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.

中文翻译：

---

对流层延迟估计的高级残差模型

全球导航卫星系统（GNSS）被广泛用于生命安全定位应用。这样的应用需要定位服务的高度完整性，可用性和连续性。完整性是通过保护级别的定义来评估的，保护级别是在极低的概率级别下对最大定位误差的估计。多频民用信号的出现和基于卫星的增强系统的可用性大大改善了电离层扰动的建模。结果，在许多应用中，对流层延迟往往成为定位的限制因素之一，尤其是在低仰角下。当前采用的完整性概念采用全局常数来对对流层剩余延迟误差的方差建模。我们介绍了一种使用极值分析技术导出对流层延​​迟误差模型的新方法。分析了十七年的全球数值天气模型领域，并为一些最近开发的对流层延迟模型推导了新的残差模型。我们的方法提供了同时考虑地理位置和气象参数的季节性变化的模型。我们的模型已使用国际GNSS服务提供的长达17年的天顶对流层延迟估计时间序列进行了验证。结果表明，所开发的模型仍是保守的，而对流层延迟的最大残留误差仍可提高39-55％。这项改进在GNSS的生命安全应用程序中提供了更高的服务可用性和连续性。