Tomasz Hadas

Near-real-time regional troposphere models for the GNSS precise point positioning technique

The GNSS precise point positioning (PPP) technique requires high quality product (orbits and clocks) application, since their error directly affects the quality of positioning. For real-time purposes it is possible to utilize ultra-rapid precise orbits and clocks which are disseminated through the Internet. In order to eliminate as many unknown parameters as possible, one may introduce external information on zenith troposphere delay (ZTD). It is desirable that the a priori model is accurate and reliable, especially for real-time application. One of the open problems in GNSS positioning is troposphere delay modelling on the basis of ground meteorological observations. Institute of Geodesy and Geoinformatics of Wroclaw University of Environmental and Life Sciences (IGG WUELS) has developed two independent regional troposphere models for the territory of Poland. The first one is estimated in near-real-time regime using GNSS data from a Polish ground-based augmentation system named ASG-EUPOS established by Polish Head Office of Geodesy and Cartography (GUGiK) in 2008. The second one is based on meteorological parameters (temperature, pressure and humidity) gathered from various meteorological networks operating over the area of Poland and surrounding countries. This paper describes the methodology of both model calculation and verification. It also presents results of applying various ZTD models into kinematic PPP in the post-processing mode using Bernese GPS Software. Positioning results were used to assess the quality of the developed models during changing weather conditions. Finally, the impact of model application to simulated real-time PPP on precision, accuracy and convergence time is discussed.

Impact and implementation of higher-order ionospheric effects on precise GNSS applications

High precision Global Navigation Satellite Systems (GNSS) positioning and time transfer require correcting signal delays, in particular higher-order ionospheric (I2+) terms. We present a consolidated model to correct second- and third-order terms, geometric bending and differential STEC bending effects in GNSS data. The model has been implemented in an online service correcting observations from submitted RINEX files for I2+ effects. We performed GNSS data processing with and without including I2+ corrections, in order to investigate the impact of I2+ corrections on GNSS products. We selected three time periods representing different ionospheric conditions. We used GPS and GLONASS observations from a global network and two regional networks in Poland and Brazil. We estimated satellite orbits, satellite clock corrections, Earth rotation parameters, troposphere delays, horizontal gradients, and receiver positions using a global GNSS solution, Real-Time Kinematic (RTK) and Precise Point Positioning (PPP) techniques. The satellite-related products captured most of the impact of I2+ corrections, with the magnitude up to 2 cm for clock corrections, 1 cm for the along- and cross-track orbit components, and below 5 mm for the radial component. The impact of I2+ on troposphere products turned out to be insignificant in general. I2+ corrections had limited influence on the performance of ambiguity resolution and the reliability of RTK positioning. Finally, we found that I2+ corrections caused a systematic shift in the coordinate domain that was time- and region-dependent, and reached up to -11 mm for the North component of the Brazilian stations during the most active ionospheric conditions. .

Optimum stochastic modeling for GNSS tropospheric delay estimation in real-time

In GNSS data processing, the station height, receiver clock and tropospheric delay (ZTD) are highly correlated to each other. Although the zenith hydrostatic delay of the troposphere can be provided with sufficient accuracy, zenith wet delay (ZWD) has to be estimated, which is usually done in a random walk process. Since ZWD temporal variation depends on the water vapor content in the atmosphere, it seems to be reasonable that ZWD constraints in GNSS processing should be geographically and/or time dependent. We propose to take benefit from numerical weather prediction models to define optimum random walk process noise. In the first approach, we used archived VMF1-G data to calculate a grid of yearly and monthly means of the difference of ZWD between two consecutive epochs divided by the root square of the time lapsed, which can be considered as a random walk process noise. Alternatively, we used the Global Forecast System model from National Centres for Environmental Prediction to calculate random walk process noise dynamically in real-time. We performed two representative experimental campaigns with 20 globally distributed International GNSS Service (IGS) stations and compared real-time ZTD estimates with the official ZTD product from the IGS. With both our approaches, we obtained an improvement of up to 10% in accuracy of the ZTD estimates compared to any uniformly fixed random walk process noise applied for all stations.

Weighting of Multi-GNSS Observations in Real-Time Precise Point Positioning

The combination of Global Navigation Satellite Systems (GNSS) may improve the accuracy and precision of estimated coordinates, as well as the convergence time of Precise Point Positioning (PPP) solutions. The key conditions are the correct functional model and the proper weighting of observations, for which different characteristics of multi-GNSS signals should be taken into account. In post-processing applications, the optimum stochastic model can be obtained through the analysis of post-fit residuals, but for real-time applications the stochastic model has to be defined in advanced. We propose five different weighting schemes for the GPS + GLONASS + Galileo + BeiDou combination, including two schemes with no intra-system differences, and three schemes that are based on signal noise and/or quality of satellite orbits. We perform GPS-only and five multi-GNSS solutions representing each weighting scheme. We analyze formal errors of coordinates, coordinate repeatability, and solution convergence time. We found that improper or equal weighting may improve formal errors but decreases coordinate repeatability when compared to the GPS-only solution. Intra-system weighting based on satellite orbit quality allows for a reduction of formal errors by 40%, for shortening convergence time by 40% and 47% for horizontal and vertical components, respectively, as well as for improving coordinate repeatability by 6%.

On the estimation of higher-order ionospheric effects in precise point positioning

Higher-order ionospheric effects, if not properly accounted for, can propagate into geodetic parameter estimates. For this reason, several investigations have led to the development and refinement of formulas for the correction of second- and third-order ionospheric errors, bending effects and total electron content variations due to excess path length. Standard procedures for computing higher-order terms typically rely on slant total electron content computed either from global ionospheric maps (GIMs) or using GNSS observations corrected using differential code biases (DCBs) provided by an external process. In this study, we investigate the feasibility of estimating slant ionospheric delay parameters accounting for both first- and second-order ionospheric effects directly within a precise point positioning (PPP) solution. It is demonstrated that proper handling of the receiver DCB is critical for the PPP method to provide unbiased estimates of the position. The proposed approach is therefore not entirely free from external inputs since GIMs are required for isolating the receiver DCB, unless the latter is provided to the PPP filter. In terms of positioning performance, the PPP approach is capable of mitigating higher-order ionospheric effects to the same level as existing approaches. Due to the inherent risks associated with constraining slant ionospheric delay parameters in PPP during disturbed ionospheric conditions, the reliability of the method can be greatly enhanced when the receiver DCB is available a priori, such as for permanent GNSS stations.