An advanced residual error model for tropospheric delay estimation

Abstract

Global navigation satellite systems (GNSS) are widely used for safety-of-life positioning applications. Such applications require high integrity, availability, and continuity of the positioning service. Integrity is assessed by the definition of a protection level, which is an estimation of the maximum positioning error at extremely low probability levels. The emergence of multi-frequency civilian signals and the availability of satellite-based augmentation systems improve the modeling of ionospheric disturbances considerably. As a result, in many applications the tropospheric delay tends to become one of the limiting factors of positioning—especially at low elevation angles. The currently adopted integrity concepts employ a global constant to model the variance of the residual tropospheric delay error. We introduce a new approach to derive residual tropospheric delay error models using the extreme value analysis technique. Seventeen years of global numerical weather model fields are analyzed, and new residual error models are derived for some recently developed tropospheric delay models. Our approach provides models that consider both the geographical location and the seasonal variation of meteorological parameters. Our models are validated with a 17-year-long time series of zenith tropospheric delay estimates as provided by the International GNSS Service. The results show that the developed models are still conservative, while the maximal residual error of the tropospheric delay is still improved by 39–55%. This improvement yields higher service availability and continuity in safety-of-life applications of GNSS.

Modeling wide-area tropospheric delay corrections for fast PPP ambiguity resolution

“…On the other hand, using the tropospheric delay estimates of a regional GNSS reference network, a correction model can be generated and broadcasted to the users within the region, that is, the tropospheric delay regional augmentation (Takeichi et al 2009;Fund et al 2011;Kalinnikov et al 2012). The regional tropospheric delay model is usually determined by either a regional grid (Rózsa et al 2020;Li et al 2021) or the polynomial function (Zou et al 2018;Zhou et al 2020). Depending on the service region and the resolution, the distances between grid points can be large and cause communicating burden, whereas the polynomial function is usually determined with up to ten coefficients (second-order) and can be easily broadcasted to users with one-way communication, which is more feasible for small-area.…”

ARAIM Stochastic Model Refinements for GNSS Positioning Applications in Support of Critical Vehicle Applications

“…When applying another tropospheric correction model, such as the GPT2/GPT2w [32], a much smaller STD would be expected. In this subsection, the general extreme value (GEV) analysis method is used to evaluate the variable σ ZPD , considering the geographical and seasonal variations of the ZPD residuals after model correction [33].…”

Transformer-Based Global Zenith Tropospheric Delay Forecasting Model

“…When global navigation satellite system (GNSS) signals travel through the troposphere, they experience a delay and bending due to tropospheric refraction, resulting in tropospheric delay errors [1]. The error can be mapped to zenith direction to obtain zenith tropospheric delay (ZTD) by a mapping function [2,3].…”

“…shows the time-series trends. The The input parameters for train the K nearest neighbor model are the ZT eliminated the outliers and corresponding time t, calculated by Equation(1). W that the ZTD series were discontinuous and unevenly spaced.…”