Development of an adequate variance model for GNSS carrier phase observations based on turbulence theory

全球导航卫星系统（GNSS）观测值的方差协方差矩阵（VCM）在GNSS分析中起着关键作用。突出的例子是载波相位模糊度、坐标和对流层天顶延迟以及导出量的确定和验证。然而，目前使用的所有协方差模型都非常简化，因此它们只允许对结果进行有限的解释。在该项目的第一部分（SCHO 1314/11）期间，朝着用于GNSS观测的更现实和完全填充的VCM的概念取得了实质性进展。与常用的经验模型相比，我们的模型的主要优点是基于湍流理论，因此它与底层物理有直接的联系。因此，我们的方法将有助于更好地了解大气湍流的复杂过程。该方法将示范性地发展对流层中的大气活动波动及其随机描述。然而，它将可转移到进一步的变化，例如，电离层振荡在这里提出的项目的第二部分中，将充分利用基于药物的氯乙烯单体的概念。一方面，我们的VCM的参数估计的上下文中的好处将进行调查。另一方面，目前未知的非平稳，时间和空间相关的波动的观测和估计参数的时间序列之间的关系将被建立。基于连续性的VCM适合于模拟具有预定义的空间和时间相关性的非平稳随机过程。这项研究将有助于显着提高高分辨率参数时间序列中的表观和实际变化之间的可分离性;这是当今基于GNSS的火山监测，海啸预测或大气研究中的一个开放问题。

The variance covariance matrix (VCM) of Global Navigation Satellite System (GNSS) observations has a key function for the GNSS analysis. Prominent examples are the determination and validation of the carrier phase ambiguities, coordinates and tropospheric zenith delays as well as derived quantities. However, all currently used covariance models are very simplified and thus they allow only a restricted interpretation of the results. During the first part of this project (SCHO1314/1 1) substantial progress was made towards a concept of more realistic and fully-populated VCM for GNSS observations. The main advantage over common-used mathematical-empirical models is that our model is based on turbulence theory and thus it has a direct link to the underlying physics. Therefore our approach will contribute to a better understanding of the complex processes of atmospheric turbulence. The methodology will be exemplarily developed for refractivity fluctuations in the troposphere and their stochastic description. However it will be transferable to further variations, like e.g., ionospheric scintillations. In the second part of the project proposed here, the concept of turbulence-based VCM will be fully exploited. On the one hand, the benefits of our VCM in the context of parameter estimated will be investigated. On the other hand, the currently unknown relationship between non-stationary, temporally and spatially correlated fluctuations in the observations and the estimated parameter time series will be established. The turbulence-based VCM is appropriate for simulating non-stationary stochastic processes with predefined spatial and temporal correlations. This research will help to significantly improve the separability between apparent and actual variations in high-resolution parameter time series; an open issue in nowadays GNSS-based volcano monitoring, tsunami prediction, or atmosphere research.