On the asymmetric troposphere modeling in PPP

Abstract

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.