角闪烁噪声下的高斯和容积卡尔曼滤波算法
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摘要
开展角闪烁噪声下的目标跟踪问题研究对提高传感器的探测性能具有重要意义,其中角闪烁噪声具有的非高斯特性是一个长期困扰研究者的难点。针对该问题,首先通过理论分析指出了容积粒子滤波(cubature particle filter,CPF)在角闪烁噪声下的性能缺陷。其次,基于高斯和滤波(Gaussian sum filter,GSF)框架和容积卡尔曼滤波(cubature Kalman filter,CKF)算法,提出了适用于角闪烁下的高斯和容积卡尔曼滤波(Gaussian sum cubature Kalman filter,GSCKF)算法,该算法将目标后验概率密度用高斯密度加权求和近似,通过多路并行的CKF实现状态预测与量测更新,同时利用模型降阶算法限制高斯分量数目的增长,能应用于非线性、非高斯条件的状态估计。最后,设计了仿真实验对GSCKF和CPF的跟踪精度、鲁棒性和计算复杂度进行了对比。
Research on target tracking with glint noise is important to improve the detection performance of sensor,in which the glint noise's non-Gaussian property has puzzled researchers for a long time.To overcome this problem,the cubature particle filter's performance deficiency in target tracking with the glint noise is theoretically analyzed.Then,a algorithm called Gaussian sum cubature Kalman filter(GSCKF)is proposed.Based on the methodology of Gaussian sum filter(GSF)and the cubature Kalman filter(CKF),the proposed algorithm models the non-Gaussian noise and the state posterior distribution as finite weighted Gaussian mixture,and a bank of CKF is running in parallel where the filtering and predictive distributions are updated by using the CKF equations.Moreover,the proposed algorithm utilizes the model reduction techniques to limit the number of Gaussian components,thus it is suitable for non-linear and non-Gaussian state estimation.In order to compare the performance of the two non-Gaussian algorithms,comparative experiments between GSCKF and CPF from the three aspects of tracking accuracy,robustness and computational complexity are carried out.
Research on target tracking with glint noise is important to improve the detection performance of sensor,in which the glint noise's non-Gaussian property has puzzled researchers for a long time.To overcome this problem,the cubature particle filter's performance deficiency in target tracking with the glint noise is theoretically analyzed.Then,a algorithm called Gaussian sum cubature Kalman filter(GSCKF)is proposed.Based on the methodology of Gaussian sum filter(GSF)and the cubature Kalman filter(CKF),the proposed algorithm models the non-Gaussian noise and the state posterior distribution as finite weighted Gaussian mixture,and a bank of CKF is running in parallel where the filtering and predictive distributions are updated by using the CKF equations.Moreover,the proposed algorithm utilizes the model reduction techniques to limit the number of Gaussian components,thus it is suitable for non-linear and non-Gaussian state estimation.In order to compare the performance of the two non-Gaussian algorithms,comparative experiments between GSCKF and CPF from the three aspects of tracking accuracy,robustness and computational complexity are carried out.
引文
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[3]RYU H R,HUBER M.A particle filter approach for multi-target tracking[C]∥Proc.of the IEEE/RSJ International Conference on Intelligent Robots and Systems,2015:2753-2760.
[4]李天成,范红旗,孙树栋.粒子滤波理论、方法及其在多目标跟踪中的应用[J].自动化学报,2015,41(12):1981-2002.LI T C,FANG H Q,SUN S D.Particle filtering:theory,approach,and application for multitarget tracking[J].Acta Automatica Sinica,2015,41(12):1981-2002.
[5]ALSPACH D,SCRENHSON H.non-linear Bayesian estimation using Gaussian sum approximation[J].IEEE Trans.on Automatic Control,1972,17(4):439-448.
[6]MOHAMMADI A,PLATANIOTIS K N.Complex-valued Gaussian sum filter for nonlinear filtering of non-Gaussian/non-circular noise[J].IEEE Signal Processing Letters,2015,22(4):440-444.
[7]DOUCET A,FREITAS N D,GORDON N.Sequential Monte-Carlo methods in practice[M].New York:Springer,2001.
[8]DOUCET A,GODSILL S J,ANDRIEU C.On sequential Monte-Carlo sampling methods for Bayesian filtering[J].Statistics and Computing,2000,89(425):197-288.
[9]ZHOU J,LOFFELD S K O.INS/GPS tightly-coupled integration using adaptive unscented particle filter[J].Journal of Navigation,2010,63(3):491-511.
[10]孙枫,唐李军.Cubature粒子滤波[J].系统工程与电子技术,2011,34(11):2554-2557.SUN F,TANG L J.Cubature particle filter[J].Systems Engineering and Electronics,2011,34(11):2554-2557.
[11]BILIK I,TABRIKIAN J.MMSE-based filtering in presence of non-Gaussian system and measurement noise[J].IEEE Trans.on Aerospace and Electronic Systems,2010,46(3):1153-1170.
[12]KWOK N M,DISSANAYAKE G,HA Q P.Bearing-only SLAM using a SPRT based Gaussian sum filter[C]∥Proc.of the IEEE International Conference on Robotics and Automation,2005:1109-1114.
[13]HONGTAO H,ZHONGLIANG J,ANPING L,et al.Target tracking in glint noise using a MCMC particle filter[J].Journal of Systems Engineering and Electronics,2005,16(2):305-309.
[14]LI H W,WANG J.Particle filter for manoeuvring target tracking via passive radar measurements with glint noise[J].IET Radar,Sonar and Navigation,2012,6(3):180-189.
[15]KIM J,TANDALE M,MENON P K,et al.Particle filter for ballistic target tracking with glint noise[J].Journal of Guidance Control&Dynamics,2010,33(6):1918-1921.
[16]ARASARATNAM I,HAYKIN S,HURD T R.Cubature Kalman filtering for continuous-discrete systems:theory and simulations[J].IEEE Trans.on Signal Processing,2010,58(10):4977-4993.
[17]张贤达.矩阵分析与应用[M].2版.北京:清华大学出版社,2013.ZHANG X D.Matrix analysis and application[M].2nd ed.Beijing:Tsinghua University Press,2013.
[18]HUBER M F.Nonlinear Gaussian filtering:theory,algorithms and applications[M].KIT Scientific Publishing,2015:73-103.
[19]FAUBEL F,MCDONOUGH J,KLAKOW D.The split and merge unscented Gaussian mixture filter[J].IEEE Signal Processing Letters,2009,16(9):786-789.