School of Transportation, Civil Engineering and Architecture, Foshan University, Foshan 528000, China.
GNSS Center, Wuhan University, Wuhan 430079, China.
Sensors (Basel). 2023 Jun 5;23(11):5356. doi: 10.3390/s23115356.
The onboard atomic frequency standard (AFS) is a crucial element of Global Navigation Satellite System (GNSS) satellites. However, it is widely accepted that periodic variations can influence the onboard AFS. The presence of non-stationary random processes in AFS signals can lead to inaccurate separation of the periodic and stochastic components of satellite AFS clock data when using least squares and Fourier transform methods. In this paper, we characterize the periodic variations of AFS using Allan and Hadamard variances and demonstrate that the Allan and Hadamard variances of the periodics are independent of the variances of the stochastic component. The proposed model is tested against simulated and real clock data, revealing that our approach provides more precise characterization of periodic variations compared to the least squares method. Additionally, we observe that overfitting periodic variations can improve the precision of GPS clock bias prediction, as indicated by a comparison of fitting and prediction errors of satellite clock bias.
星载原子频率标准（Atomic Frequency Standard，AFS）是全球导航卫星系统（Global Navigation Satellite System，GNSS）卫星的关键组成部分。然而，人们普遍认为周期性变化会影响星载 AFS。当使用最小二乘法和傅里叶变换方法时，AFS 信号中存在非平稳随机过程会导致卫星 AFS 时钟数据的周期性和随机分量的分离不准确。在本文中，我们使用 Allan 和 Hadamard 方差来描述 AFS 的周期性变化，并证明了周期项的 Allan 和 Hadamard 方差与随机分量的方差无关。我们提出的模型经过模拟和实际时钟数据的测试，结果表明与最小二乘法相比，我们的方法可以更精确地描述周期性变化。此外，我们还观察到，过度拟合周期性变化可以提高 GPS 时钟偏差预测的精度，这可以通过比较卫星时钟偏差的拟合误差和预测误差来验证。
