基于粒子滤波和滑动平均扩展Kalman滤波的多径估计算法
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摘要
多径干扰是高精度定位的主要误差源,估计多径参数对消除多径误差,提高导航系统定位精度具有重要意义。针对扩展Kalman滤波(EKF)在进行多径参数估计时,存在对初值敏感,估计结果在真值附近具有较大波动的缺点,该文提出一种基于粒子滤波(PF)和滑动平均EKF的多径估计算法。该算法首先利用PF得到多径参数的粗略估计值,并将该值作为EKF的初始估计值,以克服EKF对初值敏感的问题。接着对EKF的估计结果进行滑动平均,并将平均后的滤波结果作为多径参数的估计结果。仿真结果表明,改进后的多径估计算法可有效降低估计结果的波动幅度,同时解决了EKF对初值敏感的问题。
Multipath is the dominant error source for high-accuracy positioning systems. It is significant for eliminating the multipath error and improving the positioning accuracy to estimate multipath parameters. There are two main disadvantages for multipath parameters estimation by using the Extended Kalman Filter(EKF): it is sensitive to the initial value; filtering results fluctuate obviously around actual values. To solve these problems, an improved multipath estimation algorithm based on Particle Filter(PF) and sliding average EKF is proposed. Firstly, PF is used to obtain rough estimation values of multipath parameters, which are set as initial estimations for EKF to reduce the initial value sensitivity. Then, the EKF filtering results are smoothed by sliding average. The smoothing results are outputted as the multipath estimation. The simulation results show that the estimation results of the proposed algorithm have smaller fluctuation magnitude compared with EKF, and it is insensitive to the initial estimation.
Multipath is the dominant error source for high-accuracy positioning systems. It is significant for eliminating the multipath error and improving the positioning accuracy to estimate multipath parameters. There are two main disadvantages for multipath parameters estimation by using the Extended Kalman Filter(EKF): it is sensitive to the initial value; filtering results fluctuate obviously around actual values. To solve these problems, an improved multipath estimation algorithm based on Particle Filter(PF) and sliding average EKF is proposed. Firstly, PF is used to obtain rough estimation values of multipath parameters, which are set as initial estimations for EKF to reduce the initial value sensitivity. Then, the EKF filtering results are smoothed by sliding average. The smoothing results are outputted as the multipath estimation. The simulation results show that the estimation results of the proposed algorithm have smaller fluctuation magnitude compared with EKF, and it is insensitive to the initial estimation.
引文
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[10]程兰.软件接收机原理及多径误差研究[M].北京:国防工业出版社,2015:170-182.CHENG Lan.Software Receiver Principle and the Research of Multipath Error[M].Beijing:China National Defence Industry Press,2015:170-182.
[11]占荣辉,张军,欧建平,等.非线性滤波理论与目标跟踪应用[M].北京:国防工业出版社,2013:43-46.ZHAN Ronghui,ZHANG Jun,OU Jianping et al.Nonlinear Filtering Theory with Target Tracking Application[M].Beijing:China National Defence Industry Press,2013:43-46.
[12]朱志宇.粒子滤波算法及其应用[M].北京:科学出版社,2010:27-32.ZHU Zhiyu.Particle Filter and Its Application[M].Beijing:Science Press,2010:27-32.
[13]CHENG Lan,CHEN Jie,and XIE Gang.Model and simulation of multipath error in DLL for GPS receiver[J].Chinese Journal of Electronics,2014,23(3):508-515.
[14]Townsend B R,Fenton P C,Dierendonck K J V,et al.Performance evaluation of the multipath estimating delay lock loop[J].Journal of the Institute of Navigation,1995,42(3):502-514.doi:10.1002/j.2161-4296.1995.tb01903.x.
[2]程兰,陈杰,甘明刚.GPS接收机载波跟踪多径误差分析[C].第29届中国控制会议论文集,北京,2010:573-576.CHENG Lan,CHEN Jie,and GAN Minggang.Multipath error analysis of carrier tracking loop in GPS receiver[C].Proceedings of the 29th Chinese Control Conference,Beijing,2010:573-576.
[3]张孟阳,吕保维,宋文淼.GPS系统中的多径效应分析[J].电子学报,1998,26(3):10-14.ZHANG Mengyang,LüBaowei,and SONG Wenmiao.Analyses of multipath effects in the GPS system[J].Acta Electronica Sinica,1998,26(3):10-14.
[4]程兰,陈杰,谢刚.软件接收机中基于数据处理的多径估计方法[J].系统工程与电子技术,2013,35(10):2050-2056.doi:10.3969/j.issn.1001-506X.2013.10.06.CHENG Lan,CHEN Jie,and XIE Gang.Multipath estimation algorithms based on data processing in soft ware receiver[J].Systems Engineering and Electronics,2013,35(10):2050-2056.doi:10.3969/j.issn.1001-506X.2013.10.06.
[5]张文明,周一宇,姜文利.基于扩展卡尔曼滤波的GPS多径抑制技术[J].宇航学报,2003,24(1):53-56.doi:10.3321/j.issn:1000-1328.2003.01.010.ZHANG Wenming,ZHOU Yiyu,and JIANG Wenli.GPS multipath rejection through EKF[J].Journal of Astronautics,2003,24(1):53-56.doi:10.3321/j.issn:1000-1328.2003.01.010.
[6]ILTIS R A.Joint estimation of PN code delay and multipath using the extend kalman filter[J].IEEE Transactions on Communications,1990,38(10):1677-1685.
[7]熊伟,陈立奎,何友,等.有色噪声下的不敏卡尔曼滤波器[J].电子与信息学报,2007,29(3):598-600.XIONG Wei,CHEN Likui,HE You,et al.Unscented Kalman filter with colored noise[J].Journal of Electronics&Information Technology,2007,29(3):598-600.
[8]黄小平,王岩石.卡尔曼滤波原理及应用[M].北京:电子工业出版社,2015:89-90.HUANG Xiaoping and WANG Yanshi.Kalman Filter and Its Application[M].Beijing:Publishing House of Electronics Industry,2015:89-90.
[9]程兰,谢刚.一种基于扩展Kalman滤波的多径估计算法[J].太原理工大学学报,2012,43(5):575-579.doi:10.3969/j.issn.1007-9432.2012.05.011.CHENG Lan and XIE Gang.A multipath estimation algorithm based on extended Kalman filter[J].Journal of Taiyuan University of Technology,2012,43(5):575-579.doi:10.3969/j.issn.1007-9432.2012.05.011.
[10]程兰.软件接收机原理及多径误差研究[M].北京:国防工业出版社,2015:170-182.CHENG Lan.Software Receiver Principle and the Research of Multipath Error[M].Beijing:China National Defence Industry Press,2015:170-182.
[11]占荣辉,张军,欧建平,等.非线性滤波理论与目标跟踪应用[M].北京:国防工业出版社,2013:43-46.ZHAN Ronghui,ZHANG Jun,OU Jianping et al.Nonlinear Filtering Theory with Target Tracking Application[M].Beijing:China National Defence Industry Press,2013:43-46.
[12]朱志宇.粒子滤波算法及其应用[M].北京:科学出版社,2010:27-32.ZHU Zhiyu.Particle Filter and Its Application[M].Beijing:Science Press,2010:27-32.
[13]CHENG Lan,CHEN Jie,and XIE Gang.Model and simulation of multipath error in DLL for GPS receiver[J].Chinese Journal of Electronics,2014,23(3):508-515.
[14]Townsend B R,Fenton P C,Dierendonck K J V,et al.Performance evaluation of the multipath estimating delay lock loop[J].Journal of the Institute of Navigation,1995,42(3):502-514.doi:10.1002/j.2161-4296.1995.tb01903.x.