Prochniewicz Dominik, Wezka Kinga, Kozuchowska Joanna
Faculty of Geodesy and Cartography, Warsaw University of Technology, 00-661 Warsaw, Poland.
Sensors (Basel). 2021 Jul 3;21(13):4566. doi: 10.3390/s21134566.
The stochastic model, together with the functional model, form the mathematical model of observation that enables the estimation of the unknown parameters. In Global Navigation Satellite Systems (GNSS), the stochastic model is an especially important element as it affects not only the accuracy of the positioning model solution, but also the reliability of the carrier-phase ambiguity resolution (AR). In this paper, we study in detail the stochastic modeling problem for Multi-GNSS positioning models, for which the standard approach used so far was to adopt stochastic parameters from the Global Positioning System (GPS). The aim of this work is to develop an individual, empirical stochastic model for each signal and each satellite block for GPS, GLONASS, Galileo and BeiDou systems. The realistic stochastic model is created in the form of a fully populated variance-covariance (VC) matrix that takes into account, in addition to the Carrier-to-Noise density Ratio (C/N0)-dependent variance function, also the cross- and time-correlations between the observations. The weekly measurements from a zero-length and very short baseline are utilized to derive stochastic parameters. The impact on the AR and solution accuracy is analyzed for different positioning scenarios using the modified Kalman Filter. Comparing the positioning results obtained for the created model with respect to the results for the standard elevation-dependent model allows to conclude that the individual empirical stochastic model increases the accuracy of positioning solution and the efficiency of AR. The optimal solution is achieved for four-system Multi-GNSS solution using fully populated empirical model individual for satellite blocks, which provides a 2% increase in the effectiveness of the AR (up to 100%), an increase in the number of solutions with errors below 5 mm by 37% and a reduction in the maximum error by 6 mm compared to the Multi-GNSS solution using the elevation-dependent model with neglected measurements correlations.
随机模型与功能模型一起构成了观测的数学模型，该模型能够对未知参数进行估计。在全球导航卫星系统（GNSS）中，随机模型是一个特别重要的元素，因为它不仅影响定位模型解算的精度，还影响载波相位模糊度解算（AR）的可靠性。在本文中，我们详细研究了多GNSS定位模型的随机建模问题，迄今为止所采用的标准方法是采用来自全球定位系统（GPS）的随机参数。这项工作的目的是为GPS、格洛纳斯、伽利略和北斗系统的每个信号和每个卫星块开发一个单独的经验随机模型。实际的随机模型以一个完整的方差 - 协方差（VC）矩阵的形式创建，该矩阵除了考虑与载噪比（C/N0）相关的方差函数外，还考虑了观测之间的交叉相关性和时间相关性。利用零长度和非常短基线的每周测量数据来推导随机参数。使用改进的卡尔曼滤波器分析了不同定位场景下对AR和解算精度的影响。将创建的模型所获得的定位结果与标准仰角相关模型的结果进行比较，可以得出结论：单独的经验随机模型提高了定位解算的精度和AR的效率。对于使用针对卫星块单独的完整经验模型的四系统多GNSS解算，实现了最优解，与使用忽略测量相关性的仰角相关模型的多GNSS解算相比，AR的有效性提高了2%（高达100%），误差低于5mm的解的数量增加了37%，最大误差减少了6mm。
