06 Fakultät Luft- und Raumfahrttechnik und Geodäsie
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/7
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Item Open Access Improving PPP positioning and troposphere estimates using an azimuth-dependent weighting scheme(2024) He, Shengping; Hobiger, Thomas; Becker, DorisAsymmetric troposphere modeling is crucial in Precise Point Positioning (PPP). The functional model of the asymmetric troposphere has been thoroughly studied, while the stochastic model lacks discussion. Currently, there is no suitable stochastic model for asymmetric tropospheric conditions, potentially degrading the positioning accuracy and the reliability of Zenith Total/Wet Delay (ZTD/ZWD) estimates. This paper introduces an Azimuth-Dependent Weighting (ADW) scheme that utilizes information from asymmetric mapping functions to adaptively weight Global Navigation Satellite System (GNSS) observations affected by azimuth-dependent errors. The concept of ADW has been validated using Numerical Weather Prediction data and International GNSS Service data. The results indicate that ADW effectively improves the coordinate repeatability of the PPP solution by approximately 10%in the horizontal and 20%in the vertical direction. Additionally, ADW appears to be capable to improve the ZWD estimates during the PPP convergence period and yields smoother ZWD estimates. Consequently, it is recommended to adopt this new weighting scheme in PPP applications when an asymmetric mapping functions is employed.Item Open Access The B-spline mapping function (BMF) : representing anisotropic troposphere delays by a single self-consistent functional model(2024) He, Shengping; Hobiger, Thomas; Becker, DorisTroposphere’s asymmetry can introduce errors ranging from centimeters to decimeters at low elevation angles, which cannot be ignored in high-precision positioning technology and meteorological research. The traditional two-axis gradient model, which strongly relies on an open-sky environment of the receiver, exhibits misfits at low elevation angles due to their simplistic nature. In response, we propose a directional mapping function based on cyclic B-splines named B-spline mapping function (BMF). This model replaces the conventional approach, which is based on estimating Zenith Wet Delay and gradient parameters, by estimating only four parameters which enable a continuous characterization of the troposphere delay across any directions. A simulation test, based on a numerical weather model, was conducted to validate the superiority of cyclic B-spline functions in representing tropospheric asymmetry. Based on an extensive analysis, the performance of BMF was assessed within precise point positioning using data from 45 International GNSS Service stations across Europe and Africa. It is revealed that BMF improves the coordinate repeatability by approximately 10%horizontally and about 5% vertically. Such improvements are particularly pronounced under heavy rainfall conditions, where the improvement of 3-dimensional root mean square error reaches up to 13%.Item Open Access On the asymmetric troposphere modeling in PPP(2025) He, Shengping; Hobiger, Thomas (Prof. Dr. techn.)Tropospheric asymmetry is a crucial error term which needs to be considered for the refinement of tropospheric modeling in Precise Point Positioning (PPP). Wet asymmetry can account for more than one-fifth of the wet delay, causing residuals ranging from centimeters to decimeters at low elevation angles. Tropospheric asymmetry significantly impacts high-precision positioning applications and meteorological research. First models of tropospheric asymmetry are based on the concept of tropospheric horizontal gradient, which has prompted the development of many new models, including the widely used two-axis gradient model. However, the traditional two-axis gradient model is insufficient to represent the complex azimuthal variation of tropospheric delays. To address this issue, a directional mapping function based on cyclic B-spline functions, the so called the B-spline Mapping Function (BMF), is proposed. BMF enables a continuous characterization of tropospheric delay across any azimuth direction. The effectiveness of BMF has been validated using both numerical weather model data and Global Navigation Satellite System (GNSS) data from International GNSS Service (IGS) stations in Europe and Africa. Results reveal that compared to the conventional gradient model, BMF improves coordinate repeatability by approximately 10% horizontally and 5% vertically. The improvement in 3D-RMSE can reach up to 15% under heavy rainfall conditions. While the functional model of the asymmetric troposphere has been extensively studied, the stochastic model of the asymmetric troposphere remains unexplored. The absence of a suitable stochastic model for asymmetric troposphere reduces the accuracy of positioning and Zenith Total/Wet Delay (ZTD/ ZWD) estimates. In this work, an Azimuth-Dependent Weighting (ADW) scheme is introduced with the purpose to adaptively weight GNSS observations affected by azimuth-dependent errors using parameters from asymmetric mapping functions. Validated using NWP and IGS data, ADW improves PPP solution coordinate repeatability by approximately 10% horizontally and 20% vertically. ADW also improves ZWD estimates during the PPP convergence period and yields smoother results. Thus, this new weighting scheme is recommended for PPP applications when the asymmetric mapping functions are used. In the currently used conventional PPP processing strategies, ZWD is usually dynamically estimated as a stochastic parameter. During the convergence period, ZWD could become negative due to the lack of physical constraints. This problem increases the convergence time and reduces short-term accuracy of PPP. To address this issue, a method which incorporates physical constraints on ZWD using Non-negative Least Squares (NNLS) methods and Karush–Kuhn–Tucker (KKT) conditions is proposed. This method reduces ZWD outliers during the PPP convergence period, and effectively improves the short-term accuracy for the Up component of the position up to 20%. Similar to tropospheric delays, there are some other systematic errors that also have azimuth-dependent characteristics, such as multipath error. Consequently, when using an asymmetric troposphere model, the gradient parameters may absorb some of the multipath error, leading to biases in ZWD/ZTD estimates. Due to the site-specific nature of multipath errors, establishing a universal mathematical model is challenging. Therefore, in this thesis, a commercial simulator is employed to simulate multipath signals under different scenarios. The impact of multipath errors on estimated ZTD time series and methods to mitigate this effect by adjusting the process noise of ZWD are studied. This thesis provides an in-depth exploration of asymmetric troposphere modeling in PPP from four perspectives: functional models, stochastic models, constraint conditions, and systematic errors. It investigates methods for refining troposphere modeling and analyzes their effectiveness in PPP and GNSS meteorology.