鲁棒高斯和集合卡尔曼滤波及其在纯角度跟踪中的应用
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摘要
针对纯角度目标跟踪中量测信息易受异常值和非高斯噪声干扰的问题,提出了一种新的非线性滤波算法–鲁棒高斯和集合卡尔曼滤波(robust Gaussian-sum ensemble Kalman filter,RGSEnKF)算法.首先,采用Huber技术重塑集合卡尔曼滤波的量测更新过程,能够有效地处理量测中的异常值.随后,将改进的集合卡尔曼滤波在高斯和框架下进行扩展,得到RGSEnKF算法,可以进一步解决受非高斯噪声干扰的非线性系统的状态估计问题.此外,新算法中包含距离参数化初始化策略和高斯分量融合策略.前者是为了减小纯角度跟踪中距离信息不可观测的影响,而后者可以避免高斯分量数目随时间不断增长.大量仿真结果验证了新算法的有效性和鲁棒性.
In order to deal with the situation that measurements are easily contaminated by outliers and non-Gaussian noise, a new nonlinear filtering algorithm called the robust Gaussian-sum ensemble Kalman filter(RGSEnKF) is proposed for the bearings-only tracking problem. Firstly, the measurement update process of the ensemble Kalman filter is reformulated by using Huber technique so that outliers can be dealt with efficiently. Further, the improved ensemble Kalman filter is extended within a Gaussian-sum framework, the result is RGSEnKF algorithm which can handle the state estimation problem of nonlinear system corrupted by non-Gaussian noise. Moreover, the new algorithm includes a range-parameterized initialization strategy and a Gaussian merging strategy. The former strategy can reduce the effect of unobservability of range in bearings-only tracking and the latter can prevent the number of Gaussian components from increasing over time.Lots of simulation results validate the effectiveness and robustness of the new algorithm.
In order to deal with the situation that measurements are easily contaminated by outliers and non-Gaussian noise, a new nonlinear filtering algorithm called the robust Gaussian-sum ensemble Kalman filter(RGSEnKF) is proposed for the bearings-only tracking problem. Firstly, the measurement update process of the ensemble Kalman filter is reformulated by using Huber technique so that outliers can be dealt with efficiently. Further, the improved ensemble Kalman filter is extended within a Gaussian-sum framework, the result is RGSEnKF algorithm which can handle the state estimation problem of nonlinear system corrupted by non-Gaussian noise. Moreover, the new algorithm includes a range-parameterized initialization strategy and a Gaussian merging strategy. The former strategy can reduce the effect of unobservability of range in bearings-only tracking and the latter can prevent the number of Gaussian components from increasing over time.Lots of simulation results validate the effectiveness and robustness of the new algorithm.
引文
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[18]WU H,CHEN S,YANG B,et al.Robust derivative-free cubature Kalman filter for bearings-only tracking[J].Journal of Guidance,Control,and Dynamics,2016,39(8):1866–1871.
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[20]LIN Qing,YIN Jianjun,ZHANG Jianqiu,et al.Gaussian sum filtering methods for nonlinear non-Gaussian models[J].Systems Engineering and Electronics,2010,32(12):2493–2499.(林青,尹建君,张建秋,等.非线性非高斯模型的高斯和滤波算法[J].系统工程与电子技术,2010,32(12):2493–2499.)
[2]KAI X,WEI C,LIU L.Robust extended Kalman filtering for nonlinear systems with stochastic uncertainties[J].IEEE Transactions on Systems,Man,and Cybernetics—Part A:Systems and Humans,2010,40(2):399–405.
[3]AIDALA V,HAMMEL S.Utilization of modified polar coordinates for bearings-only tracking[J].IEEE Transactions on Automatic Control,1983,28(3):283–294.
[4]CLARK J M C,VINTER R B,YAQOOB M M.Shifted Rayleigh filter:a new algorithm for bearings-only tracking[J].IEEE Transactions on Aerospace and Electronic Systems,2007,43(4):1373–1384.
[5]PEACH N.Bearings-only tracking using a set of range-parameterised extended Kalman filters[J].IEEE Proceedings—Control Theory and Applications,1995,142(1):73–80.
[6]LANEUVILLE D,JAUFFRET C.Recursive bearings-only TMA via unscented Kalman filter:Cartesian vs.modified polar coordinates[C]//Aerospace Conference.Big Sky,MT:IEEE,2008:1–11.
[7]DUNIK J,STRAKA O,SIMANDL M,et al.Random-point-based filters:analysis and comparison in target tracking[J].IEEE Transactions on Aerospace and Electronic Systems,2015,51(2):1403–1421.
[8]LEONG P H,ARULAMPALAM S,LAMAHEWA T A,et al.A Gaussian-sum based cubature Kalman filter for bearings-only tracking[J].IEEE Transactions on Aerospace and Electronic Systems,2013,49(2):1161–1176.
[9]WANG Xiaoxu,PAN Quan,HUANG He,et al.Overview of deterministic sampling filtering algorithms for nonlinear system[J].Control and Decision,2012,27(6):801–812.(王小旭,潘泉,黄鹤,等.非线性系统确定采样型滤波算法综述[J].控制与决策,2012,27(6):801–812.)
[10]ARULAMPALAMMS,MASKELL S,GORDON N,et al.A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking[J].IEEE Transactions on Signal Processing,2002,50(2):174–188.
[11]EVENSEN G.Sequential data assimilation with a nonlinear quasigeostrophic model using Monte Carlo methods to forecast error statistics[J].Journal of Geophysical Research:Oceans,1994,99(C5):10143–10162.
[12]HU Zhentao,ZHANG Yong,LIU Xianxing.Maneuvering target tracking algorithm based on ensemble Kalman filter with observation iterated update[J].Control Theory&Applications,2014,31(11):1517–1523.(胡振涛,张勇,刘先省.基于量测迭代更新集合卡尔曼滤波的机动目标跟踪算法[J].控制理论与应用,2014,31(11):1517–1523.)
[13]LIAO Ying,LIU Guangming,WEN Yuanlan,et al.Passive Tracking Technology of Non-Cooperative Space Target and Application[M].Beijing:National Defense Industry Press,2015.(廖瑛,刘光明,文援兰,等.空间非合作目标被动跟踪技术与应用[M].北京:国防工业出版社,2015.)
[14]SONG Xiaoquan,SUN Zhongkang.Maneuvering target tracking with non-Gaussian noise[J].Acta Electronica Sinica,1998,26(9):40–46.(宋小全,孙仲康.非高斯噪声下的机动目标跟踪[J].电子学报,1998,26(9):40–46.)
[15]CHANG L,HU B,CHANG G,et al.Huber-based novel robust unscented Kalman filter[J].IET Science,Measurement&Technology,2012,6(6):502–509.
[16]KARLGAARD C D,SCHAUB H.Huber-based divided difference filtering[J].Journal of Guidance,Control,and Dynamics,2007,30(3):885–891.
[17]WANG X,CUI N,GUO J.Huber-based unscented filtering and its application to vision-based relative navigation[J].IET Radar,Sonar&Navigation,2010,4(1):134–141.
[18]WU H,CHEN S,YANG B,et al.Robust derivative-free cubature Kalman filter for bearings-only tracking[J].Journal of Guidance,Control,and Dynamics,2016,39(8):1866–1871.
[19]KOTECHA J H,DJURIC P M.Gaussian sum particle filtering[J].IEEE Transactions on Signal Processing,2003,51(10):2602–2612.
[20]LIN Qing,YIN Jianjun,ZHANG Jianqiu,et al.Gaussian sum filtering methods for nonlinear non-Gaussian models[J].Systems Engineering and Electronics,2010,32(12):2493–2499.(林青,尹建君,张建秋,等.非线性非高斯模型的高斯和滤波算法[J].系统工程与电子技术,2010,32(12):2493–2499.)