The Selection of Basic Functions for a Time-Varying Model of Unmodeled Errors in Medium and Long GNSS Baselines
The Selection of Basic Functions for a Time-Varying Model of Unmodeled Errors in Medium and Long GNSS Baselines
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DOI：
10.3390/rs15205022
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发表时间：
2023-10
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影响因子：
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通讯作者：
Jiafu Wang;Xianwen Yu;Angela Aragon-Angel;A. Rovira‐Garcia;Hao Wang
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作者：
Jiafu Wang;Xianwen Yu;Angela Aragon-Angel;A. Rovira‐Garcia;Hao Wang
未建模误差对提高全球导航卫星系统的定位精度起着至关重要的作用。很少有研究使用其时间相关性来解决中长期基线中的未建模误差，这对于实现精确和实时的解决方案非常有益。然而，在处理未建模误差之前，首先需要确定合理的基本函数来拟合这些未建模误差。因此，我们研究了两种定位模式下时变未建模误差的基本函数的选择：估计大气延迟和使用中频组合。我们选择三个基本函数：多项式，正弦函数和组合函数。利用30 ~ 220 km范围内的4条基线提供的未建模误差数据进行了拟合实验和定位实验。二阶拟合的均方根误差约为2 mm，相应的残差一般在30 s左右收敛到3 mm。在使用二阶多项式的拟合未建模误差校正观测值之后，定位结果在所有方向上显示出约40%至80%的改善。我们得出结论，二阶多项式是最佳的基本功能，在所有两种定位模式。
Unmodeled errors play a critical role in improving the positioning accuracy of Global Navigation Satellite Systems. Few studies have addressed unmodeled errors in medium and long baselines using their time correlation, which is highly beneficial for achieving a precise and real-time solution. However, before tackling unmodeled errors, it is first necessary to determine reasonable basic functions to fit such unmodeled errors. Therefore, we study the selection of basic functions for time-varying unmodeled errors in two positioning modes: estimating atmospheric delays and using an IF combination. We choose three basic functions: polynomials, sinusoidal functions, and combinatorial functions. Fitting experiments and positioning experiments are conducted using the unmodeled error data provided by four baselines ranging from 30 to 220 km. The Root Mean Square Errors fitted by the second order are approximately 2 mm. The corresponding residuals generally converge to 3 mm in about 30 s. After correcting the observations using the fitted unmodeled errors of the second-order polynomial, the positioning results show improvements of about 40% to 80% in all directions. We conclude that the second-order polynomial is the optimal basic function in all two positioning modes.