Time and Frequency Transfer Using GPS Codes and Carrier Phases: Onsite Experiments

Recent studies have shown the capabilities of Global Positioning System (GPS) carrier phases for frequency transfer based on the observations from geodetic GPS receivers driven by stable atomic clocks. This kind of receiver configuration is the kind primarily used within the framework of the International GPS Service (IGS). The International GPS Service/Bureau International des Poids et Mesures (IGS/BIPM) pilot project aims at taking advantage of these GPS receivers to enlarge the network of Time Laboratories contributing to the realization of the International Atomic Time (TAI). In this article, we outline the theory necessary to describe the abilities and limitations of time and frequency transfer using the GPS code and carrier phase observations. We report on several onsite tests and evaluate the present setup of our 12-channel IGS receiver (BRUS), which uses a hydrogen maser as an external frequency reference, to contribute to the IGS/BIPM pilot project. In the initial experimental setup, the receivers had a common external frequency reference; in the second setup, separate external frequency references were used. Independent external clock monitoring provided the necessary information to validate the results. Using two receivers with a common frequency reference and connected to the same antenna, a zero baseline, we were able to use the carrier phase data to derive a frequency stability of 6 × 10⁻¹⁶ for averaging times of one day. The main limitation in the technique originates from small ambient temperature variations of a few degrees Celsius. While these temperature variations have no effect on the functioning of the GPS receiver within the IGS network, they reduce the capacities of the frequency transfer results based on the carrier phase data. We demonstrate that the synchronization offset at the initial measurement epoch can be estimated from a combined use of the code and carrier phase observations. In our test, the discontinuity between two consecutive days was about 140 ps. ? 1999 John Wiley & Sons, Inc.     

Ionospheric calibration of single frequency VLBI and GPS observations using dual GPS data

Summary The ionospheric effect is one of the main sources of error in Very Long Baseline Interferometry (VLBI) and Global Positioning System (GPS) high precision geodesy. Although the use of two frequencies allows the estimation of this effect, in some cases dual observations are not possible due to the available equipment or the type of observation. This paper presents the ionospheric calibration of single frequency VLBI and GPS observations based on the ionospheric electron content estimated from dual frequency GPS data. The ionospheric delays obtained with this procedure and the VLBI baseline length results have been compared with those obtained with dual frequency data. For the European geodetic VLBI baselines, both solutions agree at the 3–5 parts in 10^–9 level. The noise introduced by the GPS-based calibration is in the order of 3 cm for the VLBI observables and of 10 cm for the GPS observables.     

Monitoring selective availability dither frequencies and their effect on GPS data

Summary The signals transmitted by Block II satellites of the Global Positioning System (GPS) can be degraded to limit the highest accuracy of the system (10 m or better point positioning) to authorized users. This mode of degraded operation is called Selective Availability (S/A). S/A involves the degradation in the quality of broadcast orbits and satellite clock dithering. We monitored the dithered satellite oscillator and investigated the effect of this clock dithering on high accuracy relative positioning. The effect was studied over short 3-meter and zero-baselines with two GPS receivers. The equivalent S/A effects for baselines ranging from 0 to >10,000 km can be examined with short test baselines if the receiver clocks are deliberately mis-synchronized by a known and varying amount. Our results show that the maximum effect of satellite clock dithering on GPS double difference phase residuals grows as a function of the clock synchronization error according to: S/A _effect =0.04 cm/msec, and it increases as a function of baseline length like: S/A _effect =0.014 cm/100 km. These are equations for maximum observed values of post-fit residuals due to S/A. The effect on GPS baselines is likely to be smaller than the 0.14 mm for a baseline separation of 100 km. We therefore conclude, for our limited data set, and for the level of S/A during our tests, that S/A clock dithering has negligible effect on all terrestrial GPS baselines if double difference processing techniques are employed and if the GPS receivers remain synchronized to better than 10 msec. S/A may constitute a problem, however, if accurate point processing is required, or if GPS receivers are not synchronized. We suggest and test two different methods to monitor satellite frequency offsets due to S/A. S/A modulates GPS carrier frequencies in the range of-2 Hz to +2 Hz over time periods of several minutes. The methods used in this paper to measure the satellite clock dither could be applied by the civilian GPS community to continuously monitor S/A clock dithering. The monitored frequencies may aid high accuracy point positioning applications in a postprocessing mode (Malys and Ortiz 1989), and differential GPS with poorly synchronized receivers (Feigl et al. 1991).     

基于GPS的多站实时时间传递算法

提出了一种基于GPS的多站实时时间传递算法,该算法将卫星钟差作为未知参数进行实时估计,利用测站间的共视卫星建立起各测站误差方程之间的联系,同时解算站间时间传递结果和卫星钟差。摆脱了对外部事后精密卫星钟差产品的依赖,不受卫星精密钟差产品精度和实时性的限制,只要站间有足够的共视卫星,即可实现时间传递。实验结果表明:该算法时间传递精度可以达到亚纳秒量级,能够应用于高精度实时时间传递。     

RINEX_HO: second- and third-order ionospheric corrections for RINEX observation files

When GNSS receivers capable of collecting dual-frequency data are available, it is possible to eliminate the first-order ionospheric effect in the data processing through the ionosphere-free linear combination. However, the second- and third-order ionospheric effects still remain. The first-, second- and third-order ionospheric effects are directly proportional to the total electron content (TEC), although the second- and third-order effects are influenced, respectively, by the geomagnetic field and the maximum electron density. In recent years, the international scientific community has given more attention to these kinds of effects and some works have shown that for high precision GNSS positioning these effects have to be taken into consideration. We present a software tool called RINEX_HO that was developed to correct GPS observables for second- and third-order ionosphere effects. RINEX_HO requires as input a RINEX observation file, then computes the second- and third-order ionospheric effects, and applies the corrections to the original GPS observables, creating a corrected RINEX file. The mathematical models implemented to compute these effects are presented, as well as the transformations involving the earth’s magnetic field. The use of TEC from global ionospheric maps and TEC calculated from raw pseudorange measurements or pseudoranges smoothed by phase is also investigated.     

Absolute Calibration of an Ashtech Z12-T GPS Receiver

Dual-frequency carrier phase and code measurements from geodetic type receivers are a promising tool for frequency and time transfer. In order to use them for clock comparisons, all instrumental delays should be calibrated. We have carried out the calibration of one such receiver, an Ashtech Z12-T type, by two different methods: first, by absolute calibration using a GPS simulator; second, by differential calibration with respect to a time transfer receiver that had previously been calibrated. We present the experimental set-ups and the results of the two experiments and estimate the uncertainty budget. An ultimate uncertainty of order 1 ns in the absolute calibration seems to be attainable. ? 2001 John Wiley & Sons, Inc.     

Instantaneous Precise GPS Positioning under Geomagnetic Storm Conditions

Due to the maximum of the solar cycle, ionospheric activity increased considerably last year. At frequent times warning were sent out announcing geomagnetic storms disturbing the ionospheric electron content. In this article the influence of such geomagnetic storms on fast and precise GPS positioning (for surveying applications at midlatitude regions) is studied. And here with “fast” it is aimed at the shortest observation time possible: carrier ambiguity resolution and position estimation using only one single epoch of data. To apply this instantaneous data processing technique successfully to GPS baselines of medium length (up to 50 km), additional ionospheric information is inevitable, not only under geomagnetic storm but also under more quiet conditions. However, in this article it will be shown that under geomagnetic storm conditions, even for rather short baselines (<10 km), for which the ionospheric delays under more quiet conditions could be neglected, one has to account for significant relative ionospheric delays. Therefore an important facet of this contribution is the investigation of how to process baselines of varying length in a more uniform way, making use of a permanent GPS network (if available in the surveying area) and a stochastic modeling technique of the ionospheric delays. ? 2001 John Wiley & Sons, Inc.     

Time Transfer Experiments Using GLONASS P-code Measurements from RINEX Files

We have used GLONASS P-code measurements from different geodetic GPS/GLONASS receivers involved in the IGEX campaign to perform frequency/time transfer between remote clocks. GLONASS time transfer is commonly based on the clock differences between GLONASS system time and the local clock computed by a time transfer receiver. We choose to analyze the raw P-code data available in the RINEX files. This also allows working with the data from geodetic receivers involved in the IGEX campaign. As a first point, we show that the handling of the external frequency in some of the IGEX receivers is not suited for time transfer applications. We also point out that the GLONASS broadcast ephemerides give rise to a considerable number of outliers in the time transfer, compared to the precise IGEX ephemerides. Due to receiver clock resets at day boundaries, which is a characteristic of the R100 receivers from 3S-Navigation, continuous data sets exceeding one day are not available. Invthis context, it is therefore impossible to perform RINEX-based precise frequency transfer with GLONASS P-codes on a time scale longer than one day. Because the frequencies used by GLONASS satellites are different, the time transfer results must be corrected for the different receiver hardware delays. After this correction, the final precision of our time transfer results corresponds to a root-mean-square (rms) of 1.8 nanoseconds (ns) (maximum difference of 11.8 ns) compared to a rms of about 4.4 ns (maximum difference of 31.9 ns) for time transfer based on GPS C/A code observations. ? 2001 John Wiley & Sons, Inc.     

基于大地型时频传递接收机的精密时间传递算法研究

介绍了大地型GPS时频传递接收机的特点,给出了传统GPS载波相位时间传递法与连续GPS载波相位时间传递法的算法流程,利用IGS/TAI并置站的数据进行了精密时间传递计算。     

Ambiguity resolution strategies using the results of the International GPS Geodynamics Service (IGS)

Resolving the initial phase ambiguities of GPS carrier phase observations was always considered an important aspect of GPS processing techniques. Resolution of the so-called wide-lane ambiguities using a special linear combination of theL ₁ andL ₂ carrier and code observations has become standard. New aspects have to be considered today: (1) Soon AS, the so-called Anti-Spoofing, will be turned on for all Block II spacecrafts. This means that precise code observations will be no longer available, which in turn means that the mentioned approach to resolve the wide-lane ambiguities will fail. (2) Most encouraging is the establishment of the new International GPS Geodynamics Service (IGS), from where high quality orbits, earth rotation parameters, and eventually also ionospheric models will be available. We are reviewing the ambiguity resolution problem under these new aspects: We look for methods to resolve the initial phase ambiguities without using code observations but using high quality orbits and ionospheric models from IGS, and we study the resolution of the narrow-lane ambiguities (after wide-lane ambiguity resolution) using IGS orbits.     

Modelling of differential single difference receiver clock bias for precise positioning

A receiver hardware delay should be seriously considered for time-transfer and determination of ionospheric delay corrections for wide area differential GPS positioning. A receiver hardware delay does not generally effect the common geo-position application, as suitable differences of observations are used, or equivalently, clock error parameters are introduced, epoch-wise, that also absorb the delays. This paper investigates the behavior of inter-frequency (or observation-type) receiver hardware delays by using a single difference (SD) model, which estimates the receiver delay along with the receiver clock error (and SD ambiguities of a reference satellite with carrier phase observations) for zero and short baselines. The purpose of this paper is to model the between-observation-type delays for the purpose of precise positioning, under practical circumstances. The focus is on data series of differential SD receiver clock biases, since they reflect the behavior of receiver hardware delays with time. A simple linear regression of the data series is employed to study the behavior, and test statistics are employed to assess both the significance of the parameters and the observations fit for the linear regression. The statistical analysis results indicate that almost all inter-observation type receiver delays can be modeled as the sum of a constant (offset) and a constant rate of change (slope). The analysis shows that the differential receiver delay is generally at the mm- to cm-level on phase, while at the dm-level on code for the equipment used in the experiments.     

利用GPS共视法确定重力位差及海拔高差的实验研究

阐述了GPS共视法的基本原理,讨论了利用重力频移法通过GPS共视观测数据确定重力位差和高程差的方法。利用国际权度局(BIPM)发布的时间序列数据,选取了4个守时台站之间的时间差序列进行实验。结果表明,受目前GPS共视法精度所限,高程差计算值与理论值之间的平均差异和标准差在几十m的量级水平。     

On the link between GPS pseudorange noise and day-boundary discontinuities in geodetic time transfer solutions

When neglecting calibration issues, the accuracy of GPS-based time and frequency transfer using a combined analysis of code and carrier phase measurements highly depends on the noise of the GPS codes. In particular, the pseudorange noise is responsible for day-boundary discontinuities which can reach more than 1 ns in the time transfer results obtained from geodetic analysis. These discontinuities are caused by the fact that the data are analyzed in daily data batches where the absolute clock offset is determined by the mean code value during the daily data batch. This pseudorange noise is not a white noise, in particular due to multipath and variations of instrumental delays. In this paper, the pseudorange noise behavior is characterized in order to improve the understanding of the origin of the large day-boundary discontinuities in the geodetic time transfer results. In a first step, the effect of short-term noise and multipath is estimated, and shown to be responsible for only a maximum of 150 ps (picoseconds) of the day-boundary jumps, with only one exception at NRC1 where the correction provides a jump reduction of 300 ps. In a second step, a combination of time transfer results obtained with pseudoranges only and geodetic time transfer results is used to characterize the long-term evolution of pseudorange errors. It demonstrates that the day-boundary jumps, especially those of large amplitude, can be explained by an instrumental effect imposing a common behavior on all the satellite pseudoranges. Using known influences as temperature variations at ALGO or cable damages at HOB2, it is shown that the approach developed in this study can be used to look for the origin of the day-boundary discontinuities in other stations.     

多通道时间传递接收机NTSCGPS-1的研制与测试

近20年来，GPS共视(GPS CV)技术作为一种主要技术被用于TAI时间比对。GPS时间传递接收机是进行GPSCV时间比对的主要设备。介绍了中科院国家授时中心采用Motorola VP Oncore GPS OEM板、GT200计数器研发的高精度、多通道GIPS时间传递接收机NTscGPS-1的原理和特点。并通过实际观测数据分析，认为NTSCGPS-1的观测噪声水平与其它时间传递接收机相当，并有较好的兼客性。     

GNSS three carrier ambiguity resolution using ionosphere-reduced virtual signals

This paper presents a general modeling strategy for ambiguity resolution (AR) and position estimation (PE) using three or more phase-based ranging signals from a global navigation satellite system (GNSS). The proposed strategy will identify three best “virtual” signals to allow for more reliable AR under certain observational conditions characterized by ionospheric and tropospheric delay variability, level of phase noise and orbit accuracy. The selected virtual signals suffer from minimal or relatively low ionospheric effects, and thus are known as ionosphere-reduced virtual signals. As a result, the ionospheric parameters in the geometry-based observational models can be eliminated for long baselines, typically those of length tens to hundreds of kilometres. The proposed modeling comprises three major steps. Step 1 is the geometry-free determination of the extra-widelane (EWL) formed between the two closest L-band carrier measurements, directly from the two corresponding code measurements. Step 2 forms the second EWL signal and resolves the integer ambiguity with a geometry-based estimator alone or together with the first EWL. This is followed by a procedure to correct for the first-order ionospheric delay using the two ambiguity-fixed widelane (WL) signals derived from the integer-fixed EWL signals. Step 3 finds an independent narrow-lane (NL) signal, which is used together with a refined WL to resolve NL ambiguity with geometry-based integer estimation and search algorithms. As a result, the above two AR processes performed with WL/NL and EWL/WL signals respectively, either in sequence or in parallel, can support real time kinematic (RTK) positioning over baselines of tens to hundreds of kilometres, thus enabling centimetre-to-decimentre positioning at the local, regional and even global scales in the future.     

Stability analysis of GPS carrier tracking loops by phase margin approach

Stability, which is significantly related to the loop parameters, is an important factor in the traditional GPS tracking loop design. Through the analysis of phase margin values in the discrete GPS PLL tacking loop, we are able to theoretically reveal the relationship between loop stability, equivalent noise bandwidth B _n , predetection integration time T, and loop parameters. We calculate the theoretical limitations for B _n T, that is, the product of equivalent noise bandwidth multiplied by predetection integration time, for second- and third-order phase-locked loop, respectively. The results are verified by actual data from GPS receivers.     

Precise GPS Positioning by Applying Ionospheric Corrections from an Active Control Network

In this article, initial results are presented of a method to improve fast carrier phase ambiguity resolution over longer baselines (with lengths up to about 200 km). The ionospheric delays in the global positioning system (GPS) data of these long baselines mainly hamper successful integer ambiguity resolution, a prerequisite to obtain precise positions within very short observation time spans. A way to correct the data for significant ionospheric effects is to have a GPS user operate within an active or permanently operating network use ionospheric estimates from this network. A simple way to do so is to interpolate these ionospheric estimates based on the expected spatial behaviour of the ionospheric delays. In this article such a technique is demonstrated for the Dutch Active Control Network (AGRS.NL). One hour of data is used from 4 of the 5 reference stations to obtain very precise ionospheric corrections after fixing of the integer ambiguities within this network. This is no problem because of the relatively long observation time span and known positions of the stations of the AGRS.NL. Next these interpolated corrections are used to correct the GPS data from the fifth station for its ionospheric effects. Initial conclusions about the performance of this technique are drawn in terms of improvement of integer ambiguity resolution for this baseline. ? 1999 John Wiley & Sons, Inc.     

卫星位置误差对GPS共视时间比对的影响

影响GPS共视时间比对的一种因素是卫星的位置误差,这个影响程度取决于用户对卫星的观测仰角和用户间的基线长度。当两个用户的仰角大致相同时,卫星位置误差对时间比对的影响与基线长度近似成正比,而与仰角的大小几乎无关。当两个仰角不同时,对于小于2500km的基线,两个仰角之差越小,这种影响就越小。对于5000km以内的基线,无论多大的仰角,时间比对的误差最多相当于卫星位置等价误差(卫星位置误差除以信号传播速度)的四分之一。     

Performance evaluation of different ionospheric models in single-frequency code-based differential GPS positioning

Differential ionospheric slant delays are obtained from a quiet-time, three-dimensional ionospheric electron density model, called the TaiWan Ionosphere Model (TWIM), to be used in code-based differential GPS positioning. The code observations are acquired from nine continuously operating GPS stations around Taiwan whose baseline ranged from 19 to 340 km. Daily 24-hour epoch-per-epoch positioning obtained for 70 most geomagnetic quiet days (2008–2010) for each of the 72 baselines. The performance of TWIM has been compared with the standard operational Klobuchar model (KLB) used by typical single-frequency receivers and the IGS global ionospheric model (GIM). Generally, TWIM performed well in reducing the differential ionospheric delay especially for long baselines and different levels of low solar activity. It has a much better performance compared to the operational KLB model. TWIM also performed similarly with GIM, though GIM has the best performance overall. GIM has the best ionospheric gradient estimates among the three models whose differential ionospheric delay-to-horizontal error ratio is more than 0.25. This is followed closely by TWIM with about 0.20. KLB only has a ratio of <0.10. The similarity of the performance of TWIM and GIM demonstrates the feasibility of TWIM in correcting for differential ionospheric delays in the C/A code pseudorange that is caused by electron density gradients in the ionosphere. It can provide decimeter-to-centimeter level accuracy in differential GPS positioning for single-frequency receivers during geomagnetic quiet conditions across all seasons and different levels of low solar activities.     

The Influence of Code Multipath on the Estimated Parameters of the Geometry-Free GPS Model

In this article, the influence of biases in GPS code observations on the estimated parameters of the geometry-free model is investigated. This is done for undifferenced as well as double-differenced data from short baselines, that is, baselines for which ionospheric effects may be assumed absent. It is shown how introducing a linear model for code multipath affects the original model parameters. The performance of the original and extended model is illustrated by analyzing data from a single receiver and a short baseline. ? 1999 John Wiley & Sons, Inc.