfer. This resulted in an annual term in TAI. The replacement of LORAN-C links by GPS C/A-code common-view links during the years has progressively reduced the impact of white phase noise on TAI, improving its stability up to about 80 days. During 1980s, GPS allowed, for the first, time the comparison of remote atomic clocks at their full levels of performance for averaging times of just a few days, fully satisfying needs of TAI, computed at this epoch at intervals of 10 days. However, with the improvements in clock technology made during 1980s and the resulting dramatic increase in the quality of the clocks contributing to TAI in 1990s, intercontinental GPS C/A-code single-channel common-view measurements need to be averaged sometimes over up to 20 days in order to smooth out measurement noise. This is no longer sufficient for TAI, computed at five-day intervals from 1 Jan However, the GPS multi-channel C/A-code and P3 measurements are showing better performance, and most recently geodetic PPP technique using GPS carrier-phase is showing performance close to TWSTFT 6. References 1 Wellenhof B Hofmann Lichtenegger H & Collins J, GPS Theory and Practice, 2 nd Edition (Springer-Verlag, Wien, New York), May Allan D W & Weiss M A, Accurate Time and Frequency Transfer during Common-View of a GPS Satellite, in Proceedings of 34 th Annual Symposium on Frequency control, 1980, pp Landis G Paul & White Joe, Limitation of GPS Receiver Calibrations, 34 th Annual Precise Time and Time Interval (PTTI) Meeting, pp White J. et al., Dual Frequency Absolute Calibration of a GPS Receiver for Time Transfer, Proceeding of the 15 th European Frequency and Time Forum (EFTF), 6-8 March 2001, p Bandyopadhyay T, Guha A, DasGupta S, Banerjee P & Bose A, Degradation of Navigational accuracy with Global Positioning System during periods of scintillation at equatorial latitudes, Electron Lett (UK), 33 (1997) Kirchner D, Two-Way Satellite Time and Frequency Transfer (TWSTFT): Principle, Implementation and Current

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