一种快速重叠开窗拟合算法及其在电离层拟合中的应用
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摘要
提出一种基于分段的重叠窗口拟合算法,它将分段窗口分为边界区、重叠区和内部区,通过对前后窗口重叠区拟合值的加权平均,使窗口间拟合值的变化连续。采用实测GNSS电离层数据,分别对逐历元滑动窗口、独立分段窗口和重叠窗口3种算法进行实验对比,其中在以400历元窗口对NKLG站G01的电离层拟合计算中,逐历元法耗费121.618 s,而独立分段法和重叠分段法只分别用了0.396 s和0.985 s,计算效率分别为前者的307倍和123倍。结果证明,该算法兼顾计算精度与执行效率,是处理数据量较大、连续且变化剧烈的时间序列的有效方法。
In this paper, we propose a segmentation-based overlapping window fitting algorithm that divides the segmentation window into boundary, overlapping, and inner areas. By weighted averaging the fitting values of the overlapping area of the front and back windows, the fitting value between windows changes continuously. Using GNSS ionospheric data, three algorithms of epoch-by-epoch sliding window, independent segment window and overlapping window are compared. In the ionospheric fitting calculation of G01 at NKLG station with 400 epoch windows, the epoch-by-epoch method consumes 121.618 s, while the independent and overlapping subsection methods only use 0.396 s and 0.985 s, respectively, and the calculation efficiency is 307 times and 123 times that of the former. The results show that the proposed algorithm takes account of both computational accuracy and execution efficiency, and is a good method to deal with time series with large amount of data, and continuous and drastic changes.
In this paper, we propose a segmentation-based overlapping window fitting algorithm that divides the segmentation window into boundary, overlapping, and inner areas. By weighted averaging the fitting values of the overlapping area of the front and back windows, the fitting value between windows changes continuously. Using GNSS ionospheric data, three algorithms of epoch-by-epoch sliding window, independent segment window and overlapping window are compared. In the ionospheric fitting calculation of G01 at NKLG station with 400 epoch windows, the epoch-by-epoch method consumes 121.618 s, while the independent and overlapping subsection methods only use 0.396 s and 0.985 s, respectively, and the calculation efficiency is 307 times and 123 times that of the former. The results show that the proposed algorithm takes account of both computational accuracy and execution efficiency, and is a good method to deal with time series with large amount of data, and continuous and drastic changes.
引文
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[10] Li L Y,Lü Z P,Chen Z S,et al.GNSSer:Objected-Oriented and Design Pattern-Based Software for GNSS Data Parallel Processing[J].Journal of Spatial Science,2019,10
[11] 许国昌.GPS理论、算法与应用[M].北京:清华大学出版社,2011(Xu Guochang.GPS Theory,Algorithm and Application[M].Beijing:Tsinghua University Press,2011)
[2] 袁运斌,霍星亮,张宝成.近年来我国GNSS电离层延迟精确建模及修正研究进展[J].测绘学报,2017,46(10):1 364-1 378(Yuan Yunbin,Huo Xingliang,Zhang Baocheng.Research Progress of Precise Models and Correction for GNSS Ionospheric Delay in China over Recent Years[J].Acta Geodaetica et Cartographica Sinica,2017,46(10):1 364-1 378)
[3] 谢杰,张博,侯博,等.Galileo卫星导航系统广播NeQuick模型及其参数拟合[J].空间科学学报,2012,32(6):881-886(Xie Jie,Zhang Bo,Hou Bo,et al.Simulation of NeQuick Parameters of Galileo Satellite Navigation System[J].Chinese Journal of Space Science,2012,32(6):881-886)
[4] 王建强,李建成,赵国强,等.多项式拟合快速计算扰动引力方法[J].大地测量与地球动力学,2013,33(4):52-55(Wang Jianqiang,Li Jiancheng,Zhao Guoqiang,et al.Fast Calculation of Earth’s Disturbing Gravity through Polynomial Fitting[J].Journal of Geodesy and Geodynamics,2013,33(4):52-55)
[5] 吉长东,徐爱功,冯磊.GPS精密星历拟合与插值中龙格现象的处理方法[J].测绘科学,2011,36(6):169-171(Ji Changdong,Xu Aigong,Feng Lei.Treatment of Runge’s Phenomenon in Fitting and Interpolating GPS Precise Ephemeris[J].Science of Surveying and Mapping,2011,36(6):169-171)
[6] 刘茂华,尹潇,吕志鹏,等.基于移动窗口的抗差自适应滤波算法研究[J].大地测量与地球动力学,2014,34(6):140-143(Liu Maohua,Yin Xiao,Lü Zhipeng,et al.Research of Robust Adaptive Filtering Based on Moving Window[J].Journal of Geodesy and Geodynamics,2014,34(6):140-143)
[7] 杨元喜,徐天河.基于移动开窗法协方差估计和方差分量估计的自适应滤波[J].武汉大学学报:信息科学版,2003(6):714-718(Yang Yuanxi,Xu Tianhe.An Adaptive Kalman Filter Combining Variance Component Estimation with Covariance Matrix Estimation Based on Moving Window[J].Geomatics and Information Science of Wuhan University,2003(6):714-718)
[8] 陈然,戴齐.基于重要点的时间序列固定分段数分段算法[J].计算机技术与发展,2011,21(9):103-106(Chen Ran,Dai Qi.Time Series Segmentation Based on Fixed Number of PIPs Detection[J].Computer Technology and Development,2011,21(9):103-106)
[9] 喻高瞻,彭宏,胡劲松,等.时间序列数据的分段线性表示[J].计算机应用与软件,2007(12):17-18(Yu Gaozhan,Peng Hong,Hu Jinsong,et al.Piecewise Linear Representation of Time Series Data[J].Computer Applications and Software,2007(12):17-18)
[10] Li L Y,Lü Z P,Chen Z S,et al.GNSSer:Objected-Oriented and Design Pattern-Based Software for GNSS Data Parallel Processing[J].Journal of Spatial Science,2019,10
[11] 许国昌.GPS理论、算法与应用[M].北京:清华大学出版社,2011(Xu Guochang.GPS Theory,Algorithm and Application[M].Beijing:Tsinghua University Press,2011)