基于Huber的鲁棒广义高阶容积卡尔曼滤波算法
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摘要
为提高随机变量非高斯分布时广义高阶容积卡尔曼滤波(GHCKF)的鲁棒性,提出一种基于Huber的鲁棒GHCKF算法.从近似贝叶斯估计角度,解释Huber方法作用于卡尔曼滤波的本质是对新息进行截断平均.采用Huber方法处理观测量,进行标准的GHCKF量测更新,从而实现算法的鲁棒化.所提出算法充分利用容积变换的优势,无需通过统计线性回归模型对系统的非线性量测模型进行近似.仿真结果表明,所提出算法具有鲁棒性强和估计精度高的特点.
To further improve the filtering accuracy and robustness of generalized high-degree cubature Kalman filter when the random variable is with non-Gaussian distribution, a filtering algorithm named Huber-based robust generalized high-degree cubature Kalman filter algorithm is proposed. It is interpreted that the basic idea of the Huber method acting on the Kalman filter can be described as truncating the average from the perspective of recursive Bayesian approximation estimation. The observation vector is preprocessed by using the Huber method, and the normal measurement update is implemented, so that the robustness of the GHCKF algorithm is realized. The proposed method doesn't need approximating nonlinear measurements model by using the statistical linear regression model. The simulation results show that the proposed method has superior performance in robustness and estimation precision.
To further improve the filtering accuracy and robustness of generalized high-degree cubature Kalman filter when the random variable is with non-Gaussian distribution, a filtering algorithm named Huber-based robust generalized high-degree cubature Kalman filter algorithm is proposed. It is interpreted that the basic idea of the Huber method acting on the Kalman filter can be described as truncating the average from the perspective of recursive Bayesian approximation estimation. The observation vector is preprocessed by using the Huber method, and the normal measurement update is implemented, so that the robustness of the GHCKF algorithm is realized. The proposed method doesn't need approximating nonlinear measurements model by using the statistical linear regression model. The simulation results show that the proposed method has superior performance in robustness and estimation precision.
引文
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[6]Zhang X C.Cubature information filters using high-degree and embedded cubature rules[J].Circuits System Signal Process,2014,33(3):1799-1818.
[7]Huber P.Robust estimation of a location parameter[J].Annals of Mathematical Statistics,1964,35(2):73-101.
[8]Karlgaard C D,Schaub H.Huber-based divided difference filtering[J].J of Guidance,Control,and Dynamics,2007,30(3):885-891.
[9]Lefebvre T,Bruyinckx H,de Schutter J.Comment on“A new method for the nonlinear trans formation of means and covariances in filters and estimators”[J].IEEE Trans on Automatic Control,2002,47(8):1406-1409.
[10]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.
[11]黄玉,武立华,孙枫.基于Huber M估计的鲁棒Cubature卡尔曼滤波算法[J].控制与决策,2014,29(3):572-577.(Huang Y,Wu L H,Sun F.Robust cubature Kalman filter based on Huber M estimator[J].Control and Decision,2014,29(3):572-577.)
[12]张文杰,王世元,冯亚丽,等.基于Huber的高阶容积卡尔曼跟踪算法[J].物理学报,2016,65(8):088401-1-088401-9.(Zhang W J,Wang S Y,Feng Y L,et al.Huber-based high-degree cubature Kalman tracking algorithm[J].Acta Physica Sinica,2016,65(8):088401-1-088401-9.)
[13]Mcnamee J,Stenger F.Construction of fully symmetric numerical integration formulas[J].Numerische Mathmatik,1967,10(4):327-344.
[14]Zhang X C,Teng Y L.A new derivation of the cubature Kalman filters[J].Asian J of Control,2014,16(5):1501-1510.
[2]Julier S J,Uhlman J K,Durrant-Whyte H F.A new method for the nonlinear transformation of means and covariances in filters and estimators[J].IEEE Trans on Automatic Control,2000,45(3):477-482.
[3]Norgaard M,Poulsen N K,Ravn O.New developments in state estimation for nonlinear systems[J].Automatica,2000,36(11):1627-1638.
[4]Arasaratnam I,Haykin S.Cubature Kalman filtrs[J].IEEE Trans on Automatic Control,2009,54(6):1254-1269.
[5]Bin Jia,Ming Xin,Yang Cheng.High-degree cubature Kalman filters[J].Automatica,2013,49(4):510-518.
[6]Zhang X C.Cubature information filters using high-degree and embedded cubature rules[J].Circuits System Signal Process,2014,33(3):1799-1818.
[7]Huber P.Robust estimation of a location parameter[J].Annals of Mathematical Statistics,1964,35(2):73-101.
[8]Karlgaard C D,Schaub H.Huber-based divided difference filtering[J].J of Guidance,Control,and Dynamics,2007,30(3):885-891.
[9]Lefebvre T,Bruyinckx H,de Schutter J.Comment on“A new method for the nonlinear trans formation of means and covariances in filters and estimators”[J].IEEE Trans on Automatic Control,2002,47(8):1406-1409.
[10]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.
[11]黄玉,武立华,孙枫.基于Huber M估计的鲁棒Cubature卡尔曼滤波算法[J].控制与决策,2014,29(3):572-577.(Huang Y,Wu L H,Sun F.Robust cubature Kalman filter based on Huber M estimator[J].Control and Decision,2014,29(3):572-577.)
[12]张文杰,王世元,冯亚丽,等.基于Huber的高阶容积卡尔曼跟踪算法[J].物理学报,2016,65(8):088401-1-088401-9.(Zhang W J,Wang S Y,Feng Y L,et al.Huber-based high-degree cubature Kalman tracking algorithm[J].Acta Physica Sinica,2016,65(8):088401-1-088401-9.)
[13]Mcnamee J,Stenger F.Construction of fully symmetric numerical integration formulas[J].Numerische Mathmatik,1967,10(4):327-344.
[14]Zhang X C,Teng Y L.A new derivation of the cubature Kalman filters[J].Asian J of Control,2014,16(5):1501-1510.