EMD-RLS联合滤波算法及其在北斗多路径削弱误差中的应用
|
摘要
多路径误差是全球导航卫星系统高精度定位的主要误差源。针对北斗导航定位系统的多路径特性,结合经验模态分解(EMD)和递归最小二乘算法(RLS)算法的优势,提出了一种EMD-RLS联合滤波算法来削弱北斗多路径特性的影响。首先,利用EMD将原始信号分解成固有模态函数(IMF),利用两个指标将其细化成三类,即噪声IMFs、混合IMFs和信息IMFs;然后,利用RLS算法对混合IMFs进行滤波,将经RLS滤波后得到的"干净"的数据与信息IMFs进行重构,最终达到去噪结果,即得到北斗多路径误差改正模型。仿真数据和北斗实测数据的处理结果表明:EMD-RLS算法相对于EMD和RLS算法,降噪效果更好;其建立的多路径误差改正模型有效地削弱多路径效应的影响,N、E、U三个方向精度分别提高了39%、70%、58%。
Multipath error is the main error source for high-precision positioning of global navigation satellite system. Aiming at the multipath characteristics of Beidou navigation and positioning system, and com-bined with the advantages of the empirical mode decomposition(EMD) and the recursive least-squares algorithm(RLS), An EMD+RLS combined filtering algorithm is proposed to weaken the influence of BeiDou multipath characteristics. EMD is applied to decompose the coordinate sequence into an intrinsic mode function(IMF), which is then divided into three categories(i.e. noise IMFs, mixed IMFs, and information IMFs) by using two indices. The RLS algorithm is used to process the mixed IMFs. The "clean" data and information IMFs obtained after RSL filtering are reconstructed to obtain the BeiDou multi-path error correction model.The processing results of simulation data and BDS measured data show that the EMD-RLS algorithm has better noise reduction effect than the EMD and RLS algorithms, and the improvement of BDS positioning result is more significant. The established multipath error correction model effectively weakens the influence of multipath, and the accuracy of N, E, and U directions is increased by 39%, 70%, and 58%, respectively.
Multipath error is the main error source for high-precision positioning of global navigation satellite system. Aiming at the multipath characteristics of Beidou navigation and positioning system, and com-bined with the advantages of the empirical mode decomposition(EMD) and the recursive least-squares algorithm(RLS), An EMD+RLS combined filtering algorithm is proposed to weaken the influence of BeiDou multipath characteristics. EMD is applied to decompose the coordinate sequence into an intrinsic mode function(IMF), which is then divided into three categories(i.e. noise IMFs, mixed IMFs, and information IMFs) by using two indices. The RLS algorithm is used to process the mixed IMFs. The "clean" data and information IMFs obtained after RSL filtering are reconstructed to obtain the BeiDou multi-path error correction model.The processing results of simulation data and BDS measured data show that the EMD-RLS algorithm has better noise reduction effect than the EMD and RLS algorithms, and the improvement of BDS positioning result is more significant. The established multipath error correction model effectively weakens the influence of multipath, and the accuracy of N, E, and U directions is increased by 39%, 70%, and 58%, respectively.
引文
[1]高旺.多系统多频GNSS融合快速精密定位关键技术研究[D].南京:东南大学,2018.Gao W.Study on the key technologies of fast precise positioning based on the fusion of multi-system and multi-frequency GNSS[D].Nanjing:Southeast University,2018.
[2]Cai C,Chang H,Santerre R,et al.A comparative analysis of measurement noise and multipath for four constellations:GPS,BeiDou,GLONASS and Galileo[J].Empire Survey Review,2015,48(349):287-295.
[3]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.
[4]蒋光伟,程传录,王斌,等.影响GNSS数据质量的多路径效应相关性分析[J].地球物理学进展,2018,33(2):461-466.Jiang G,Chen C,Wang B,et al.Effection of data quality relativity analysis of multipath[J].Progress in Geophysics,2018,33(2):461-466.
[5]罗飞雪,戴吾蛟,唐成盼,等.参考经验模态分解独立分量分析及其在GPS多路径误差处理中的应用[J].测绘学报,2012,41(3):366-371.Luo F,Dai W,Tang C,et al.EMD-ICA with reference signal method and its application in GPS multipath[J].Acta Geodaetica et Cartographica Sinica,2012,41(3):366-371.
[6]Yu S,Guo F,Zhang X,et al.A new method for GNSSmultipath mitigation with an adaptive frequency domain filter[J].Sensors,2018,18(8):2514.
[7]Satirapod C,Rizos C.Multipath mitigation by wavelet analysis for GNSS base station applications[J].Empire Survey Review,2005,38(295):2-10.
[8]Su M,Zheng J,Yang Y,et al.A new multipath mitigation method based on adaptive thresholding wavelet denoising and double reference shift strategy[J].GPS Solutions,2018,22(2):40.
[9]Huang N,Shen Z,Long S,et al.The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[J].Proceedings Mathematical Physical&Engineering Sciences,1998,454:903-995.
[10]戴吾蛟,丁晓利,朱建军,等.基于经验模式分解的滤波去噪法及其在GPS多路径效应中的应用[J].测绘学报,2006,35(4):321-327.Dai W,Ding X,Zhu J,et al.EMD filter method and its application in GPS multipath[J].Acta Geodaetica et Cartographica Sinica,2006,35(4):321-327.
[11]崔冰波,陈熙源.基于一种改进EMD算法的GPS多径效应抑制方法[J].中国惯性技术学报,2014,22(3):346-351.Cui B,Chen X.Multipath mitigation of GPS signal based on improved EMD algorithm[J].Journal of Chinese Inertial Technology,2014,22(3):346-351.
[12]Wang J,Wang J,Roberts C.Reducing carrier phase errors with EMD-wavelet for precise GPS positioning[J].Survey Review,2009,41:152-161.
[13]Li X,Li X,Liu G,et al.Spatial-temporal characteristic of BDS phase delays and PPP ambiguity resolution with GEO/IGSO/MEO satellites[J].GPS Solutions,2018,22(4):123.
[14]Ye S,Chen D,Liu Y,et al.Carrier phase multipath mitigation for BeiDou navigation satellite system[J].GPSSolutions,2015,19(4):545-557.
[15]Wang G,De Jong K,Zhao Q,et al.Multipath analysis of code measurements for BeiDou geostationary satellites[J].GPS Solutions,2015,19(1),129-139.
[16]Zhao Q,Wang G,Liu Z,et al.Analysis of BeiDou satellite measurements with code multipath and geometry-free ionosphere-free combinations[J].Sensors,2016,16(1):123.
[17]Dai W,Shi Q,Cai C.Characteristics of the BDS carrier phase multipath and its mitigation methods in relative positioning[J].Sensors,2017,17(4):796.
[18]Zhang Q,Yang W,Zhang S,et al.Characteristics of BeiDou navigation satellite system multipath and its mitigation method based on Kalman Filter and RauchTung-Striebel smoother[J].Sensors,2018,18(2):198.
[19]许兆新,李航洲,李亮,等.基于EKF/SF的BDS短基线多径抑制方法[J].系统工程与电子技术,2017,39(6):1334-1340.Xu Z,Li H,Li L,et al.EKF/SF-based short-baseline BDSmultipath mitigation method[J].Systems Engineering and Electronics,2017,39(6):1334-1340.
[20]张双成,何月帆,李振宇,等.EMD用于GPS时间序列降噪分析[J].大地测量与地球动力学,2017,37(12):1248-1252.Zhang S,He Y,Li Z,et al.EMD for noise reduction of GPS time series[J].Journal of Geodesy and Geodynamics,2017,37(12):1248-1252.
[21]Peixoto M L C,Nepomuceno E G,Martins S A M,et al.Computation of the largest positive Lyapunov exponent using rounding mode and recursive least square algorithm[J].Chaos Solitons&Fractals,2018,112:36-43.
[22]Guo X,Sun C,Wang P,et al.Hybrid methods for MEMSgyro signal noise reduction with fast convergence rate and small steady-state error[J].Sensors&Actuators APhysical,2017,269(1):145-159.
[23]陈健,岳东杰,刘志强,等.基于参考信号的广义特征值分解盲源分离算法及其在北斗多路径效应削弱中的应用[J].中国惯性技术学报,2018,26(1):18-23.Chen J,Yue D,Liu Z,et al.Blind source separation algorithm of generalized eigen-value decomposition based on reference signal and its application in BDS multipath[J].Journal of Chinese Inertial Technology,2018,26(1):18-23.
[2]Cai C,Chang H,Santerre R,et al.A comparative analysis of measurement noise and multipath for four constellations:GPS,BeiDou,GLONASS and Galileo[J].Empire Survey Review,2015,48(349):287-295.
[3]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.
[4]蒋光伟,程传录,王斌,等.影响GNSS数据质量的多路径效应相关性分析[J].地球物理学进展,2018,33(2):461-466.Jiang G,Chen C,Wang B,et al.Effection of data quality relativity analysis of multipath[J].Progress in Geophysics,2018,33(2):461-466.
[5]罗飞雪,戴吾蛟,唐成盼,等.参考经验模态分解独立分量分析及其在GPS多路径误差处理中的应用[J].测绘学报,2012,41(3):366-371.Luo F,Dai W,Tang C,et al.EMD-ICA with reference signal method and its application in GPS multipath[J].Acta Geodaetica et Cartographica Sinica,2012,41(3):366-371.
[6]Yu S,Guo F,Zhang X,et al.A new method for GNSSmultipath mitigation with an adaptive frequency domain filter[J].Sensors,2018,18(8):2514.
[7]Satirapod C,Rizos C.Multipath mitigation by wavelet analysis for GNSS base station applications[J].Empire Survey Review,2005,38(295):2-10.
[8]Su M,Zheng J,Yang Y,et al.A new multipath mitigation method based on adaptive thresholding wavelet denoising and double reference shift strategy[J].GPS Solutions,2018,22(2):40.
[9]Huang N,Shen Z,Long S,et al.The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[J].Proceedings Mathematical Physical&Engineering Sciences,1998,454:903-995.
[10]戴吾蛟,丁晓利,朱建军,等.基于经验模式分解的滤波去噪法及其在GPS多路径效应中的应用[J].测绘学报,2006,35(4):321-327.Dai W,Ding X,Zhu J,et al.EMD filter method and its application in GPS multipath[J].Acta Geodaetica et Cartographica Sinica,2006,35(4):321-327.
[11]崔冰波,陈熙源.基于一种改进EMD算法的GPS多径效应抑制方法[J].中国惯性技术学报,2014,22(3):346-351.Cui B,Chen X.Multipath mitigation of GPS signal based on improved EMD algorithm[J].Journal of Chinese Inertial Technology,2014,22(3):346-351.
[12]Wang J,Wang J,Roberts C.Reducing carrier phase errors with EMD-wavelet for precise GPS positioning[J].Survey Review,2009,41:152-161.
[13]Li X,Li X,Liu G,et al.Spatial-temporal characteristic of BDS phase delays and PPP ambiguity resolution with GEO/IGSO/MEO satellites[J].GPS Solutions,2018,22(4):123.
[14]Ye S,Chen D,Liu Y,et al.Carrier phase multipath mitigation for BeiDou navigation satellite system[J].GPSSolutions,2015,19(4):545-557.
[15]Wang G,De Jong K,Zhao Q,et al.Multipath analysis of code measurements for BeiDou geostationary satellites[J].GPS Solutions,2015,19(1),129-139.
[16]Zhao Q,Wang G,Liu Z,et al.Analysis of BeiDou satellite measurements with code multipath and geometry-free ionosphere-free combinations[J].Sensors,2016,16(1):123.
[17]Dai W,Shi Q,Cai C.Characteristics of the BDS carrier phase multipath and its mitigation methods in relative positioning[J].Sensors,2017,17(4):796.
[18]Zhang Q,Yang W,Zhang S,et al.Characteristics of BeiDou navigation satellite system multipath and its mitigation method based on Kalman Filter and RauchTung-Striebel smoother[J].Sensors,2018,18(2):198.
[19]许兆新,李航洲,李亮,等.基于EKF/SF的BDS短基线多径抑制方法[J].系统工程与电子技术,2017,39(6):1334-1340.Xu Z,Li H,Li L,et al.EKF/SF-based short-baseline BDSmultipath mitigation method[J].Systems Engineering and Electronics,2017,39(6):1334-1340.
[20]张双成,何月帆,李振宇,等.EMD用于GPS时间序列降噪分析[J].大地测量与地球动力学,2017,37(12):1248-1252.Zhang S,He Y,Li Z,et al.EMD for noise reduction of GPS time series[J].Journal of Geodesy and Geodynamics,2017,37(12):1248-1252.
[21]Peixoto M L C,Nepomuceno E G,Martins S A M,et al.Computation of the largest positive Lyapunov exponent using rounding mode and recursive least square algorithm[J].Chaos Solitons&Fractals,2018,112:36-43.
[22]Guo X,Sun C,Wang P,et al.Hybrid methods for MEMSgyro signal noise reduction with fast convergence rate and small steady-state error[J].Sensors&Actuators APhysical,2017,269(1):145-159.
[23]陈健,岳东杰,刘志强,等.基于参考信号的广义特征值分解盲源分离算法及其在北斗多路径效应削弱中的应用[J].中国惯性技术学报,2018,26(1):18-23.Chen J,Yue D,Liu Z,et al.Blind source separation algorithm of generalized eigen-value decomposition based on reference signal and its application in BDS multipath[J].Journal of Chinese Inertial Technology,2018,26(1):18-23.