GNSS时间序列中随机漫步消噪的改进半软阈值算法及其评估

doi:10.11947/j.AGCS.2016.F022

测绘学报 ›› 2016, Vol. 45 ›› Issue (S2): 22-30.doi: 10.11947/j.AGCS.2016.F022

GNSS时间序列中随机漫步消噪的改进半软阈值算法及其评估

吴浩^1,3, 曹庭泉¹, 花向红², 邹进贵², 史文中³, 卢楠¹

1. 武汉理工大学资源与环境工程学院, 湖北武汉 430070;
2. 武汉大学测绘学院, 湖北武汉 430079;
3. 香港理工大学土地测量与地理资讯学系, 香港 999077

收稿日期:2016-11-25 修回日期:2016-12-20 出版日期:2017-05-20 发布日期:2017-05-20
作者简介:吴浩(1977-),男,博士,教授,研究方向为卫星导航定位技术及应用。E-mail:haowu1977@163.com
基金资助:
中国工程院重点咨询研究（2016-XZ-13）；国家自然科学基金（41671406）；湖北省自然科学基金（2016CFA013；2016AHB015）

An Improved Semisoft Threshold Algorithm and Its Evaluation for Denoising Random Walk in GNSS Time Series

WU Hao^1,3, CAO Tingquan¹, HUA Xianghong², ZOU Jingui², SHI Wenzhong³, LU Nan¹

1. School of Resources and Environmental Engineering, Wuhan University of Technology, Wuhan 430070, China;
2. School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China;
3. Department of Land Surveying and Geo-Informatics, Hong Kong Polytechnic University, Hong Kong 999077, China

Received:2016-11-25 Revised:2016-12-20 Online:2017-05-20 Published:2017-05-20
Supported by:
The Key Consulting Project of Chinese Academy of Engineering (No.2016-XZ-13);The National Natural Science Foundation of China (No. 41671406);The Hubei Provincial Natural Science Foundation of China (Nos. 2016CFA013;2016AHB015)

摘要/Abstract

摘要：

全球导航卫星定位系统在卫星定轨和信号质量等方面存在的差异性，造成GNSS时间序列中的随机漫步噪声十分复杂，已经成为制约GNSS技术在高精度变形监测行业领域深入应用的瓶颈。本文针对具有量级小、频率低、敏感性差等复杂特征的随机漫步噪声，提出了一种改进的半软阈值算法，通过引入可变因子形成了统一的半软阈值函数体系，提高了常规半软阈值对随机漫步噪声的适应性。为了验证和评估改进半软阈值算法的效果，利用MATLAB平台仿真生成有线性趋势项、年周期项和随机漫步噪声的GNSS时间序列，共1700个历元。结果表明，改进的半软阈值法较经典方法在信噪比和均方根误差上表现出更加优良的性能。自相关分析的评估结果表明，改进方法所消除的噪声与随机漫步噪声在形态特征上具有高度的一致性。谱指数分析评估结果，进一步从定量角度验证了改进方法对随机漫步噪声的特有适用性。

关键词: GNSS, 时间序列分析, 随机漫步噪声, 改进半软阈值法

Abstract:

The differences in the satellite orbit and signal quality of global navigation satellite positioning system, resulting in the complexity of random walk noise in GNSS time series, has become a bottleneck problem in applying GNSS technology to the high precision deformation monitoring industry. For the complex characteristics of random walk noise, small magnitude, low frequency and low sensitivity, an improved semisoft threshold algorithm is presented. Then it forms a unified system of semisoft threshold function, so as to improve the adaptability of conventional semisoft threshold for random walk noise. In order to verify and evaluate the effect of improved semisoft threshold algorithm, MATLAB platform is used to generate a linear trend, periodic and random walk noise of the GNSS time series, a total of 1700 epochs. The results show that the improved semisoft threshold method is better than the classical method, and has better performance in the SNR and root mean square error. The evaluation results show that the morphological character has been performanced high consistency between the noise reduced by improved method with random walk noise. Further from the view of quantitative point, the evaluation results of spectral index analysis verify the applicability of the improved method for random walk noise.

Key words: GNSS, time series analysis, random walk noise, improved semisoft threshold algorithm

中图分类号:

P228

吴浩, 曹庭泉, 花向红, 邹进贵, 史文中, 卢楠. GNSS时间序列中随机漫步消噪的改进半软阈值算法及其评估[J]. 测绘学报, 2016, 45(S2): 22-30.

WU Hao, CAO Tingquan, HUA Xianghong, ZOU Jingui, SHI Wenzhong, LU Nan. An Improved Semisoft Threshold Algorithm and Its Evaluation for Denoising Random Walk in GNSS Time Series[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(S2): 22-30.

参考文献

[1] 刘基余. GNSS全球导航卫星系统的新发展[J]. 遥测遥控, 2007, 28(4):1-6. LIU Jiyu. Recent Development of the Global Navigation Satellite System[J]. Journal of Telemetry, Tracking, and Command, 2007, 28(4):1-6.
[2] 杨元喜. 卫星导航的不确定性、不确定度与精度若干注记[J]. 测绘学报, 2012, 41(5):646-650. YANG Yuanxi. Some Notes on Uncertainty, Uncertainty Measure and Accuracy in Satellite Navigation[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(5):646-650.
[3] MAO Ailin, HARRISON C G A, DIXON T H. Noise in GPS Coordinate Time Series[J]. Journal of Geophysical Research:Solid Earth, 1999, 104(B2):2797-2816.
[4] WILLIAMS S D P, BOCK Y, FANG Peng, et al. Error Analysis of Continuous GPS Position Time Series[J]. Journal of Geophysical Research:Solid Earth, 2004, 109(B3):B03412.
[5] LANGBEIN J, JOHNSON H. Correlated Errors in Geodetic Time Series:Implications for Time-dependent Deformation[J]. Journal of Geophysical Research:Solid Earth, 1997, 102(B1):591-603.
[6] 黄立人, 符养. GPS连续观测站的噪声分析[J]. 地震学报, 2007, 29(2):197-202. HUANG Liren, FU Yang. Analysis on the Noises from Continuously Monitoring GPS Sites[J]. Acta Seismologica Sinica, 2007, 29(2):197-202.
[7] 苏利娜, 丁晓光, 张彦芬, 等. 陕西连续GPS基准站坐标时间序列分析[J]. 大地测量与地球动力学, 2014, 34(5):106-109, 113. SU Li'na, DING Xiaoguang, ZHANG Yanfen, et al. Study on Coordinate Time Series of Shaanxi Continuous GPS Refrence Stations[J]. Journal of Geodesy and Geodynamics, 2014, 34(5):106-109, 113.
[8] 李昭, 姜卫平, 刘鸿飞, 等. 中国区域IGS基准站坐标时间序列噪声模型建立与分析[J]. 测绘学报, 2012, 41(4):496-503. LI Zhao, JIANG Weiping, LIU Hongfei, et al. Noise Model Establishment and Analysis of IGS Reference Station Coordinate Time Series inside China[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(4):496-503.
[9] KAIVOSOJA J, LINKOLEHTO R. GNSS Error Simulator for Farm Machinery Navigation Development[J]. Computers and Electronics in Agriculture, 2015(119):166-177.
[10] DMITRIEVA K, SEGALL P, DEMETS C. Network-based Estimation of Time-dependent Noise in GPS Position Time Series[J]. Journal of Geodesy, 2015, 89(6):591-606.
[11] 杨元喜, 崔先强. 动态定位有色噪声影响函数——以一阶AR模型为例[J]. 测绘学报, 2003, 32(1):6-10. YANG Yuanxi, Cui Xianqiang. Influence Functions of Colored Noises on Kinematic Positioning——Taking the AR Model of First Class as an Example[J]. Acta Geodaetica et Cartographica Sinica, 2003, 32(1):6-10.
[12] 吴富梅, 杨元喜. 基于小波阈值消噪自适应滤波的GPS/INS组合导航[J]. 测绘学报, 2007, 36(2):124-128, 140. WU Fumei, YANG Yuanxi. GPS/INS Integrated Navigation by Adaptive Filtering Based on Wavelet Threshold De-noising[J]. Acta Geodaetica et Cartographica Sinica, 2007, 36(2):124-128, 140.
[13] 黄声享, 刘经南. GPS变形监测系统中消除噪声的一种有效方法[J]. 测绘学报, 2002, 31(2):104-107. HUANG Shengxiang, LIU Jingnan. A Novel Method for Reducing Noises in GPS Deformation Monitoring System[J]. Acta Geodaetica et Cartographica Sinica, 2002, 31(2):104-107.
[14] DONOHO D L. De-noising by Soft-Thresholding[J]. IEEE Transactions on Information Theory, 1995, 41(3):613-627.
[15] DONOHO D L, JOHNSTONE I M. Ideal Spatial Adaptation by Wavelet Shrinkage[J]. Biometrika, 1994, 81(3):425-455.
[16] BRUCE A G, GAO Hongye. WaveShrink:Shrinkage Functions and Thresholds[C]//Proceedings of the SPIE SPIE 2569, Wavelet Applications in Signal and Image Processing Ⅲ. San Diego, CA:SPIE, 1995(2569):270.
[17] 魏文畅, 杨俊杰, 蔡建立. 基于小波变换的半软阈值参数算法研究[J]. 计算机工程与应用, 2009, 45(1):73-76. WEI Wenchang, YANG Junjie, CAI Jianli. Parameters' Algorithm of Semisoft Shrinkage Based on Wavelet Transforms[J]. Computer Engineering and Applications, 2009, 45(1):73-76.
[18] 李昊. 新阈值函数及其小波去噪研究[J]. 合肥工业大学学报(自然科学版), 2008, 31(10):1672-1675. LI Hao. A New Shrinkage Function and Wavelet Shrinkage Denoising[J]. Journal of Hefei University of Technology, 2008, 31(10):1672-1675.
[19] 王京港, 黄雨青. 基于一种新阈值函数的小波阈值去噪方法研究[J]. 数字技术与应用, 2012(9):43-45. WANG Jinggang, HUANG Yuqing. A De-noising Algorithm of Wavelet Threshold Based on a New Threshold Function[J]. Digital Technology & Application, 2012(9):43-45.
[20] WU Hao, LI Kui, SHI Wenzhong, et al. A Wavelet-based Hybrid Approach to Remove the Flicker Noise and the White Noise from GPS Coordinate Time Series[J]. GPS Solutions, 2015, 19(4):511-523.
[21] ZHANG Jie, BOCK Y, JOHNSON H, et al. Southern California Permanent GPS Geodetic Array:Error Analysis of Daily Position Estimates and Site Velocities[J]. Journal of Geophysical Research:Solid Earth, 1997, 102(B8):18035-18055.
[22] AMIRI-SIMKOOEI A R, TIBERIUS C C J M. Assessing Receiver Noise Using GPS Short Baseline Time Series[J]. GPS Solutions, 2007, 11(1):21-35.
[23] TEFERLE F N, WILLIAMS S D P, KIERULF H P, et al. A Continuous GPS Coordinate Time Series Analysis Strategy for High-accuracy Vertical Land Movements[J]. Physics and Chemistry of the Earth, Parts A/B/C, 2008, 33(3-4):205-216.
[24] 黄立人. GPS基准站坐标分量时间序列的噪声特性分析[J]. 大地测量与地球动力学, 2006, 26(2):31-33, 38. HUANG Liren. Noise Properties in Time Series of Coordinate Component at GPS Fiducial Stations[J]. Journal of Geodesy and Geodynamics, 2006, 26(2):31-33, 38.
[25] NIKOLAIDIS R. Observation of Geodetic and Seismic Deformation with the Global Positioning System[D]. San Diego, CA:University of California, 2002.

GNSS时间序列中随机漫步消噪的改进半软阈值算法及其评估

An Improved Semisoft Threshold Algorithm and Its Evaluation for Denoising Random Walk in GNSS Time Series

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