摘要因为时间序列本身的非线性，要得到精确地预测结果很难，而且，数据缺失是现实中一个普遍存在的现象，所以在数据缺失的情况下对时间序列进行精确预测就更难。为了解决上述问题，本文用独立伯努利随机变量来表示观测数据中的随机缺失，并基于扩展卡尔曼滤波(EKF)首先推导出观测数据随机缺失下的非线性滤波算法；接着通过神经网络的权值和输出写出状态方程和观测方程，以此来建立适合于时间序列预测模型。论文主要完成的工作包括：84510

    (1) 概述了时间序列预测的基本概念，并对观测数据缺失下的时间序列预测所研究的目的意义和背景以及国内外的研究现状进行了总结和分析；

    (2) 主要介绍了BP神经网络的结构组成、主要算法和计算步骤，给出了数据缺失下扩展卡尔曼滤波的推导过程，同时也对其算法和性质做出了介绍；

    (3) 主要运用数据缺失下的EKF滤波和神经网络结合，对Mackey-Glass混沌时间序列进行了MATLAB仿真实验；

    (4) 对全文所完成的研究内容和以后有待进一步深入研究的内容作了总结。

    实验结果表明，利用推广的卡尔曼滤波和BP神经网络结合，有效地提高了观测的精度和复杂性。

毕业论文关键词：时间序列预测；观测量的随机缺失；扩展卡尔曼滤波

Abstract Because nonlinear time series itself, it is difficult to get accurate predictions, and the missing data is a reality of widespread phenomenon, so it is difficult to accurate predictions in the case of missing data for time series 。 To solve the problem, so it will sequence of independent Bernoulli random variable represents the observed data in the random outages and extended Kalman filter （EKF）based on nonlinear filtering algorithm first derived random interruption of observation data; followed by Neural Network weights and write the output state equation and observation equation, in order to establish a predictive model for time series。 Thesis work done include:

  (1)  the paper gives a brief overview of the time series and a summary analysis of  the missing observational under time series prediction studied object and the background and significance of the current research;

   (2)  it introduces  the structure of BP neural network, the main algorithms and calculation steps, given the extended Kalman filter Missing Data derivation process, and makes its algorithm and nature introduction;

   (3)  The paper uses EKF filtering and neural network mainly, and Mackey-Glass chaotic time series and terrestrial radiation intensity time series of MATLAB simulation。

   (4)  The contents of the full text of research needs to be done further research and later summarized。

 Experimental results show that using an Extended Kalman filter and BP neural network, effectively improve the precision and complexity of observations。

Keywords：time series prediction  random missing of the observational data  extended Kalman filtering (EKF) 

目 录

第一章 绪　论 1

1。1 时间序列 2

   1。1。1 时间序列简介 2

1。2 研究主题背景 2

1。3国内外研究现状 4

1。4 本论文研究主题 4

    1。5 本章小结 5

第二章 神经网络 6

2。1 人工神经网络