线性/非线性系统的混合动态滤波理论及应用
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摘要
针对既有线性状态又有非线性状态的系统,本文给出了混合动态滤波的概念。即分別用非线性滤波算法和线性滤波算汉估计系统中的非线性状态和线性状态,并提出了多种混合动态滤波算法,包括四种高斯混合动态滤波算法和三种非高斯混合动态滤波算法。其中高斯混合动态滤波算法为:扩展卡尔曼滤波-卡尔曼滤波(extended Kalman filtering-Kalman filtering,EKF-KF)、unscented卡尔曼滤波-卡尔曼滤波(unscented Kalman filtering-Kalman filtering,UKF-KF)、中心差分滤波-卡尔曼滤波(central difference filtering-Kalman filtering,CDF-KF)、高斯厄米特滤波-卡尔曼滤波(Gaussian Hermite filtering-Kalman filtering,GHF-KF)算法;非高斯混合动态滤波算法为:边缘Rao-Blackwellized粒子滤波(marginalRao-Blackwellized particle filtering,MRBPF)、多项式预测滤波-卡尔曼滤波(polynomial predictive filtering-Kalman filtering,PPF-KF)、高斯和滤波-卡尔曼滤波(Gaussian sum filtering-Kalman filtering,GSF-KF)算法。在这些混合动态滤波算法中,我们分別用EKF、UKF、CDF、GHF、边缘粒子滤波器(marginal particlefilter,MPF)、PPF、GSF进行非线性状态的估计,而线性状态均由KF进行估计。
进一步,本文详细推导并分析了提出的高斯混合动态滤波算法的性能和适用场合,分析的结果表明,EKF-KF、UKF-KF、CDF-KF、GHF-KF算法的估计精度由高到低依次为:GHF-KF、UKF-KF(CDF-KF)、EKF-KF;同时本文给出了MPF算法的收敛性证明,并定性分析了MRBPF算法及其他非高斯混合动态滤波算法的性能及具体适用情况。
此外,本文还将提出的混合动态滤波算法应用于地形辅助导航和机动目标跟踪。地形辅助导航的仿真结果表明,MRBPF算法在状态估计的均方根误差(rootmean square error,RMSE)、估计稳定性、独立粒子数、粒子权重、估计收敛性等方而均优于RBPF:机动目标跟踪的仿真结果表明,提出的算法虽然在估计精度上略低于RBPF,却明显降低了算法复杂度,提高了算法实时性,平均计算时间比RBPF降低一个数量级以上,各种混合动态滤波算法精度由高到低依次为:GHF-KF、CDF-KF(UKF-KF)、GSF-KF(EKF-KF)、PPF-KF,这个结果与我们的理论分析一致。
In this thesis,we present the concept of mixed dynamic filtering,which is to use nonlinear and linear filtering methods to estimate nonlinear and linear states respectively,for models where the states have both linear and nonlinear parts.And also several mixed filtering dynamic algorithms are propose,which are composed of Gaussian mixed dynamic filtering algorithm and non-Gaussian mixed dynamic filtering algorithm,which includes extended Kalman filtering-Kalman filtering (EKF-KF),unscented Kalman filtering-Kalman filtering(UKF-KF),central difference filtering-Kalman filtering(CDF-KF),Gaussian Hermite filtering-Kalman filtering (GHF-KF) and marginal Rao-Blackwellized particle filtering(MRBPF),polynomial predictive filtering-Kalman filtering(PPF-KF),Gaussian sum filtering-Kalman filtering(GSF-KF) respectively,where we use EKE UKF,CDF,GHF,marginal particle filter(MPF),PPF,GSF to estimate the nonlinear states of the models respectively,while the linear states are all estimated by the KF.
Moreover we analyze the performance of the proposed Gaussian mixed dynamic filtering algorithms and the application environments.The analysis results show that the order of the Gaussian mixed filtering algorithm in errors(sort ascending) is: GHF-KF、UKF-KF(CDF-KF)、EKF-KF.Meanwhile we prove of the convergence results of the MPF and also give the qualitative analysis of the performance of the MRBPF and the other non-Gaussian mixed dynamic filtering algorithms,together with their application environments.
Further more the proposed algorithms are simulated in the terrain aided navigation(TAN) and the maneuvering target tracking(MTT) domains.The results of the TAN show that the MRBPF outperforms the RBPF in root mean square errors (RMSE) of the state estimate,stability,unique particle count,convergence properties and the particle weight variance.And the results of the MTT show that the proposed algorithm only consume less than 10%the computing time required by the RBPF with just a little filtering performance decline.The performances sequence in descending in MTT simulation is:GHF-KF、CDF-KF(UKF-KF)、GSF-KF(EKF-KF)、PPF-KF, which coincides with the analysis results.
进一步,本文详细推导并分析了提出的高斯混合动态滤波算法的性能和适用场合,分析的结果表明,EKF-KF、UKF-KF、CDF-KF、GHF-KF算法的估计精度由高到低依次为:GHF-KF、UKF-KF(CDF-KF)、EKF-KF;同时本文给出了MPF算法的收敛性证明,并定性分析了MRBPF算法及其他非高斯混合动态滤波算法的性能及具体适用情况。
此外,本文还将提出的混合动态滤波算法应用于地形辅助导航和机动目标跟踪。地形辅助导航的仿真结果表明,MRBPF算法在状态估计的均方根误差(rootmean square error,RMSE)、估计稳定性、独立粒子数、粒子权重、估计收敛性等方而均优于RBPF:机动目标跟踪的仿真结果表明,提出的算法虽然在估计精度上略低于RBPF,却明显降低了算法复杂度,提高了算法实时性,平均计算时间比RBPF降低一个数量级以上,各种混合动态滤波算法精度由高到低依次为:GHF-KF、CDF-KF(UKF-KF)、GSF-KF(EKF-KF)、PPF-KF,这个结果与我们的理论分析一致。
In this thesis,we present the concept of mixed dynamic filtering,which is to use nonlinear and linear filtering methods to estimate nonlinear and linear states respectively,for models where the states have both linear and nonlinear parts.And also several mixed filtering dynamic algorithms are propose,which are composed of Gaussian mixed dynamic filtering algorithm and non-Gaussian mixed dynamic filtering algorithm,which includes extended Kalman filtering-Kalman filtering (EKF-KF),unscented Kalman filtering-Kalman filtering(UKF-KF),central difference filtering-Kalman filtering(CDF-KF),Gaussian Hermite filtering-Kalman filtering (GHF-KF) and marginal Rao-Blackwellized particle filtering(MRBPF),polynomial predictive filtering-Kalman filtering(PPF-KF),Gaussian sum filtering-Kalman filtering(GSF-KF) respectively,where we use EKE UKF,CDF,GHF,marginal particle filter(MPF),PPF,GSF to estimate the nonlinear states of the models respectively,while the linear states are all estimated by the KF.
Moreover we analyze the performance of the proposed Gaussian mixed dynamic filtering algorithms and the application environments.The analysis results show that the order of the Gaussian mixed filtering algorithm in errors(sort ascending) is: GHF-KF、UKF-KF(CDF-KF)、EKF-KF.Meanwhile we prove of the convergence results of the MPF and also give the qualitative analysis of the performance of the MRBPF and the other non-Gaussian mixed dynamic filtering algorithms,together with their application environments.
Further more the proposed algorithms are simulated in the terrain aided navigation(TAN) and the maneuvering target tracking(MTT) domains.The results of the TAN show that the MRBPF outperforms the RBPF in root mean square errors (RMSE) of the state estimate,stability,unique particle count,convergence properties and the particle weight variance.And the results of the MTT show that the proposed algorithm only consume less than 10%the computing time required by the RBPF with just a little filtering performance decline.The performances sequence in descending in MTT simulation is:GHF-KF、CDF-KF(UKF-KF)、GSF-KF(EKF-KF)、PPF-KF, which coincides with the analysis results.
引文
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