神经网络在GPS精密星历数据拟合中的应用

The Application of Neural Network in GPS Precise Ephemeris Data Fitting

由于经典的拉格朗日多项式内插在对GPS精密星历(SP3)进行插值时,多项式阶数过高会导致拟合的精密星历坐标差值较大点均集中在重合区两端,并且坐标差值影响可达20mm,甚至更大,目前IGS提供的最终轨道精度优于25mm,因此,精密星历拟合中龙格现象的影响不可忽略。为了减少这种现象,利用神经网络对GPS精密星历进行数据拟合,采用建立前馈网络的方法,通过对训练函数、传输函数、输入结点个数等参数进行调整,得出了利用神经网络对GPS精密星历进行拟合的最佳参数设置。研究结果表明,当训练算法采用trainlm,隐层结点个数为4时,两个隐含层分别采用传输函数logsig()和tansig()的训练效果明显好于其他组合,只用41步就能得到极小的拟合误差2.16081e-020,远小于设计的训练精度。

Because of the classic Lagrange Polynomial Interpolation to GPS precise ephemeris (SP3) for interpolation, polynomial high order number will cause the fitting precise ephemeris larger coordinates difference points concentrated at both ends of the overlap area, and coordinate difference influence could be 20 mm, even more, at present the IGS provide the final orbit accurate than 25 mm, therefore, the Runge's Phenomenon in the precise ephemeris fitting can not be ignored. In order to reduce this kind of phenomenon, using neural networks to GPS precise ephemeris for data fitting. Through the establishment of feed forward network test, the training function, the transfer function, the number of input nodes is adjusted. The results of the study show that, when the training algorithm uses trainlm, the number of hidden layer nodes is 4,two hidden layers were used to the transfer function logsig() and tansig() training effect was significantly better than other combinations, only 41 epochs can get tiny fitting error 2.16081e-020,is far less than the design training accuracy.