In a satellite navigation system, high-precision prediction of satellite clock bias directly determines the accuracy of navigation, positioning, and time synchronization and is the key to realizing autonomous navigation. To further improve satellite clock bias prediction accuracy, we establish a satellite clock bias prediction model by using long short-term memory (LSTM) that can accurately express the nonlinear characteristics of the navigation satellite clock bias. Outliers in the original clock bias should be preprocessed before using the clock bias for prediction. By analyzing the working principle of the traditional median absolute deviations method, the ambiguity of the mathematical model of that method was improved. Experimental results show that the improved method is better than the traditional method at detecting gross errors. The single difference sequence of the preprocessed satellite clock bias was taken as the research object. First, a quadratic polynomial model was fit to the trend term of the single difference sequence. Second, based on the LSTM neural network model and the basic principles of supervised learning, a supervised learning LSTM network model (SL-LSTM) was proposed that models cyclic and random terms. Finally, the prediction function of the satellite clock bias was realized by extrapolating the model by adding a trend term. We adopt the GPS precision satellite clock bias of International GNSS Service data forecast experiments and apply wavelet neural network (WNN), autoregressive integrated moving average (ARIMA), and quadratic polynomial (QP) models to compare their prediction effects. The average prediction RMSE for 3 h, 6 h, 12 h, 1 d, and 3 d based on the SL-LSTM improved by approximately −21.80, −1.85, 8.57, 2.27, and 40.79%, respectively, compared with the results of the WNN. The average prediction RMSE based on the SL-LSTM improved by approximately 38.23, 65.48, 80.22, 85.18, and 94.51% compared with the ARIMA results. The average prediction RMSE based on the SL-LSTM improved by approximately 82.37, 75.88, 67.24, 45.71, and 58.22% compared with the QP results. Compared with the WNN, the SL-LSTM method has no obvious advantages in the prediction accuracy and stability in short-term prediction but achieves a better long-term prediction accuracy and stability. With an increased prediction duration, the SL-LSTM method is clearly better than the other three methods in terms of the prediction accuracy and stability. The results indicated that the quality of satellite clock bias prediction by the SL-LSTM method is better than that of the above three methods and is more suitable for the middle- and long-term prediction of satellite clock bias.

在卫星导航系统中，卫星时钟偏差的高精度预测直接决定导航，定位和时间同步的准确性，是实现自主导航的关键。为了进一步提高卫星时钟偏差的预测精度，我们通过使用长短期记忆（LSTM）建立了卫星时钟偏差的预测模型，该模型可以准确表示导航卫星时钟偏差的非线性特征。在使用时钟偏差进行预测之前，应先对原始时钟偏差中的异常值进行预处理。通过分析传统中值绝对偏差方法的工作原理，改进了该方法的数学模型的歧义。实验结果表明，改进的方法在检测粗差方面优于传统方法。以预处理后的卫星时钟偏差的单差序列为研究对象。首先，二次多项式模型适合单差序列的趋势项。其次，基于LSTM神经网络模型和监督学习的基本原理，提出了一种对循环项和随机项进行建模的监督学习LSTM网络模型（SL-LSTM）。最后，通过添加趋势项对模型进行外推，从而实现了卫星时钟偏差的预测功能。我们采用国际GNSS服务数据预测实验的GPS精确卫星时钟偏差，并应用小波神经网络（WNN），自回归综合移动平均值（ARIMA）和二次多项式（QP）模型来比较它们的预测效果。3 h，6 h，12 h，1 d的平均预测RMSE，与WNN的结果相比，基于SL-LSTM的3 d和3 d分别提高了约-21.80％，-1.85％，8.57％，2.27％和40.79％。与ARIMA结果相比，基于SL-LSTM的平均预测RMSE分别提高了约38.23％，65.48、80.22、85.18和94.51％。与QP结果相比，基于SL-LSTM的平均预测RMSE分别提高了约82.37％，75.88、67.24、45.71和58.22％。与WNN相比，SL-LSTM方法在短期预测中的预测准确性和稳定性方面没有明显优势，但可以实现更好的长期预测准确性和稳定性。随着预测持续时间的增加，就预测准确性和稳定性而言，SL-LSTM方法明显优于其他三种方法。