大气折射的映射函数与神经网络拟合比较分析

Atmospheric Refraction Numerical Fitting Research Based on Mapping Function and Neural Network

首先介绍映射函数和神经网络模拟方法在大气折射研究领域中的应用情况,总结映射函数的基本形式,分析BPNN的基本原理,进而研究了基本映射函数的BPNN变换。最终利用普尔科沃大气折射表这一数据平台与MATLAB7中的神经网络工具箱,建立与映射函数对应的BPNN模型,对普尔科沃大气折射表进行BPNN模拟。与相关文献的映射函数模拟进行比较分析:BPNN的模拟精度是4阶分式映射函数的2倍,不仅证明大气折射的映射函数模拟存在较大的拟合残差,而且表明BPNN对大气折射的非线性拟合优于映射函数,同时也为BPNN的隐层神经元具备挖掘高阶隐含信息提供了一个研究实例。

In the atmospheric refraction integral function numerical fitting, generally, approximate solution can be obtained by Mapping Function （MF） which theory and method have been matured and comprehended. But there is bigger fitting residual error by the MF, which consists of the atmospheric mode error and the parameter computation accumulated error. In 1980s intermediate stages, Parker and Rumelhart proposed the forward feed type error hack-propagating neural network algorithm （BPNN）, the modeling principle of which needs not any supposition mode and does not have the computation accumulated error that can effectively eliminate or weaken the residual error origin in the MF modehng, so the study of both approximate ability by the help of MATLAB7 BP toolbox and the Pulkovo atmospheric refraction table. First, it is introduced both application actuality at the atmospheric refraction field, summarized fundamental modes of the MF. The basic principle of the BPNN modehng has been analyzed. The BPNN transformation of the basic MF has been studied. Finally using the Pulkovo refraction table and the BPNN toolbox, BPNN model,established in correspondence with the MF, has carried on the BPNN fitting to the refraction table has been established. Simulation compare both the reference [6] and the BPNN shows that the BPNN is more feasible which accuracy is double of the 4-degree fraction form MF. The scheme not only proves that the MF fitting exits bigger residual error but also shows that nonlinear fitting ability of the BPNN is superior to the MF and obtains a better research example for that the hidden layer units of BPNN can mine the higher order hidden information.