Zenith Tropospheric Delay Estimates Research Articles

Potential of Cost-Efficient Single Frequency GNSS Receivers for Water Vapor Monitoring

Dual-frequency Global Navigation Satellite Systems (GNSSs) enable the estimation of Zenith Tropospheric Delay (ZTD) which can be converted to Precipitable Water Vapor (PWV). The density of existing GNSS monitoring networks is insufficient to capture small-scale water vapor variations that are especially important for extreme weather forecasting. A densification with geodetic-grade dual-frequency receivers is not economically feasible. Cost-efficient single-frequency receivers offer a possible alternative. This paper studies the feasibility of using low-cost receivers to increase the density of GNSS networks for retrieval of PWV. We processed one year of GNSS data from an IGS station and two co-located single-frequency stations. Additionally, in another experiment, the Radio Frequency (RF) signal from a geodetic-grade dual-frequency antenna was split to a geodetic receiver and two low-cost receivers. To process the single-frequency observations in Precise Point Positioning (PPP) mode, we apply the Satellite-specific Epoch-differenced Ionospheric Delay (SEID) model using two different reference network configurations of 50–80 km and 200–300 km mean station distances, respectively. Our research setup can distinguish between the antenna, ionospheric interpolation, and software-related impacts on the quality of PWV retrievals. The study shows that single-frequency GNSS receivers can achieve a quality similar to that of geodetic receivers in terms of RMSE for ZTD estimations. We demonstrate that modeling of the ionosphere and the antenna type are the main sources influencing the ZTD precision.

Real-time precise point positioning-based zenith tropospheric delay for precipitation forecasting

GPS-based Zenith Tropospheric Delay (ZTD) estimation should be easily obtained in a cost-effective way, however, the most previous studies focus on post-processed ZTD estimates using satellite orbit and clock products with at least 3–9 hours latency provided by International GNSS Service (IGS), which limits the GNSS meteorological application for nowcasting. With the development of IGS’s real-time pilot project (RTPP), this limitation was removed by April, 2013 as real-time satellite orbit and clock products can be obtained on-line. In this paper, on the one hand, the GPS-derived ZTD estimation was evaluated using the IGS final and real-time satellite products based on independently developed PPP software. On the other hand, the analysis of the time series of GPS-derived ZTD by least-square fitting of a broken line tendency for a full year of observations, and a forecasting method for precipitation is proposed based on the ZTD slope in the ascending period. The agreement between ZTD slope and the ground rainfall records suggested that the proposed method is useful for the assisted forecasting, especially for short-term alarms.

MSE-impact of PPP-RTK ZTD estimation strategies

In PPP-RTK network processing, the wet component of the zenith tropospheric delay (ZTD) cannot be precisely modelled and thus remains unknown in the observation equations. For small networks, the tropospheric mapping functions of different stations to a given satellite are almost equal to each other, thereby causing a near rank-deficiency between the ZTDs and satellite clocks. The stated near rank-deficiency can be solved by estimating the wet ZTD components relatively to that of the reference receiver, while the wet ZTD component of the reference receiver is constrained to zero. However, by increasing network scale and humidity around the reference receiver, enlarged mismodelled effects could bias the network and the user solutions. To consider both the influences of the noise and the biases, the mean-squared errors (MSEs) of different network and user parameters are studied analytically employing both the ZTD estimation strategies. We conclude that for a certain set of parameters, the difference in their MSE structures using both strategies is only driven by the square of the reference wet ZTD component and the formal variance of its solution. Depending on the network scale and the humidity condition around the reference receiver, the ZTD estimation strategy that delivers more accurate solutions might be different. Simulations are performed to illustrate the conclusions made by analytical studies. We find that estimating the ZTDs relatively in large networks and humid regions (for the reference receiver) could significantly degrade the network ambiguity success rates. Using ambiguity-fixed network-derived PPP-RTK corrections, for networks with an inter-station distance within 100 km, the choices of the ZTD estimation strategy is not crucial for single-epoch ambiguity-fixed user positioning. Using ambiguity-float network corrections, for networks with inter-station distances of 100, 300 and 500 km in humid regions (for the reference receiver), the root-mean-squared errors (RMSEs) of the estimated user coordinates using relative ZTD estimation could be higher than those under the absolute case with differences up to millimetres, centimetres and decimetres, respectively.

Assessment of the Impact of GNSS Processing Strategies on the Long-Term Parameters of 20 Years IWV Time Series

Advanced processing of collected global navigation satellite systems (GNSS) observations allows for the estimation of zenith tropospheric delay (ZTD), which in turn can be converted to the integrated water vapour (IWV). The proper estimation of GNSS IWV can be affected by the adopted GNSS processing strategy. To verify which of its elements cause deterioration and which improve the estimated GNSS IWV, we conducted eight reprocessings of 20 years of GPS observations (01.1996–12.2015). In each of them, we applied a different mapping function, the zenith hydrostatic delay (ZHD) a priori value, the cut-off angle, software, and the positioning method. Obtained in such a way, the ZTD time series were converted to the IWV using the meteorological parameters sourced from the ERA-Interim. Then, based on them, the long-term parameters were estimated and compared to those obtained from the IWV derived from the radio sounding (RS) observations. In this paper, we analyzed long-term parameters such as IWV mean values, linear trends, and amplitudes of annual and semiannual oscillations. A comparative analysis showed, inter alia, that in terms of the investigation of the IWV linear trend the precise point positioning (PPP) method is characterized by higher accuracy than the differential one. It was also found that using the GPT2 model and the higher elevation mask brings benefits to the GNSS IWV linear trend estimation.

Real-Time Tropospheric Delay Retrieval from Multi-GNSS PPP Ambiguity Resolution: Validation with Final Troposphere Products and a Numerical Weather Model

The multiple global navigation satellite systems (multi-GNSS) bring great opportunity for the real-time retrieval of high-quality zenith tropospheric delay (ZTD), which is a critical quality for atmospheric science and geodetic applications. In this contribution, a multi-GNSS precise point positioning (PPP) ambiguity resolution (AR) analysis approach is developed for real-time tropospheric delay retrieval. To validate the proposed multi-GNSS ZTD estimates, we collected and processed data from 30 Multi-GNSS Experiment (MGEX) stations; the resulting real-time tropospheric products are evaluated by using standard post-processed troposphere products and European Centre for Medium-Range Weather Forecasts analysis (ECMWF) data. An accuracy of 4.5 mm and 7.1 mm relative to the Center for Orbit Determination in Europe (CODE) and U.S. Naval Observatory (USNO) products is achievable for real-time tropospheric delays from multi-GNSS PPP ambiguity resolution after an initialization process of approximately 5 min. Compared to Global Positioning System (GPS) results, the accuracy of retrieved zenith tropospheric delay from multi-GNSS PPP-AR is improved by 16.7% and 31.7% with respect to USNO and CODE final products. The GNSS-derived ZTD time-series exhibits a great agreement with the ECMWF data for a long period of 30 days. The average root mean square (RMS) of the real-time zenith tropospheric delay retrieved from multi-GNSS PPP-AR is 12.5 mm with respect to ECMWF data while the accuracy of GPS-only results is 13.3 mm. Significant improvement is also achieved in terms of the initialization time of the multi-GNSS tropospheric delays, with an improvement of 50.7% compared to GPS-only fixed solutions. All these improvements demonstrate the promising prospects of the multi-GNSS PPP-AR method for time-critical meteorological applications.

Reduction of ZTD outliers through improved GNSS data processing and screening strategies

Abstract. Though Global Navigation Satellite System (GNSS) data processing has been significantly improved over the years, it is still commonly observed that zenith tropospheric delay (ZTD) estimates contain many outliers which are detrimental to meteorological and climatological applications. In this paper, we show that ZTD outliers in double-difference processing are mostly caused by sub-daily data gaps at reference stations, which cause disconnections of clusters of stations from the reference network and common mode biases due to the strong correlation between stations in short baselines. They can reach a few centimetres in ZTD and usually coincide with a jump in formal errors. The magnitude and sign of these biases are impossible to predict because they depend on different errors in the observations and on the geometry of the baselines. We elaborate and test a new baseline strategy which solves this problem and significantly reduces the number of outliers compared to the standard strategy commonly used for positioning (e.g. determination of national reference frame) in which the pre-defined network is composed of a skeleton of reference stations to which secondary stations are connected in a star-like structure. The new strategy is also shown to perform better than the widely used strategy maximizing the number of observations available in many GNSS programs. The reason is that observations are maximized before processing, whereas the final number of used observations can be dramatically lower because of data rejection (screening) during the processing. The study relies on the analysis of 1 year of GPS (Global Positioning System) data from a regional network of 136 GNSS stations processed using Bernese GNSS Software v.5.2. A post-processing screening procedure is also proposed to detect and remove a few outliers which may still remain due to short data gaps. It is based on a combination of range checks and outlier checks of ZTD and formal errors. The accuracy of the final screened GPS ZTD estimates is assessed by comparison to ERA-Interim reanalysis.

Analysing the Zenith Tropospheric Delay Estimates in On-line Precise Point Positioning (PPP) Services and PPP Software Packages.

As Global Navigation Satellite System (GNSS) signals travel through the troposphere, a tropospheric delay occurs due to a change in the refractive index of the medium. The Precise Point Positioning (PPP) technique can achieve centimeter/millimeter positioning accuracy with only one GNSS receiver. The Zenith Tropospheric Delay (ZTD) is estimated alongside with the position unknowns in PPP. Estimated ZTD can be very useful for meteorological applications, an example is the estimation of water vapor content in the atmosphere from the estimated ZTD. PPP is implemented with different algorithms and models in online services and software packages. In this study, a performance assessment with analysis of ZTD estimates from three PPP online services and three software packages is presented. The main contribution of this paper is to show the accuracy of ZTD estimation achievable in PPP. The analysis also provides the GNSS users and researchers the insight of the processing algorithm dependence and impact on PPP ZTD estimation. Observation data of eight whole days from a total of nine International GNSS Service (IGS) tracking stations spread in the northern hemisphere, the equatorial region and the southern hemisphere is used in this analysis. The PPP ZTD estimates are compared with the ZTD obtained from the IGS tropospheric product of the same days. The estimates of two of the three online PPP services show good agreement (<1 cm) with the IGS ZTD values at the northern and southern hemisphere stations. The results also show that the online PPP services perform better than the selected PPP software packages at all stations.

Evaluation of spatial and temporal characteristics of GNSS-derived ZTD estimates in Nigeria

This study presents an in-depth analysis to comprehend the spatial and temporal variability of zenith tropospheric delay (ZTD) over Nigeria during the period 2010–2014, using estimates from Global Navigation Satellite Systems (GNSS) data. GNSS data address the drawbacks in traditional techniques (e.g. radiosondes) by means of observing periodicities in ZTD. The ZTD estimates show weak spatial dependence among the stations, though this can be attributed to the density of stations in the network. Tidal oscillations are noticed at the GNSS stations. These oscillations have diurnal and semi-diurnal components. The diurnal components as seen from the ZTD are the principal source of the oscillations. This upshot may perhaps be ascribed to temporal variations in atmospheric water vapour on a diurnal scale. In addition, the diurnal ZTD cycles exhibited noteworthy seasonal dependence, with larger amplitudes in the rainy (wet) season and smaller ones in the harmattan (dry) season. Notably, the stations in the northern part of the country reach very high amplitudes in the months of June, July and August at the peak of the wet season, characterized by very high rainfall. This pinpoints the fact that in view of the small amount of atmospheric water vapour in the atmosphere, usually around 10%, its variations greatly influence the corresponding diurnal and seasonal discrepancies of ZTD. This study further affirms the prospective relevance of ground-based GNSS data to atmospheric studies. GNSS data analysis is therefore recommended as a tool for future exploration of Nigerian weather and climate.

Assessment of Three Tropospheric Delay Models (IGGtrop, EGNOS and UNB3m) Based on Precise Point Positioning in the Chinese Region.

Tropospheric delays are one of the main sources of errors in the Global Navigation Satellite System (GNSS). They are usually corrected by using tropospheric delay models, which makes the accuracy of the models rather critical for accurate positioning. To provide references for suitable models to be chosen for GNSS users in China, we conduct herein a comprehensive study of the performances of the IGGtrop, EGNOS and UNB3m models in China. Firstly, we assess the models using 5 years’ Global Positioning System (GPS) derived Zenith Tropospheric Delay (ZTD) series from 25 stations of the Crustal Movement Observation Network of China (CMONOC). Then we study the effects of the models on satellite positioning by using various Precise Point Positioning (PPP) cases with different tropospheric delay resolutions, the observation data processed in PPP is from 21 base stations of CMONOC for a whole year of 2012. The results show that: (1) the Root Mean Square (RMS) of the IGGtrop model is about 4.4 cm, which improves the accuracy of ZTD estimations by about 24% for EGNOS and 19% for UNB3m; (2) The positioning error in the vertical component of the PPP solution obtained by using the IGGtrop model is about 15.0 cm, which is about 30% and 21% smaller than those of the EGNOS and UNB3m models, respectively. In summary, the IGGtrop model achieves the best performance among the three models in the Chinese region.

EFFECTS OF OCEAN TIDE MODELS ON GNSS-ESTIMATED ZTD AND PWV IN TURKEY

Abstract. Global Navigation Satellite System (GNSS) observations can precisely estimate the total zenith tropospheric delay (ZTD) and precipitable water vapour (PWV) for weather prediction and atmospheric research as a continuous and all-weather technique. However, apart from GNSS technique itself, estimations of ZTD and PWV are subject to effects of geophysical models with large uncertainties, particularly imprecise ocean tide models in Turkey. In this paper, GNSS data from Jan. 1st to Dec. 31st of 2014 are processed at 4 co-located GNSS stations (GISM, DIYB, GANM, and ADAN) with radiosonde from Turkish Met-Office along with several nearby IGS stations. The GAMIT/GLOBK software has been used to process GNSS data of 30-second sample using the Vienna Mapping Function and 10° elevation cut-off angle. Also tidal and non-tidal atmospheric pressure loadings (ATML) at the observation level are also applied in GAMIT/GLOBK. Several widely used ocean tide models are used to evaluate their effects on GNSS-estimated ZTD and PWV estimation, such as IERS recommended FES2004, NAO99b from a barotropic hydrodynamic model, CSR4.0 obtained from TOPEX/Poseidon altimetry with the model FES94.1 as the reference model and GOT00 which is again long wavelength adjustments of FES94.1 using TOPEX/Poseidon data at 0.5 by 0.5 degree grid. The ZTD and PWV computed from radiosonde profile observations are regarded as reference values for the comparison and validation. In the processing phase, five different strategies are taken without ocean tide model and with four aforementioned ocean tide models, respectively, which are used to evaluate ocean tide models effects on GNSS-estimated ZTD and PWV estimation through comparing with co-located Radiosonde. Results showed that ocean tide models have greatly affected the estimation of the ZTD in centimeter level and thus the precipitable water vapour in millimeter level, respectively at stations near coasts. The ocean tide model FES2004 that is the product of assimilation of the altimetric data of ERS2, TOPEX/POSEIDON and the data of a global tide gauge network, gave the most accurate results when compared to radiosonde with ±1.99 mm in PWV at stations near coastline. While other ocean tides models agree each other at millimeter level in PWV. However, at inland GNSS stations, ocean tide models have less effects on GNSS-estimated ZTD and PWV, e.g., with ±1.0 mm in ZTD and ±0.1 mm in PWV.

Monitoring Climate Changes on Small Scale Networks Using Ground Based GPS and Meteorological Data

Abstract The total zenith tropospheric delay (ZTD) and its components, hydrostatic and wet parts are important parameters of the atmosphere and directly or indirectly reflect climate processes. This possibility can be more adaptive when meteorological data are combined to co-located meteorological sensors with GPS stations. In this paper eighteen months with one hour time interval ZTD estimates of a permanent GPS station are analyzed with the associated atmospheric parameters provided from a co-located meteorological sensor. The mathematical relationship through the multiple stepwise regression analysis reflects the plausible physical link of temperature and relative humidity values with ZTD’s. This regression equation is assessed by a second data set performed by a small GPS baseline few months later for the same study area. It was found that mainly due to the zenith wet delay variations and with the help of fundamental meteorological equations the behavior of water vapor pressure can be monitored and estimated. This is possible when an appropriate setup of GPS stations and a co-located meteorological sensor exist and if the GPS stations sound the same part of atmosphere. Therefore, the GPS tropospheric products are good indicators for a climate monitoring tool and can help address the physics of a climate model.

Comparison of individual and combined zenith tropospheric delay estimations during CONT08 campaign

CONT campaigns are 2-week campaigns of continuous VLBI observations. The IERS working group on combination at the observation level uses these campaigns to study such combinations. In this work, combinations of DORIS, GPS, SLR, and VLBI technique measurements are studied during CONT08. We present different results concerning the use of common zenith tropospheric delay (ZTD) during the combination. We compare the ZTD obtained separately using each individual technique data processing, the combined ZTD, and the ZTD derived from a meteorological model. This resulted in a high level of consistency between each of these ZTD at a sub-centimeter level, a consistency which especially depends on the number of observations per estimated ZTD and the humidity level in the troposphere. We noted that GPS provides the main information about the combined ZTD, the other techniques providing complementary information when a lack of GPS observations occurs.

A high-quality, homogenized, global, long-term (1993-2008) DORIS precipitable water data set for climate monitoring and model verification

For the first time a high-quality, consistent, global, long-term data set of zenith tropospheric delay (ZTD) and precipitable water (PW) is produced from Doppler orbitography radiopositioning integrated by satellite (DORIS) measurements at 81 sites. The data set was screened using a two-level procedure. First, postprocessing information is used to apply range checks and outlier checks to ZTD and formal error estimates. Second, outliers are detected by comparing DORIS ZTD with European Centre for Medium-Range Weather Forecasts reanalysis (ERA-Interim) data. These procedures reject 3% and 1% of the data, respectively. A linear drift is evidenced in the screened DORIS ZTD data compared to ERA-Interim and Global Positioning System (GPS) data, which potentially results from biases introduced by the progressive replacement of Alcatel antennas with Starec antennas. The DORIS PW is homogenized by applying a bias correction computed form comparison with ERA-Interim data each time station equipment is changed. The homogenized DORIS data are in excellent agreement with GPS data (correlation of 0.98 and standard deviation of differences of 1.5 kg m−2) and with ERA-Interim and satellite PW data (correlation > 0.95 and standard deviation of differences < 2.7 kg m−2). The agreement with radiosonde data is less good. Preliminary results of water vapor trends and variability are shown for 31 sites with more than 10 years of data. Good consistency is found between DORIS PW trends and ERA-Interim trends, which demonstrates the high potential of the DORIS PW data set for climate monitoring and model verification. The final DORIS PW data set is freely available in the supporting information.

A comparative study of zenith tropospheric delay and precipitable water vapor estimates using scientific GPS processing software and web based automated PPP service

The zenith tropospheric delay (ZTD) is a significant error source which affects the GPS signal propagation time. ZTD time series can directly or indirectly reflect the weather variations. In geodetic studies their computation is important since it improves position accuracy. Sophisticated software packages using network data of ground-based GPS receivers are used for this purpose. During the last years, various web based precise point positioning (PPP) services can provide position solutions. Additional products, such as ZTD estimates, can be derived both from PPP as well as from network solutions. Research institutes and laboratories like JPL provide similar services. This study’s objective is twofold. In a first instance we used the Bernese and GAMIT software packages and the PPP service via the JPL webpage to estimate ZTD values every hour for a period of one month. We selected a geographical area in Greece, where seasonal weather variations are frequent and GPS permanent station infrastructure is available. The estimated ZTD values derived from GPS processing for a single station were compared with the ZTD estimates derived directly from the Saastamoinen model using meteorological data from a co-located meteorological sensor as input to this model. The results show an rms agreement of about 45 mm. The second scope of this study is to compare precipitable water (PW) values between different processing schemes. For this purpose, we used the derived zenith wet delay estimates of each processing scheme and a global formula for the computation of the weighted mean temperature of the atmosphere for our area of study. The rms differences between the web PPP solution and the Bernese derived estimates were 0.35 mm. The rms of the differences between and the web PPP solution and the GAMIT derived estimates of PW were 1.67 mm. We conclude that this difference follows from the zenith hydrostatic delay component that needs to be properly modeled when high accuracy results are required.

Establishment of a new tropospheric delay correction model over China area

The tropospheric delay is one of the main error sources for radio navigation technologies and other ground- or space-based earth observation systems. In this paper, the spatial and temporal variations of the zenith tropospheric delay (ZTD), especially their dependence on altitude over China region, are analyzed using ECMWF (European Centre for Medium-Range Weather Forecast) pressure-level atmospheric data in 2004 and the ZTD series in 1999-2007 measured at 28 GPS stations from the Crustal Movement Observation Network of China (CMONC). A new tropospheric delay correction model (SHAO) is derived and a regional realization of this model for China region named SHAO-C is established. In SHAO-C model, ZTD is modeled directly by a cosine function together with an initial value and an amplitude at a reference height in each grid, and the variation of ZTD along altitude is fitted with a second-order polynomial. The coefficients of SHAO-C are generated using the meteorology data in China area and given at two degree latitude and longitude interval, featuring regional characteristics in order to facilitate a wide range of navigation and other surveying applications in and around China. Compared with the EGNOS (European Geostationary Navigation Overlay Service) model, which has been used globally and recommended by the European Union Wide Area Augmentation System, the ZTD prediction (in form of spatial and temporal projection) accuracy of the SHAO-C model is significantly improved over China region, especially at stations of higher altitudes. The reasons for the improvement are: (1) the reference altitude of SHAO-C parameters are given at the average height of each grid, and (2) more detailed description of complicated terrain variations in China is incorporated in the model. Therefore, the accumulated error at higher altitude can be reduced considerably. In contrast, the ZTD has to be calculated from the mean sea level with EGNOS and other models. Compared with the direct estimation of ZTD from the 28 GPS stations, the accuracy of the derived ZTD using the SHAO-C model can be improved by 60.5% averagely compared with the EGNOS model. The overall bias and rms are 2.0 and 4.5 cm, respectively, which should be sufficient to satisfy the requirements of most GNSS navigation or positioning applications in terms of the tropospheric delay correction.

Effect of broadcast and precise satellite orbits in the estimation of Zenith tropospheric delay and integrated precipitable water vapour from GPS

Global Positioning System (GPS) estimates the total delay in zenith direction by the propagation delay of the neutral atmosphere in presence of water vapour present in the troposphere. This total delay has been treated as a nuisance parameter for many years by the geodesists. The above delay have two parts dry delay and wet delay and known as Zenith Hydrostatic Delay (ZHD) and Zenith Wet Delay (ZWD) respectively. The Integrated Precipitable Water Vapour (IPWV) is estimated through ZWD overlying the receiver at ground-based station. The accuracy of the above said estimates depends on the quality of the predicted satellite orbits, which are not the same for each individual satellite. India Meteorological Department (IMD) is operationally estimating the IPWV on near real time basis at five places and matches fairly well (error ~6.7 mm) with Radisonde (RS) data. This paper examine the effect of International GPS Service (IGS) predicted precise orbits and near real time predicted rapid or broadcast orbits supplied by the Scripps Orbit and Permanent Array Center (SOPAC) on Zenith Total Delay (ZTD) and IPWV estimates by calculating the mean Bias and Root Mean Square Error (RMSE) for ZTD and IPWV in mm for all the five stations. The observed bias for ZTD is almost of the order of less than 1 mm in most cases and RMSE is less than 6 mm. Similarly the bias observed in the case of derived IPWV is almost negligible and RMSE is less than 1 mm.

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.

Accuracy improvement of zenith tropospheric delay estimation based on GPS precise point positioning algorithm

In the precise point positioning (PPP), some impossible accurately simulated systematic errors still remained in the GPS observations and will inevitably degrade the precision of zenith tropospheric delay (ZTD) estimation. The stochastic models used in the GPS PPP mode are compared. In this paper, the research results show that the precision of PPP-derived ZTD can be obviously improved through selecting a suitable stochastic model for GPS measurements. Low-elevation observations can cover more troposphere information that can improve the estimation of ZTD. A new stochastic model based on satellite low elevation cosine square is presented. The results show that the stochastic model using satellite elevation-based cosine square function is better than previous stochastic models.

Assessment of GPS data for meteorological applications over Africa: Study of error sources and analysis of positioning accuracy

The aim of this study is to assess the availability and quality of data from the International GNSS Service (IGS) Global Positioning System (GPS) network in Africa, especially for retrieving zenith tropospheric delay (ZTD), from which precipitable water vapour (PWV) can be derived, in view of application to the African Monsoon Multidisciplinary Analysis (AMMA) project. Three major error sources for the GPS data analysis evaluating PWV in Africa are the accuracy of the satellite orbits, the correction for the radio delay induced by the ionosphere and the vertical site displacements due to ocean loading. The first part of this study examines these error sources and the validity of GPS data for meteorological applications in Africa in dedicated analyses spanning the year 2001. These analyses were performed using the IGS precise orbits. Weak degradation of baseline precision with increasing baseline lengths suggests that the average orbital error is not limiting the GPS analysis in Africa. The impact of the ionosphere has been evaluated during a maximum of solar activity in 2001. The loss of L 2 data has actually been observed. It amounts to 2% on average for 2001, with maxima of 8% during magnetic storm events. A slight decrease in formal accuracy of ZTD seems to be related to the loss of L 2 data at the end of the day. This indicates that scintillation effects are present in the GPS observations but however are not a major limitation. The impact of ocean loading is found to be significant on ZTD estimates (up to ±2 mm in equivalent PWV). The use of a proper ocean loading model eliminates this effect. The second aspect of this study concerns the IGS analysis quality for the African stations. The accuracy has been assessed through position dispersion between individual solutions and the most recent version of the IGS combined solution IGb00, and residuals from the transformation of the IGS combined solution into the International Terrestrial Reference Frame 2005. The positioning performance of the IGS analysis is consistent with an accuracy in ZTD of ±6 mm (±1 mm in PWV), as requested for meteorological applications such as planned in AMMA.

GPS measurements of ocean loading and its impact on zenith tropospheric delay estimates: a case study in Brittany, France

The results from a global positioning system (GPS) experiment carried out in Brittany, France, in October 1999, aimed at measuring crustal displacements caused by ocean loading and quantifying their effects on GPS-derived tropospheric delay estimates, are presented. The loading effect in the vertical and horizontal position time series is identified, however with significant disagreement in amplitude compared to ocean loading model predictions. It is shown that these amplitude misfits result from spatial tropospheric heterogeneities not accounted for in the data processing. The effect of ocean loading on GPS-derived zenith total delay (ZTD) estimates is investigated and a scaling factor of 4.4 between ZTD and station height for a 10° elevation cutoff angle is found (i.e. a 4.4-cm station height error would map into a 1-cm ZTD error). Consequently, unmodeled ocean loading effects map into significant errors in ZTD estimates and ocean loading modeling must be properly implemented when estimating ZTD parameters from GPS data for meteorological applications. Ocean loading effects must be known with an accuracy of better than 3 cm in order to meet the accuracy requirements of meteorological and climatological applications of GPS-derived precipitable water vapor.