基于混沌理论的GPS电离层预测研究
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摘要
地球上的大气是环境的重要组成要素,其中的电离层作为近地空间环境的重要组成部分,对于涉及电磁波信号传播的导航、大地测量、通信等工程领域有着重要的影响。随着GPS卫星导航系统的迅速发展及其导航定位精度的不断提高,电离层延迟对电磁波信号的影响越来越成为人们关注的热点,利用GPS系统对电离层进行现报和预报的需求也越来越强烈。
自然科学和社会经济各个领域对时间序列预测理论和方法有着广阔的需求,学者们提出了基于统计理论的各种各样的线性和非线性方法。然而,看似随机的系统可能有着确定性的动力学机制,看似无规则的时间序列数据可能是规则轨迹的一个侧面,20世纪末发现的这一混沌现象及其理论为非线性时间序列分析和预测提供了一个崭新的思路。
本文基于混沌理论,重点研究了电离层TEC时间序列,从定性和定量的角度分析了电离层的混沌特性。在此基础上,利用相空间重构恢复电离层TEC系统的动力学特征,进而在时间序列的噪声去除、预测方法方面进行了系统和深入的研究。
首先,论述了利用GPS技术计算并提取电离层TEC的方法和流程。针对汶川地震,利用重庆GPS-CORS站计算并探测地震之前TEC数据异常变化。利用我国境内的IGS站观测数据分析了日食前电离层的异常变化,验证了前人的结论。
其次,利用混沌分析的理论和方法,对电离层TEC进行了相空间重构,从重构的相图和重构后轨迹的最大Laypunov指数等可以判断出电离层TEC序列的混沌特性。分析不同纬度处的最大Laypunov指数变化规律,初步得出了可预测的时间尺度。不同时间采样率的TEC数据重构后相空间的比较可以看出它们所包含的系统动力学信息不完全相同。
第三,对电离层TEC数据进行了时频分析和多尺度分析,结合了TEC的主要影响因素进行了电离层的相关分析,为后续进行时间序列分析和预测提供了一些基础信息。利用电离层TEC时间序列的相空间重构,结合小波分解进行了消噪方法的研究,TEC数据本身的混沌特性的充分应用提高了消噪效果。
第四,根据混沌相空间轨迹的局部相似特性理论,采用一阶局域法进行了预测,和常用的方法进行比较,认为混沌局域法时间序列预测并没有明显优势。进一步借助神经网络方法,充分利用TEC时间序列的混沌特性,构造了一个混沌神经网络模型进行TEC预测分析,解决了神经网络结构确定的问题,并改善了训练的学习算法。
最后,基于多变量时间序列分析的理论,将电离层TEC与其相关的变量进行了组合预测,一定程度上改善了预测精度。
本文是混沌理论在电离层TEC分析中的一次全面而深入的实践,所得到的时间序列的混沌特征参数又充分地应用到了数据的分析和预测方法中。针对电离层TEC时间序列,在数据的消噪、构建神经网络预测模型以及神经网络的学习方法三个方面引入混沌思想后得到了较为理想的结果。本文的研究成果对于时间序列数据的处理、预测等方面的工作具有重要的参考意义和实用价值。
The earth atmosphere is an important component of the close-earth spatial environment. Among it, the ionosphere is greatly influencing the electromagnetic wave signal transmission related engineerig applications, such as navigation, geodetic and telecommunications, etc. With the fast development of the GPS satellite navigation system and the continuous improvement of its positioning and navigation accuracy, the impact of the ionospheric time delay on electromagnetic wave signal has increasingly become a hot topic concerned by human being. The requirement on the ionospheric real-time broadcast and forecast has also become more and more forceful, with the help of GPS.
The time series prediction theory and methods are widely applied to every field of the natural science and social economy. For them, many scholars have put forwards various linear and nonlinear methods. Afterwards, some scholars found that there is perhaps a fixed dynamic mechanism for the seemingly random system, and there is perhaps a regular track profile in the seemingly irregular time series data. At the end of the 20s century, the finding of chaotic phenomena and its theory provided a fully innovative thinking way for the analysis and prediction on the nonlinear time series.
This thesis mainly studies the chaotic characteristics of ionospheric TEC time series. Its chaotic characteristics are analyzed from both qualitative and quantitative angles. On this basis, the systematically dynamic characteristic of ionospheric TEC is renewed by means of phase space reconstruction. Moreover, the systematic and deep research is performed on the denoising and prediction of the time series.
Firstly, some methods and workflows are described on the ionospheric TEC to be calculated and extracted by GPS technology. Regarding the Wenchuan Earthquake, the abnormal variation on TEC data ahead of the disaster is calculated and detected by means of Chongqing GPS-CORS stations. The ionospheric abnormal variation before solar eclipse is analyzed by means of the IGS station observations in China and the past conclusion is proved.
Secondly, based on the theory and method of chaotic analysis, we re-construct the phase space for the ionospheric TEC. Its chaotic characteristic can be judged through the re-constructed phase diagram and trajectory Laypunov index and so on. By analyzing the variation rule of the maximum Laypunov index at different latitudes, we preliminarily get the time scale for prediction. The comparison of phase space after TEC data reconstrucation with different time sampling rates shows that their included systematic dynamics information is not wholly the same.
Thirdly, we do the time-frequency analysis and multi-scale analysis on the ionospheric TEC data. Combining with some major influencing factors on TEC, we also do the relevant ionospheric analysis. These provide some fundamental information for the next time series analysis and prediction. By utilizing the phase space reconstruction on the ionospheric TEC time series as well as combing the wavelet decompostion in denoising methods research, the denoising result is improved through the full applicaion of the chaotic characteristic of the TEC data itself.
Fourthly, according to the local similarity feature theory of the chaotic time series prediction, we use the one-rank local-region method to predict. Comparing with the common methods, we think there is not obvious advantage on time series prediction by chaotic local-region method. Moreover, by means of the neural networks method, we fully use the chaotic characteristic of the time series and set up a chaotic artificial nerual networks for TEC prediction and analysis. The issue related to determining the neural networks structure is solved. And the learning algorithm for training is improved.
Finally, based on the multi-variable time series analysis theory, we put the ionospheric TEC and its related variables together for combined prediction. Therefore, the prediction result is improved to some extent.
This thesis is a full and deep practice of the chaos theory to the ionospheric TEC analysis. The parameters of the chaotic characeristic being acquired in the time series have also been applied to the data analysis and prediction methods. As far as the ionospheric TEC time series are concerned, some faily good results have been found through three respective aspects, namely data denoising, neural networks prediction model construction and nerual networks learning method. Its research results have an important reference meaning and a practical value for time series data processsing and prediction related work.
自然科学和社会经济各个领域对时间序列预测理论和方法有着广阔的需求,学者们提出了基于统计理论的各种各样的线性和非线性方法。然而,看似随机的系统可能有着确定性的动力学机制,看似无规则的时间序列数据可能是规则轨迹的一个侧面,20世纪末发现的这一混沌现象及其理论为非线性时间序列分析和预测提供了一个崭新的思路。
本文基于混沌理论,重点研究了电离层TEC时间序列,从定性和定量的角度分析了电离层的混沌特性。在此基础上,利用相空间重构恢复电离层TEC系统的动力学特征,进而在时间序列的噪声去除、预测方法方面进行了系统和深入的研究。
首先,论述了利用GPS技术计算并提取电离层TEC的方法和流程。针对汶川地震,利用重庆GPS-CORS站计算并探测地震之前TEC数据异常变化。利用我国境内的IGS站观测数据分析了日食前电离层的异常变化,验证了前人的结论。
其次,利用混沌分析的理论和方法,对电离层TEC进行了相空间重构,从重构的相图和重构后轨迹的最大Laypunov指数等可以判断出电离层TEC序列的混沌特性。分析不同纬度处的最大Laypunov指数变化规律,初步得出了可预测的时间尺度。不同时间采样率的TEC数据重构后相空间的比较可以看出它们所包含的系统动力学信息不完全相同。
第三,对电离层TEC数据进行了时频分析和多尺度分析,结合了TEC的主要影响因素进行了电离层的相关分析,为后续进行时间序列分析和预测提供了一些基础信息。利用电离层TEC时间序列的相空间重构,结合小波分解进行了消噪方法的研究,TEC数据本身的混沌特性的充分应用提高了消噪效果。
第四,根据混沌相空间轨迹的局部相似特性理论,采用一阶局域法进行了预测,和常用的方法进行比较,认为混沌局域法时间序列预测并没有明显优势。进一步借助神经网络方法,充分利用TEC时间序列的混沌特性,构造了一个混沌神经网络模型进行TEC预测分析,解决了神经网络结构确定的问题,并改善了训练的学习算法。
最后,基于多变量时间序列分析的理论,将电离层TEC与其相关的变量进行了组合预测,一定程度上改善了预测精度。
本文是混沌理论在电离层TEC分析中的一次全面而深入的实践,所得到的时间序列的混沌特征参数又充分地应用到了数据的分析和预测方法中。针对电离层TEC时间序列,在数据的消噪、构建神经网络预测模型以及神经网络的学习方法三个方面引入混沌思想后得到了较为理想的结果。本文的研究成果对于时间序列数据的处理、预测等方面的工作具有重要的参考意义和实用价值。
The earth atmosphere is an important component of the close-earth spatial environment. Among it, the ionosphere is greatly influencing the electromagnetic wave signal transmission related engineerig applications, such as navigation, geodetic and telecommunications, etc. With the fast development of the GPS satellite navigation system and the continuous improvement of its positioning and navigation accuracy, the impact of the ionospheric time delay on electromagnetic wave signal has increasingly become a hot topic concerned by human being. The requirement on the ionospheric real-time broadcast and forecast has also become more and more forceful, with the help of GPS.
The time series prediction theory and methods are widely applied to every field of the natural science and social economy. For them, many scholars have put forwards various linear and nonlinear methods. Afterwards, some scholars found that there is perhaps a fixed dynamic mechanism for the seemingly random system, and there is perhaps a regular track profile in the seemingly irregular time series data. At the end of the 20s century, the finding of chaotic phenomena and its theory provided a fully innovative thinking way for the analysis and prediction on the nonlinear time series.
This thesis mainly studies the chaotic characteristics of ionospheric TEC time series. Its chaotic characteristics are analyzed from both qualitative and quantitative angles. On this basis, the systematically dynamic characteristic of ionospheric TEC is renewed by means of phase space reconstruction. Moreover, the systematic and deep research is performed on the denoising and prediction of the time series.
Firstly, some methods and workflows are described on the ionospheric TEC to be calculated and extracted by GPS technology. Regarding the Wenchuan Earthquake, the abnormal variation on TEC data ahead of the disaster is calculated and detected by means of Chongqing GPS-CORS stations. The ionospheric abnormal variation before solar eclipse is analyzed by means of the IGS station observations in China and the past conclusion is proved.
Secondly, based on the theory and method of chaotic analysis, we re-construct the phase space for the ionospheric TEC. Its chaotic characteristic can be judged through the re-constructed phase diagram and trajectory Laypunov index and so on. By analyzing the variation rule of the maximum Laypunov index at different latitudes, we preliminarily get the time scale for prediction. The comparison of phase space after TEC data reconstrucation with different time sampling rates shows that their included systematic dynamics information is not wholly the same.
Thirdly, we do the time-frequency analysis and multi-scale analysis on the ionospheric TEC data. Combining with some major influencing factors on TEC, we also do the relevant ionospheric analysis. These provide some fundamental information for the next time series analysis and prediction. By utilizing the phase space reconstruction on the ionospheric TEC time series as well as combing the wavelet decompostion in denoising methods research, the denoising result is improved through the full applicaion of the chaotic characteristic of the TEC data itself.
Fourthly, according to the local similarity feature theory of the chaotic time series prediction, we use the one-rank local-region method to predict. Comparing with the common methods, we think there is not obvious advantage on time series prediction by chaotic local-region method. Moreover, by means of the neural networks method, we fully use the chaotic characteristic of the time series and set up a chaotic artificial nerual networks for TEC prediction and analysis. The issue related to determining the neural networks structure is solved. And the learning algorithm for training is improved.
Finally, based on the multi-variable time series analysis theory, we put the ionospheric TEC and its related variables together for combined prediction. Therefore, the prediction result is improved to some extent.
This thesis is a full and deep practice of the chaos theory to the ionospheric TEC analysis. The parameters of the chaotic characeristic being acquired in the time series have also been applied to the data analysis and prediction methods. As far as the ionospheric TEC time series are concerned, some faily good results have been found through three respective aspects, namely data denoising, neural networks prediction model construction and nerual networks learning method. Its research results have an important reference meaning and a practical value for time series data processsing and prediction related work.
引文
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