顾及有色噪声的卡尔曼滤波在多路径误差削弱中的应用
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摘要
多路径误差为一时空环境效应,难以构建准确数学模型消除其影响,且该误差在基线两端不具有空间相关性,运用现有差分技术也无法很好消除,是高精度短基线测量中主要误差之一.为进一步削弱多路径误差,本文以监测站坐标时间序列中多路径误差为研究对象,根据多路径误差在历元间的时变特性,建立多路径误差状态空间模型,采用标准卡尔曼滤波和顾及有色噪声的卡尔曼滤波从监测站第一天双差固定解坐标残差序列中估计多路径误差改正序列,并根据多路径误差的周日重复特性,利用第一天得到的多路径误差改正序列对之后各天坐标序列进行改正.最后通过实验分析,得出顾及有色噪声的卡尔曼滤波估计方法优于标准卡尔曼滤波的结论.研究方法对提高GNSS定位精度具有重要实用价值.
Multi-path error is a space-time environment effect,it is difficult to eliminate it through building accurate mathematical model,and the error also has no spatial correlation at both ends of the baseline,it can't eliminate it through using the differential technology,it is one of the main errors in GNSS high accuracy measurement of short baseline.To further mitigate the multi-path error,this paper take the multi-path error in GNSS carrier phase observation value as the research object,establish the multi-path error state space model,estimate the multipath error correction sequence from coordinate residual sequence adopt the standard Kalman filter and the Kalman filter with colored noise,and based on the daily repetition characteristics of multi-path error,correct the coordinate sequences of the subsequent days using the multi-path error correction sequence obtained on the first day.Finally,through the experimental analysis,it is concluded that the Kalman filter with colored noise estimation method is better than the standard Kalman filter.The research results are of great practical value to improve GNSS positioning accuracy.
Multi-path error is a space-time environment effect,it is difficult to eliminate it through building accurate mathematical model,and the error also has no spatial correlation at both ends of the baseline,it can't eliminate it through using the differential technology,it is one of the main errors in GNSS high accuracy measurement of short baseline.To further mitigate the multi-path error,this paper take the multi-path error in GNSS carrier phase observation value as the research object,establish the multi-path error state space model,estimate the multipath error correction sequence from coordinate residual sequence adopt the standard Kalman filter and the Kalman filter with colored noise,and based on the daily repetition characteristics of multi-path error,correct the coordinate sequences of the subsequent days using the multi-path error correction sequence obtained on the first day.Finally,through the experimental analysis,it is concluded that the Kalman filter with colored noise estimation method is better than the standard Kalman filter.The research results are of great practical value to improve GNSS positioning accuracy.
引文
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[15]邱卫宁,陶本藻,姚宜斌,等.测量数据处理理论与方法[M].武汉:武汉大学出版社,2008.
[16]刘星,李川,石明旺,等.卡尔曼滤波算法的GPS双差观测值周跳探测与修复[J].测绘科学,2018,43(1):1-5,19.
[2]李征航,黄劲松.GPS测量与数据处理[M].武汉:武汉大学出版社,2010:116-119.
[3]李川,刘星,石明旺,等.GPS多路径误差特性分析及削弱方法[J].导航定位学报,2017,5(1):103-107.
[4]过静珺,商瑞斌,李毓麟.多路径效应对GPS定位影响的研究[J].工程勘察,1995,1(2):46-49.
[5]VANDIERENDONCK A J,FENTON P,FORD T.Theory and performance of narrow correlator spacing in a GPS Receiver[J].Navigation,1993,39(9):265-283.
[6]TOWNSEND B R,FENTON P C.A practical approach to the reduction of pseudorange multipath errors in a L1GPS receiver.//Proceedings of International Technical Meeting of the Satellite Division of the Institute of Navigation,1994:143-148.
[7]NEE R D J V,SIEREVELD J,FENTON P C,et al.The multipath estimating delay lock loop:approaching theoretical accuracy limits[C]//Position Location and Navigation Symposium.IEEE,1994:11-15.
[8]CHEN X,DOVIS F,PINI M,et al,Turbo architecture for multipath mitigation in global navigation satellite system receivers,[J].IET Radar Sonar and Navigation,2011,5(5):517-527.
[9]DONG D,WANG M,CHEN W,et al.Mitigation of multipath effect in GNSS short baseline positioning by the multipath hemispherical map[J].Journal of Geodesy,2016,90(3):255-262.
[10]刘永义,党亚民,薛树强.基于海面环境多路径效应建模初探[J].测绘科学,2013,38(1):122-124.
[11]KLAMAN.R E A new approach to linear filtering and prediction problems[J].Journal of Basic Engineering.1960(82):35-45.
[12]王法胜,鲁明羽,赵清杰,等.粒子滤波算法[J].计算机学报,2014,37(8):1679-1694.
[13]朱志宇.粒子滤波算法及其应用[M].北京:科学出版社,2010.
[14]黄声享,尹晖,蒋征,等.变形监测数据处理[M].武汉:武汉大学出版社,2010.
[15]邱卫宁,陶本藻,姚宜斌,等.测量数据处理理论与方法[M].武汉:武汉大学出版社,2008.
[16]刘星,李川,石明旺,等.卡尔曼滤波算法的GPS双差观测值周跳探测与修复[J].测绘科学,2018,43(1):1-5,19.