Ultra-rapid clock products provide the main parameters for real-time or near real-time precise point positioning services. However, it has been found that BeiDou ultra-rapid clock offsets do not meet the requirements for high-accuracy applications because of their low accuracy, especially regarding the prediction parts. This study proposes an improved model for BDS satellite ultra-rapid clock offset prediction based on BDS-2 and BDS-3 combined estimation. First, the preprocessing of the clock offset based on frequency data and a denoising method that employed a Tikhonov regularization algorithm was introduced to refine the observed series for predictive modeling. Second, given the coexistence of BDS-2 and BDS-3 satellites and the advantages of the BDS-3 onboard atomic clock, inter-satellite correlations between different satellites were used to adjust the stochastic function in estimating the coefficients for the prediction model. Third, to further improve the accuracy of the prediction model, the residuals of the clock offsets were analyzed by partial least squares regression, in which the main components related to the clock offsets were modeled by a back-propagation neural network. Six experimental schemes were introduced to verify the improved model. Experiments were divided into two groups to compare the preprocessing strategy and prediction model. The experimental results indicated: (1) both the BDS-2 and BDS-3 predicted clock offsets were mutually beneficial in the improved model; (2) because of the lower quality of the observed clock offset from BDS-3, preprocessing was used to improve the prediction accuracy by 1.0–15.2% for BDS-2, and reaching 23.2–31.9% for BDS-3; (3) the accuracy of the clock offsets were improved by 30.7–47.3% for BDS-2, and by 49.9–59.3% for BDS-3 within an 18-h period. The proposed improved model was found to have a significant effect on optimizing the ultra-rapid clock products of the International GNSS Monitoring and Assessment Service and GNSS analysis centers.

中文翻译：

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基于BDS-2和BDS-3组合估计的BDS卫星超快速时钟偏移预​​测改进模型。

超快速时钟产品为实时或接近实时的精确点定位服务提供主要参数。但是，已经发现北斗超快时钟偏移量由于其精度低而不能满足高精度应用的要求，特别是在预测零件方面。本研究提出了一种基于BDS-2和BDS-3组合估计的BDS卫星超快时钟偏移预​​测模型。首先，介绍了基于频率数据的时钟偏移的预处理和采用Tikhonov正则化算法的降噪方法，以完善观测序列以进行预测建模。其次，鉴于BDS-2和BDS-3卫星共存以及BDS-3车载原子钟的优势，在估计预测模型的系数时，使用不同卫星之间的卫星间相关性来调整随机函数。第三，为了进一步提高预测模型的准确性，通过偏最小二乘回归分析了时钟偏移的残差，其中与时钟偏移相关的主要成分是通过反向传播神经网络建模的。引入了六个实验方案来验证改进的模型。将实验分为两组，比较预处理策略和预测模型。实验结果表明：（1）BDS-2和BDS-3预测时钟偏移量在改进模型中是互利的；（2）由于观测到的BDS-3时钟偏移的质量较低，预处理用于将BDS-2的预测准确性提高1.0–15.2％，并将BDS-3的预测准确性提高至23.2–31.9％；（3）在18小时内，BDS-2的时钟偏移精度提高了30.7–47.3％，BDS-3的时钟偏移精度提高了49.9–59.3％。发现提出的改进模型对优化国际GNSS监视和评估服务以及GNSS分析中心的超快时钟产品具有重大影响。