广义回归神经网络在卫星钟差短期预报中的应用

近年来，神经网络(Neural Network,简称NN)在非线性系统的预测方面取得了广泛的应用。考虑到卫星钟差包含了复杂的非线性因素，所以将一种新型神经网络-广义回归神经网络(Generalized Regression Neural Network,GRNN)应用于钟差预报中。采用“滑动窗”方式构建样本数据以提高数据利用率，为提高网络的泛化能力，利用K重交叉验证法(K-fold Cross-Validation)对网络进行训练学习，并根据最小均方根误差(Root Mean Square Error,RMSE)确定最优平滑因子。利用国际GNSS服务(International GNSS Service,IGS)公布的精密GPS卫星钟差数据进行预报实验，并与传统二次多项式模型对比分析。结果表明：GRNN模型在24h的预报跨度内的误差可达ns级，并较多项式模型有更好的稳定性；对于线性钟差，GRNN模型要逊于多项式模型，而对于非线性钟差，GRNN模型则明显优于多项式模型，初步验证了GRNN用于钟差预报的可行性、有效性以及实用性。

Application of Generalized Regression Neural Network in Short-time Prediction for Satellite Clock Error

Neural Network(NN) has been widely used in forecast of nonlinear systems over the past years. Generalized Regression Neural Network(GRNN), which is a new kind of NN, is proposed to predict satellite clock error because of its nonlinear characteristic. An slip window pattern is used organize sample data, which can raise utilization rate of data. In order to improve forecast ability of GRNN, the method called K-fold Cross-Validation is employed to train network. Furthermore, the optimal smoothing factor is determined in terms of Root Mean Square Error(RMSE). An experiment is carried out to verify GRNN effectiveness. Real satellite clock error data from International GNSS Service(IGS) is trained to construct the GRNN model, then this model is used to predict clock error. And also Clock error is forecasted using quadratic polynomial. Results show that GRNN model can reach ns-level prediction accuracy within 24 hour. Moreover, GNRR is more stable in comparison with quadratic polynomial. GRNN is worse than quadratic polynomial when predicting linear clock error, however, the former is obviously better than the latter when nonlinear clock error.