Combination methods of tropospheric time series

In this article we present two methods for combination of different Global Navigation Satellite Systems (GNSS) Zenith Total Delay (ZTD) time-series for the same GNSS site, but from different producers or different processing setups. One method has been setup at ASI/CGS, the other at KNMI. Using Near Real-Time (NRT) ZTD data covering 1 year from the E-GVAP project, the performance of the two methods is inter-compared and validation is made against a combined ZTD solution from EUREF, based on post-processed ZTDs. Further, validation of the ASI combined solutions is made against independent ZTDs derived from radiosonde, Numerical Weather Prediction (NWP) model and Very Long Baseline Interferometry (VLBI) ZTD.     

Retrieval of the change of precipitable water vapor with zenith tropospheric delay in the Chinese mainland

As a preliminary step for assessing the impact of global positioning system (GPS) refractive delay data in numerical weather prediction (NWP) models, the GPS zenith tropospheric delays (ZTD) are analyzed from 28 permanent GPS sites in the Chinese mainland. The objectives are to estimate the GPS ZTD and their variability in this area. The differences between radiosonde precipitable water vapor (PWV) and GPS PWV have a standard deviation of 4 mm in delay, a bias of 0.24 mm in delay, and a correlation coefficient of 0.94. The correlation between GPS ZTD and radiosonde PWV amounts to 0.89, indicating that the variety of tropospheric zenith delay can reflect the change of precipitable water vapor. The good agreement also guarantees that the information provided by GPS will benefit the NWP models. The time series of GPS ZTD, which were derived continuously from 2002 to 2004, are used to analyze the change of precipitable water vapor in Chinese mainland. It shows that the general trend of GPS ZTD is diminishing from the south-east coastland to the north-west inland, which is in accordance with the distribution of Chinese annual amount of rainfall. The temporal distribution of GPS ZTD in the Chinese mainland is that the GPS ZTD reaches maximum in summer, and it reaches minimum in winter. The long term differences between the observational data sources require further study before GPS derived data become useful for climate studies.     

An inter-comparison of zenith tropospheric delays derived from DORIS and GPS data

Doppler Orbitography Radiopositioning Integrated by Satellite (DORIS) and Global Positioning System (GPS) techniques are similarly affected by propagation delays in the neutral atmosphere (troposphere) and hence make use of similar data processing strategies for reducing this effect. We compare Zenith Tropospheric Delays (ZTDs) estimated from 52 DORIS and GPS station pairs co-located at 35 sites over the 2005–2008 period. We find an overall systematic negative mean bias of −4 mm and a median bias of −2 mm, with a large site-to-site scatter and especially stronger biases over South America, potentially linked to remaining problems related to the South Atlantic Anomaly (SAA) in the current DORIS data processing. The standard deviation of ZTD differences is in the range 4–12 mm over the globe (8 mm on average), with larger values located in the southern hemisphere. The spatial variability of differences is consistent with previous work but remains largely unexplained. DORIS is shown to be much less sensitive to instrumental changes than GPS (only the switch from Alcatel to Starec antenna at Toulouse is detected as an offset of −4 mm in the ZTD time series). On the opposite, discontinuities and spurious annual signals are found in the GPS ZTD solutions. A discontinuity of +5 mm is found on 5 November 2006, linked to the switch from relative to absolute GPS antenna models used in the data processing. The use of modified GPS antennas (e.g. at GODE) or improved antenna models is shown to reduce the spurious annual signal (e.g. from 5 mm to 2 mm at METS). Overall, the agreement between both techniques is good, though DORIS shows a significantly larger random scatter. The high stability and good spatial and temporal coverage make DORIS a potential candidate technique for meteorology and climate studies as long as reasonable time averaging can be applied (e.g. differences are reduced from 8.6 to 2.4 mm with 5-day averages) and no real-time application is considered. This technique could be considered as a potential contributor to Global Geodetic Observing System (GGOS) for climatology.     

Exploration and analysis of the factors influencing GNSS PWV for nowcasting applications

Precipitable water vapor (PWV) can be assimilated into a numerical weather model (NWM) to improve the prediction accuracy of numerical weather prediction. In this study, taking GNSS data for the Beijing Fangshan station (BJFS) as an example, based on the method of Pearson correlation coefficient combined with quantitative analysis, GNSS datasets are used to study the relationships between GNSS-derived PWV (GNSS PWV__Met) and its influencing factors, including the internal influencing factors zenith troposphere delay (ZTD), zenith hydrostatic delay (ZHD), zenith wet delay (ZWD), and surface temperature (T_s), and the external influencing factor haze (mainly PM_2.5). Firstly, based on the strong correlation between PWV__Met and ZTD hourly sequences from the International GNSS Service Network’s BJFS station for DOYS 182–212, 2015, the results of experiment prove that the reliability of GNSS ZTD is used to forecast PWV_Met in short-term forecasting. Secondly, based on hourly data of BJFS in 2016, the correlation between PWV__Met and ZTD, ZWD, ZHD, pressure (P) and T_s is analyzed, and then, with the rate of ZTD variation as the main factor, ZTD variation as auxiliary factor, the prediction success rate is 88.24% from hourly data of precipitation event for DOYs 183–213 in Beijing. The experiment indicates that ZTD can help forecast short-term precipitation. Thirdly, based on data from three hazy periods with relatively stable weather conditions, no heavy rainfall, and relatively continuous data in the past three years, the correlation between GNSS PWV_Met/ZTD and PM_2.5 hourly series is analyzed. The results of the experiments suggests that GNSS ZTD should be considered to assist in haze monitoring. So in the absence of radiosonde stations and meteorological elements, ZTDs on retrieval of GNSS stations have more application value in short-term forecast.     

Effects of physical correlations on long-distance GPS positioning and zenith tropospheric delay estimates

The global positioning system (GPS) has become an essential tool for the high precision navigation and positioning. The quality of GPS positioning results mainly depends on the model’s formulations regarding GPS observations, including both a functional model, which describes the mathematical relationships between the GPS measurements and unknown parameters, and a stochastic model, which reflects the physical properties of the measurements. Over the past two decades, the functional models for GPS measurements have been investigated in considerable detail. However, the stochastic models of GPS observation data are simplified, assuming that all the GPS measurements have the same variance and are statistically independent. Such assumptions are unrealistic. Although a few studies of GPS stochastic models were performed, they are restricted to short baselines and short time session lengths. In this paper, the stochastic modeling for GPS long-baseline and zenith tropospheric delay (ZTD) estimates with a 24-h session is investigated using the residual-based and standard stochastic models. Results show that using the different stochastic modelling methods, the total differences can reach as much as 3–6 mm in the baseline component, especially in the height component, and 10 mm in the ZTD estimation. Any misspecification in the stochastic models will result in unreliable GPS baseline and ZTD estimations. Using the residual-based stochastic model, not only the precision of GPS baseline and ZTD estimation is obviously improved, but also the baseline and ZTD estimations are closer to the reference value.     

High temporal resolution global PWV dataset of 2005–2016 by using a neural network approach to determine the mean temperature of the atmosphere

Atmospheric water vapour plays an important role in phenomena related to the global hydrologic cycle and climate change. However, the rapid temporal–spatial variation in global tropospheric water vapour has not been well investigated due to a lack of long-term, high-temporal-resolution precipitable water vapour (PWV). Accordingly, this study generates an hourly PWV dataset for 272 ground-based International Global Navigation Satellite System (GNSS) Service (IGS) stations over the period of 2005–2016 using the zenith troposphere delay (ZTD) derived from global-scale GNSS observation. The root mean square (RMS) of the hourly ZTD obtained from the IGS tropospheric product is approximately 4 mm. A fifth-generation reanalysis dataset of the European Centre for Medium-range Weather Forecasting (ECMWF ERA5) is used to obtain hourly surface temperature (T) and pressure (P), which are first validated with GNSS synoptic station data and radiosonde data, respectively. Then, T and P are used to calculate the water vapour-weighted atmospheric mean temperature (Tm) and zenith hydrostatic delay (ZHD), respectively. T and P at the GNSS stations are obtained via an interpolation in the horizontal and vertical directions using the grid-based ERA5 reanalysis dataset. Here, Tm is calculated using a neural network model, whereas ZHD is obtained using an empirical Saastamoinen model. The RMS values of T and P at the collocated 693 radiosonde stations are 1.6 K and 3.1 hPa, respectively. Therefore, the theoretical error of PWV caused by the errors in ZTD, T and P is on the order of approximately 2.1 mm. A practical comparison experiment is performed using 97 collocated radiosonde stations and 23 GNSS stations equipped with meteorological sensors. The RMS and bias of the hourly PWV dataset are 2.87/?0.16 and 2.45/0.55 mm, respectively, when compared with radiosonde and GNSS stations equipped with meteorological sensors. Additionally, preliminary analysis of the hourly PWV dataset during the EI Niño event of 2014–2016 further indicates the capability of monitoring the daily changes in atmospheric water vapour. This finding is interesting and significant for further climate research.     

Estimation and analysis of GPS receiver differential code biases using KGN in Korean Peninsula

The total electron content (TEC) estimation by the Global Positioning System (GPS) can be seriously affected by the differential code biases (DCB), referred to as inter-frequency biases (IFB), of the satellite and receiver so that an accuracy of GPS–TEC value is dependent on the error of DCBs estimation. In this paper, we proposed the singular value decomposition (SVD) method to estimate the DCB of GPS satellites and receivers using the Korean GPS network (KGN) in South Korea. The receiver DCBs of about 49 GPS reference stations in KGN were determined for the accurate estimation of the regional ionospheric TEC. They obtained from the daily solution have large biases ranging from +5 to +27 ns for geomagnetic quiet days. The receiver DCB of SUWN reference station was compared with the estimates of IGS and JPL global ionosphere map (GIM). The results have shown comparatively good agreement at the level within 0.2 ns. After correction of receiver DCBs and knowing the satellite DCBs, the comparison between the behavior of the estimated TEC and that of GIMs was performed for consecutive three days. We showed that there is a good agreement between KASI model and GIMs.     

The impact of microwave absorber and radome geometries on GNSS measurements of station coordinates and atmospheric water vapour

We have used microwave absorbing material in different geometries around ground-based Global Navigation Satellite System (GNSS) antennas in order to mitigate multipath effects on the estimates of station coordinates and atmospheric water vapour. The influence of a hemispheric radome – of the same type as in the Swedish GPS network SWEPOS – was also investigated. Two GNSS stations at the Onsala Space Observatory were used forming a 12 m baseline. GPS data from October 2008 to November 2009 were analyzed by the GIPSY/OASIS II software using the Precise Point Positioning (PPP) processing strategy for five different elevation cutoff angles from 5° to 25°. We found that the use of the absorbing material decreases the offset in the estimated vertical component of the baseline from ∼27 mm to ∼4 mm when the elevation cutoff angle varies from 5° to 20°. The horizontal components are much less affected. The corresponding offset in the estimates of the atmospheric Integrated Water Vapour (IWV) decreases from ∼1.6 kg/m² to ∼0.3 kg/m². Changes less than 5 mm in the offsets in the vertical component of the baseline are seen for all five elevation cutoff angle solutions when the antenna was covered by a hemispheric radome. Using the radome affects the IWV estimates less than 0.4 kg/m² for all different solutions. IWV comparisons between a Water Vapour Radiometer (WVR) and the GPS data give consistent results.     

Improving the estimation of zenith dry tropospheric delays using regional surface meteorological data

Global Navigation Satellite Systems (GNSS) are emerging as possible tools for remote sensing high-resolution atmospheric water vapour that improves weather forecasting through numerical weather prediction models. Nowadays, the GNSS-derived tropospheric zenith total delay (ZTD), comprising zenith dry delay (ZDD) and zenith wet delay (ZWD), is achievable with sub-centimetre accuracy. However, if no representative near-site meteorological information is available, the quality of the ZDD derived from tropospheric models is degraded, leading to inaccurate estimation of the water vapour component ZWD as difference between ZTD and ZDD. On the basis of freely accessible regional surface meteorological data, this paper proposes a height-dependent linear correction model for a priori ZDD. By applying the ordinary least-squares estimation (OLSE), bootstrapping (BOOT), and leave-one-out cross-validation (CROS) methods, the model parameters are estimated and analysed with respect to outlier detection. The model validation is carried out using GNSS stations with near-site meteorological measurements. The results verify the efficiency of the proposed ZDD correction model, showing a significant reduction in the mean bias from several centimetres to about 5 mm. The OLSE method enables a fast computation, while the CROS procedure allows for outlier detection. All the three methods produce consistent results after outlier elimination, which improves the regression quality by about 20% and the model accuracy by up to 30%.     

DORIS and GPS monitoring of the Gavdos calibration site in Crete

Due to its specific geographical location as well as its geodetic equipment (DORIS, GNSS, microwave transponder and tide gauges), the Gavdos station in Crete, Greece is one of the very few sites around the world used for satellite altimetry calibration. To investigate the quality of the Gavdos geodetic coordinates and velocities, we analyzed and compared here DORIS and GPS-derived results obtained during several years of observations. The DORIS solution is the latest ignwd11 solution at IGN, expressed in ITRF2008, while the GPS solution was obtained using the GAMIT software package. Current results show that 1–2 mm/yr agreement can be obtained for 3-D velocity, showing a good agreement with current geophysical models. In particular, the agreement obtained for the vertical velocity is around 0.3–0.4 mm/yr, depending on the terrestrial reference frame. As a by-product of these geodetic GPS and DORIS results, Zenith Tropospheric Delays (ZTDs) estimations were also compared in 2010 between these two techniques, and compared to ECMWF values, showing a 6.6 mm agreement in dispersion without any significant difference between GPS and DORIS (with a 97.6% correlation), but with a 13–14 mm agreement in dispersion when comparing to ECMWF model (with only about 90% correlation for both techniques). These tropospheric delay estimations could also provide an external calibration of the tropospheric correction used for the geophysical data of satellite altimetry missions.     

Development of a GNSS water vapour tomography system using algebraic reconstruction techniques

A GNSS water vapour tomography system developed to reconstruct spatially resolved humidity fields in the troposphere is described. The tomography system was designed to process the slant path delays of about 270 German GNSS stations in near real-time with a temporal resolution of 30 min, a horizontal resolution of 40 km and a vertical resolution of 500 m or better. After a short introduction to the GPS slant delay processing the framework of the GNSS tomography is described in detail. Different implementations of the iterative algebraic reconstruction techniques (ART) used to invert the linear inverse problem are discussed. It was found that the multiplicative techniques (MART) provide the best results with least processing time, i.e., a tomographic reconstruction of about 26,000 slant delays on a 8280 cell grid can be obtained in less than 10 min. Different iterative reconstruction techniques are compared with respect to their convergence behaviour and some numerical parameters. The inversion can be considerably stabilized by using additional non-GNSS observations and implementing various constraints. Different strategies for initialising the tomography and utilizing extra information are discussed. At last an example of a reconstructed field of the wet refractivity is presented and compared to the corresponding distribution of the integrated water vapour, an analysis of a numerical weather model (COSMO-DE) and some radiosonde profiles.     

Mitigation of receiver biases in ionospheric observables from PPP with ambiguity resolution

PPP (Precise Point Positioning) is a GNSS (Global Navigation Satellite Systems) positioning method that requires SSR (State Space Representation) corrections in order to provide solutions with an accuracy of centimetric level. The so-called RT-PPP (Real-time PPP) is possible thanks to real-time precise SSR products, for orbits and clocks, provided by IGS (International GNSS Service) and its associate analysis centers such as CNES (Centre National d'Etudes Spatiales). CNES SSR products also enable RT-PPP with integer ambiguity resolution. In GNSS related literature, PPP with ambiguity resolution (PPP-AR) in real-time is often referred as PPP-RTK (PPP – Real Time Kinematic). PPP-WIZARD (PPP - With Integer and Zero-difference Ambiguity Resolution Demonstrator) is a software that is made available by CNES. This software is capable of performing PPP-RTK. It estimates slant ionospheric delays and other GNSS positioning parameters. Since ionospheric effects are spatially correlated by GNSS data from active networks, it is possible to model and provide ionospheric delays for any position in the network coverage area. The prior knowledge ionospheric delays can reduce positioning convergence for PPP-RTK users. Real-time ionospheric models could benefit from highly precise ionospheric delays estimated in PPP-AR. In this study, we demonstrate that ionospheric delays obtained throughout PPP-AR estimation are actu ally ionospheric observables. Ionospheric observables are biased by an order of few meters caused by the receiver hardware biases. These biases prohibit the use of PPP-WIZARD ionospheric delays to produce ionospheric models. Receiver biases correction is essential to provide ionospheric delays while using PPP-AR based ionospheric observables. In this contribution, a method was implemented to estimate and mitigate receiver hardware biases influence on slant ionospheric observables from PPP-AR. In order to assess the proposed approach, PPP-AR data from 12 GNSS stations were processed over a two-month period (March and April 2018). A comparison between IGS ionospheric products and PPP-AR based ionospheric observables corrected for receiver biases, resulted in a mean of differences of −39 cm and 51 cm standard deviation. The results are consistent with the accuracy of the IGS ionospheric products, 2–8 TECU, considering that 1 TECU is ~16 cm in L1. In another analysis, a comparison of ionospheric delays from 5 pairs of short baselines GNSS stations found an agreement of 0.001 m in mean differences with 22 cm standard deviation after receiver biases were corrected. Therefore, the proposed solution is promising and could produce high quality (1–2 TECU) slant ionospheric delays. This product can be used in a large variety of modeling approaches, since ionospheric delays after correction are unbiased. These results indicate that the proposed strategy is promising, and could benefit applications that require accuracy of 1–2 TECU (~16–32 cm in L1).     

GNSS water vapour tomography – Expected improvements by combining GPS,GLONASS and Galileo observations

The German Research Centre for Geosciences (GFZ) operates a GNSS water vapour tomography system using about 350 German GNSS stations. The GNSS data processing at the GFZ works in near real-time and provides zenith total delays, integrated water vapour and slant delay data operationally. This large data set of more than 50,000 slant delays per hour is used to reconstruct spatially resolved humidity fields by means of tomographic techniques. It can be expected that additional observations from the future Galileo system provide more information with improved quality. A simulation study covering 12 h at 14 July 2009 was therefore started to estimate the impact of GPS, Galileo and GLONASS data on the GNSS tomography. It is shown that the spatial coverage of the atmosphere with slant paths is highly improved by combining observations from two or three satellite systems. Equally important for a reliable tomographic reconstruction is the distribution of slant path intersections as they are required to locate the integrated delay information. The number of intersection points can be increased by a factor of 4 or 8 if two or three systems are combined and their distribution will cover larger regions of the atmosphere. The combined data sets can be used to increase the spatiotemporal resolution of the reconstructed humidity fields up to 30 km horizontally, 300 m vertically and 15 min. The reconstruction quality could not be improved considerably using the currently available techniques.     

GPS phase difference variation statistics: A comparison between phase scintillation index and proxy indices

Scintillated GPS phase observations are traditionally characterized by the phase scintillation index, derived from specialized GPS receivers usually tracking at 50 Hz. Geodetic quality GPS receivers, on the other hand, are normally tracking at frequencies up to 1 Hz. However, availability of continuously operating geodetic receivers both in time and geographical location are superior to scintillation receiver’s coverage in many parts of the world. This motivates scintillation studies using regional and global geodetic GPS networks. Previous studies have shown the usefulness of GPS estimated total electron content variations for detecting ionospheric irregularities. In this paper, collocated geodetic and scintillation receivers are employed to compare proxy indices derived from geodetic receivers with the phase scintillation index during quiet and moderately disturbed ionospheric conditions. Sensitivity of the phase scintillation indices at high latitude stations to geomagnetic activity is discussed. Global mapping of ionospheric disturbances using proxy indices from real-time 1 Hz GPS stations are also presented.     

The impact on tsunami detection from space using GNSS-reflectometry when combining GPS with GLONASS and Galileo

The devastating Sumatra tsunami in 2004 demonstrated the need for a tsunami early warning system in the Indian Ocean. Such a system has been installed within the German-Indonesian Tsunami Early Warning System (GITEWS) project. Tsunamis are a global phenomenon and for global observations satellites are predestined. Within the GITEWS project a feasibility study on a future tsunami detection system from space has therefore been carried out. The Global Navigation Satellite System Reflectometry (GNSS-R) is an innovative way of using GNSS signals for remote sensing. It uses ocean reflected GNSS signals for sea surface altimetry. With a dedicated Low Earth Orbit (LEO) constellation of satellites equipped with GNSS-R receivers, densely spaced sea surface height measurements could be established to detect tsunamis. Some general considerations on the geometry between LEO and GNSS are made in this simulation study. It exemplary analyzes the detection performance of a GNSS-R constellation at 900 km altitude and 60° inclination angle when applied to the Sumatra tsunami as it occurred in 2004. GPS is assumed as signal source and the combination with GLONASS and Galileo signals is investigated. It can be demonstrated, that the combination of GPS and Galileo is advantageous for constellations with few satellites while the combination with GLONASS is preferable for constellations with many satellites. If all three GNSS are combined, the best detection performance can be expected for all scenarios considered. In this case an 18 satellite constellation will detect the Sumatra tsunami within 17 min with certainty, while it takes 53 min if only GPS is considered.     

Ambiguity resolution in precise point positioning with hourly data for global single receiver

Integer ambiguity resolution (IAR) can improve precise point positioning (PPP) performance significantly. IAR for PPP became a highlight topic in global positioning system (GPS) community in recent years. More and more researchers focus on this issue. Progress has been made in the latest years. In this paper, we aim at investigating and demonstrating the performance of a global zero-differenced (ZD) PPP IAR service for GPS users by providing routine ZD uncalibrated fractional offsets (UFOs) for wide-lane and narrow-lane. Data sets from all IGS stations collected on DOY 1, 100, 200 and 300 of 2010 are used to validate and demonstrate this global service. Static experiment results show that an accuracy better than 1 cm in horizontal and 1–2 cm in vertical could be achieved in ambiguity-fixed PPP solution with only hourly data. Compared with PPP float solution, an average improvement reaches 58.2% in east, 28.3% in north and 23.8% in vertical for all tested stations. Results of kinematic experiments show that the RMS of kinematic PPP solutions can be improved from 21.6, 16.6 and 37.7 mm to 12.2, 13.3 and 34.3 mm for the fixed solutions in the east, north and vertical components, respectively. Both static and kinematic experiments show that wide-lane and narrow-lane UFO products of all satellites can be generated and provided in a routine way accompanying satellite orbit and clock products for the PPP user anywhere around the world, to obtain accurate and reliable ambiguity-fixed PPP solutions.     

Near real-time estimation of tropospheric water vapour content from ground based GNSS data and its potential contribution to weather now-casting in Austria

The importance of high resolution meteorological analysis of the atmosphere increased over the past years. A detailed analysis of the humidity field is an important precondition for a better monitoring of local and regional extreme precipitation events and for forecasts with improved spatial resolution. For this reason, the Austrian Meteorological Agency (ZAMG) is operating the spatial and temporal high resolution INCA system (Integrated Now-casting through Comprehensive Analysis) since begin of 2005. Errors in this analysis occur mainly in the areas of rapidly changing and hard to predict weather conditions or rugged topography with extreme differences in height such as the alpine area of Austria. The aim of this work is to provide GNSS based measurements of the tropospheric water vapour content with a temporal resolution of 1 h and a temporal delay of less than 1 h to assimilate these estimates into the INCA system. Additional requirement is an accuracy of better than 1 mm of the precipitable water (PW) estimates.     

Estimation of GPS instrumental biases from small scale network

With 4 GPS receivers located in the equatorial anomaly region in southeast China, this paper proposes a grid-based algorithm to determine the GPS satellites and receivers biases, and at the same time to derive the total electron content (TEC) with time resolution of 15 min and spatial resolution of 1° by 3.5° in latitude and longitude. By assuming that the TEC is identical at any point within a given grid block and the biases do not vary within a day, the algorithm arranges unknown biases and TECs with slant path TEC from the 4 receivers’ observations into a set of equations. Then the instrumental biases and the TECs are determined by using the least squares fitting technique. The performance of the method is examined by applying it to the GPS receiver chain observations selected from 16 geomagnetically quiet days in four seasons of 2006. It is found that the fitting agrees with the data very well, with goodness of fit ranging from 0.452 TECU to 1.914 TECU. Having a mean of 0.9 ns, the standard deviations for most of the GPS satellite biases are less than 1.0 ns for the 16 days. The GPS receiver biases are more stable than that of the GPS satellites. The standard deviation in the 4 receiver bias is from 0.370 ns to 0.855 ns, with a mean of 0.5 ns. Moreover, the instrumental biases are highly correlated with those derived from CODE and JPL with independent methods. The typical precision of the derived TEC is 5 TECU by a conservative estimation. These results indicate that the proposed algorithm is valid and qualified for small scale GPS network.     

Ionospheric differential error determination using ray tracing for a short baseline

Since the United States government discontinued Selective Availability (SA) on 1 May 2000, ionospheric effects have been responsible for the largest errors in GPS systems. The standard Differential GPS (DGPS) method is incapable of completely eliminating the ionospheric error. This paper describes a new approach to determine the differential ionospheric error between geographically distributed receiver stations. The ray paths of GPS signals were simulated using a modified Jones 3D ray tracing programme that includes the effect of the geomagnetic field. A Nelder–Mead optimisation algorithm was embedded in the program to precisely determine the satellite-to-station path. A realistic ionospheric model is essential for accurate ray tracing results and for estimates of differential error that are accurate on sub-centimetre scales. Here, the ionospheric model used in the ray tracing programme was developed by fitting realistic ionosphere profiles with a number of exponential functions. Results were compared to the theoretical approach. Results show that the differential delay is about 1–5 cm at low elevation angles for a short baseline of 10 km, as reported in other literature. This delay is often neglected in DGPS application. The differential delay also shows a pattern similar to that predicted by the Klobuchar model. The method proposed here can be used to improve future GPS applications.     

Towards PPP-RTK: Ambiguity resolution in real-time precise point positioning

Integer ambiguity resolution at a single station can be achieved by introducing predetermined uncalibrated phase delays (UPDs) into the float ambiguity estimates of precise point positioning (PPP). This integer resolution technique has the potential of leading to a PPP-RTK (real-time kinematic) model where PPP provides rapid convergence to a reliable centimeter-level positioning accuracy based on an RTK reference network. Nonetheless, implementing this model is technically subject to how rapidly we can fix wide-lane ambiguities, stabilize narrow-lane UPD estimates, and achieve the first ambiguity-fixed solution. To investigate these issues, we used 7 days of 1-Hz sampling GPS data at 91 stations across Europe. We find that at least 10 min of observations are required for most receiver types to reliably fix about 90% of wide-lane ambiguities corresponding to high elevations, and over 20 min to fix about 90% of those corresponding to low elevations. Moreover, several tens of minutes are usually required for a regional network before a narrow-lane UPD estimate stabilizes to an accuracy of far better than 0.1 cycles. Finally, for hourly data, ambiguity resolution can significantly improve the accuracy of epoch-wise position estimates from 13.7, 7.1 and 11.4 cm to 0.8, 0.9 and 2.5 cm for the East, North and Up components, respectively, but a few tens of minutes is required to achieve the first ambiguity-fixed solution. Therefore, from the timeliness aspect, our PPP-RTK model currently cannot satisfy the critical requirement of instantaneous precise positioning where ambiguity-fixed solutions have to be achieved within at most a few seconds. However, this model can still be potentially applied to some near-real-time remote sensing applications, such as the GPS meteorology.