Lv Yifei, Dai Zhiqiang, Zhao Qile, Yang Sheng, Zhou Jinning, Liu Jingnan
GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China.
Sensors (Basel). 2017 Jun 6;17(6):1308. doi: 10.3390/s17061308.
The application of real-time precise point positioning (PPP) requires real-time precise orbit and clock products that should be predicted within a short time to compensate for the communication delay or data gap. Unlike orbit correction, clock correction is difficult to model and predict. The widely used linear model hardly fits long periodic trends with a small data set and exhibits significant accuracy degradation in real-time prediction when a large data set is used. This study proposes a new prediction model for maintaining short-term satellite clocks to meet the high-precision requirements of real-time clocks and provide clock extrapolation without interrupting the real-time data stream. Fast Fourier transform (FFT) is used to analyze the linear prediction residuals of real-time clocks. The periodic terms obtained through FFT are adopted in the sliding window prediction to achieve a significant improvement in short-term prediction accuracy. This study also analyzes and compares the accuracy of short-term forecasts (less than 3 h) by using different length observations. Experimental results obtained from International GNSS Service (IGS) final products and our own real-time clocks show that the 3-h prediction accuracy is better than 0.85 ns. The new model can replace IGS ultra-rapid products in the application of real-time PPP. It is also found that there is a positive correlation between the prediction accuracy and the short-term stability of on-board clocks. Compared with the accuracy of the traditional linear model, the accuracy of the static PPP using the new model of the 2-h prediction clock in N, E, and U directions is improved by about 50%. Furthermore, the static PPP accuracy of 2-h clock products is better than 0.1 m. When an interruption occurs in the real-time model, the accuracy of the kinematic PPP solution using 1-h clock prediction product is better than 0.2 m, without significant accuracy degradation. This model is of practical significance because it solves the problems of interruption and delay in data broadcast in real-time clock estimation and can meet the requirements of real-time PPP.
实时精密单点定位（PPP）的应用需要实时精密轨道和时钟产品，这些产品应在短时间内进行预测，以补偿通信延迟或数据间隙。与轨道校正不同，时钟校正难以建模和预测。广泛使用的线性模型很难用小数据集拟合长周期趋势，并且在使用大数据集进行实时预测时会出现显著的精度下降。本研究提出了一种用于维持短期卫星时钟的新预测模型，以满足实时时钟的高精度要求，并在不中断实时数据流的情况下提供时钟外推。快速傅里叶变换（FFT）用于分析实时时钟的线性预测残差。通过FFT获得的周期项被用于滑动窗口预测，以显著提高短期预测精度。本研究还分析和比较了使用不同长度观测值的短期预报（小于3小时）的精度。从国际全球导航卫星系统服务（IGS）最终产品和我们自己的实时时钟获得的实验结果表明，3小时预测精度优于0.85纳秒。新模型可在实时PPP应用中替代IGS超快产品。还发现预测精度与车载时钟的短期稳定性之间存在正相关。与传统线性模型的精度相比，使用新模型的2小时预测时钟在N、E和U方向上的静态PPP精度提高了约50%。此外，2小时时钟产品的静态PPP精度优于0.1米。当实时模型出现中断时，使用1小时时钟预测产品的动态PPP解算精度优于0.2米，精度没有显著下降。该模型具有实际意义，因为它解决了实时时钟估计中数据广播的中断和延迟问题，能够满足实时PPP的要求。
