Filtering is a recursive estimation of hidden states of a dynamic system from noisy measurements.Such problems appear in several branches of science and technology,ranging from target tracking to biomedical monitoring...Filtering is a recursive estimation of hidden states of a dynamic system from noisy measurements.Such problems appear in several branches of science and technology,ranging from target tracking to biomedical monitoring.A commonly practiced approach of filtering with nonlinear systems is Gaussian filtering.The early Gaussian filters used a derivative-based implementation,and suffered from several drawbacks,such as the smoothness requirements of system models and poor stability.A derivative-free numerical approximation-based Gaussian filter,named the unscented Kalman filter(UKF),was introduced in the nineties,which offered several advantages over the derivativebased Gaussian filters.Since the proposition of UKF,derivativefree Gaussian filtering has been a highly active research area.This paper reviews significant developments made under Gaussian filtering since the proposition of UKF.The review is particularly focused on three categories of developments:i)advancing the numerical approximation methods;ii)modifying the conventional Gaussian approach to further improve the filtering performance;and iii)constrained filtering to address the problem of discrete-time formulation of process dynamics.This review highlights the computational aspect of recent developments in all three categories.The performance of various filters are analyzed by simulating them with real-life target tracking problems.展开更多
The paper deals with state estimation problem of nonlinear non-Gaussian discrete dynamic systems for improvement of accuracy and consistency. An efficient new algorithm called the adaptive Gaussian-sum square-root cub...The paper deals with state estimation problem of nonlinear non-Gaussian discrete dynamic systems for improvement of accuracy and consistency. An efficient new algorithm called the adaptive Gaussian-sum square-root cubature Kalman filter（AGSSCKF） with a split-merge scheme is proposed. It is developed based on the squared-root extension of newly introduced cubature Kalman filter（SCKF） and is built within a Gaussian-sum framework. Based on the condition that the probability density functions of process noises and initial state are denoted by a Gaussian sum using optimization method, a bank of SCKF are used as the sub-filters to estimate state of system with the corresponding weights respectively, which is adaptively updated. The new algorithm consists of an adaptive splitting and merging procedure according to a proposed split-decision model based on the nonlinearity degree of measurement. The results of two simulation scenarios（one-dimensional state estimation and bearings-only tracking） show that the proposed filter demonstrates comparable performance to the particle filter with significantly reduced computational cost.展开更多
星间精密测距是导航星座实现自主导航的核心技术。针对导航星座中码测量值精度低但无整周模糊度,载波相位测量值精度高但存在整周模糊度的特点,该文根据贝叶斯递推原理提出了一种衰减记忆高斯和滤波(Fading Memory Gaussian Sum Filter,...星间精密测距是导航星座实现自主导航的核心技术。针对导航星座中码测量值精度低但无整周模糊度,载波相位测量值精度高但存在整周模糊度的特点,该文根据贝叶斯递推原理提出了一种衰减记忆高斯和滤波(Fading Memory Gaussian Sum Filter,FMGSF)的伪距估计方法。该方法用高斯和形式近似表示系统后验概率密度,并根据卡尔曼滤波原理来更新高斯项的均值和方差,同时引入衰减记忆因子克服由于模型失配导致的滤波结果发散问题,利用重采样解决由于载波相位测量值不确定导致的算法复杂度增加问题。理论分析和仿真结果表明,该文提出的方法不仅能够克服周跳对伪距估计的影响,而且可以获得更好的测距精度。展开更多
通过将模型的状态噪声和观测噪声均表示成高斯和的形式,推导出非线性非高斯状态空间模型的高斯和递推算法,进一步提出了对应的扩展卡尔曼和滤波器(extended Kalman sum filter,EKSF)和高斯厄密特和滤波器(Gauss-Hermite sum filter,GHSF...通过将模型的状态噪声和观测噪声均表示成高斯和的形式,推导出非线性非高斯状态空间模型的高斯和递推算法,进一步提出了对应的扩展卡尔曼和滤波器(extended Kalman sum filter,EKSF)和高斯厄密特和滤波器(Gauss-Hermite sum filter,GHSF)。EKSF和GHSF分别用扩展卡尔曼滤波器(extended Kalman filter,EKF)和高斯厄密特滤波器(Gauss-Hermite filter,GHF)作为高斯子滤波器。分析的结果表明,现有的高斯和滤波算法是本文算法的特例;仿真结果表明,EKSF和GHSF能有效处理非线性非高斯模型的状态滤波问题,与高斯和粒子滤波器(Gaussian sum particle filter,GSPF)相比,EKSF和GHSF在保证精度的同时,大大降低了计算量,仿真时间分别约为GSPF的5%和6%。展开更多
算法将模型中的条件线性状态方程代入观测方程,并融合线性状态的过程噪声和观测噪声,再与非线性状态方程联立,由高斯和滤波器(Gaussian sum filter,GSF)获得非线性状态的估计;然后将估计值代入线性状态方程与观测方程,由卡尔曼滤波器(Ka...算法将模型中的条件线性状态方程代入观测方程,并融合线性状态的过程噪声和观测噪声,再与非线性状态方程联立,由高斯和滤波器(Gaussian sum filter,GSF)获得非线性状态的估计;然后将估计值代入线性状态方程与观测方程,由卡尔曼滤波器(Kalman Filter,KF)获得线性状态的估计。此外,获得的非线性状态估计的方差还用于修正线性状态的估计。将GSF-KF算法应用于目标跟踪的仿真结果表明,与现有Rao-Blackwellized粒子滤波器(Rao-Blackwellized Particle Filter,RBPF)相比,新方法在保证精度的同时,明显提高了实时性,计算时间仅约为RBPF的7%。展开更多
为了提高非线性变换的近似精度,提出了一种高阶无迹变换(High orderUnscented Transform,HUT)机制,利用HUT确定采样点并进行数值积分去近似状态的后验概率密度函数,建立了高阶无迹卡尔曼滤波(High-order UnscentedKalman Filter,HUKF)算...为了提高非线性变换的近似精度,提出了一种高阶无迹变换(High orderUnscented Transform,HUT)机制,利用HUT确定采样点并进行数值积分去近似状态的后验概率密度函数,建立了高阶无迹卡尔曼滤波(High-order UnscentedKalman Filter,HUKF)算法.进一步的为了解决非线性、非高斯系统的状态估计问题,将HUKF与高斯和滤波(Gaussian Sum Filter,GSF)相结合,提出了一种高斯和高阶无迹卡尔曼滤波算法(Gaussian Sum High order Unscented Kalman filter,GS-HUKF),该算法的核心思想是利用一组高斯分布的和去近似状态的后验概率密度,同时针对每一个高斯分布采用高阶无迹卡尔曼滤波算法进行估计.数值仿真实验结果表明,提出的HUT机制与普通的无迹变换(Unscented Transform,UT)相比,具有更高的近似精度;提出的GS-HUKF与传统的GSF以及高斯和粒子滤波器(Gaussian Sum Particle Filter,GS-PF)相比,兼容了二者的优点,即具有计算复杂度低和估计精度高的特性.展开更多
文摘Filtering is a recursive estimation of hidden states of a dynamic system from noisy measurements.Such problems appear in several branches of science and technology,ranging from target tracking to biomedical monitoring.A commonly practiced approach of filtering with nonlinear systems is Gaussian filtering.The early Gaussian filters used a derivative-based implementation,and suffered from several drawbacks,such as the smoothness requirements of system models and poor stability.A derivative-free numerical approximation-based Gaussian filter,named the unscented Kalman filter(UKF),was introduced in the nineties,which offered several advantages over the derivativebased Gaussian filters.Since the proposition of UKF,derivativefree Gaussian filtering has been a highly active research area.This paper reviews significant developments made under Gaussian filtering since the proposition of UKF.The review is particularly focused on three categories of developments:i)advancing the numerical approximation methods;ii)modifying the conventional Gaussian approach to further improve the filtering performance;and iii)constrained filtering to address the problem of discrete-time formulation of process dynamics.This review highlights the computational aspect of recent developments in all three categories.The performance of various filters are analyzed by simulating them with real-life target tracking problems.
基金supported by the National Natural Science Foundation of China(No. 61032001)Shandong Provincial Natural Science Foundation of China (No. ZR2012FQ004)
文摘The paper deals with state estimation problem of nonlinear non-Gaussian discrete dynamic systems for improvement of accuracy and consistency. An efficient new algorithm called the adaptive Gaussian-sum square-root cubature Kalman filter（AGSSCKF） with a split-merge scheme is proposed. It is developed based on the squared-root extension of newly introduced cubature Kalman filter（SCKF） and is built within a Gaussian-sum framework. Based on the condition that the probability density functions of process noises and initial state are denoted by a Gaussian sum using optimization method, a bank of SCKF are used as the sub-filters to estimate state of system with the corresponding weights respectively, which is adaptively updated. The new algorithm consists of an adaptive splitting and merging procedure according to a proposed split-decision model based on the nonlinearity degree of measurement. The results of two simulation scenarios（one-dimensional state estimation and bearings-only tracking） show that the proposed filter demonstrates comparable performance to the particle filter with significantly reduced computational cost.
文摘星间精密测距是导航星座实现自主导航的核心技术。针对导航星座中码测量值精度低但无整周模糊度,载波相位测量值精度高但存在整周模糊度的特点,该文根据贝叶斯递推原理提出了一种衰减记忆高斯和滤波(Fading Memory Gaussian Sum Filter,FMGSF)的伪距估计方法。该方法用高斯和形式近似表示系统后验概率密度,并根据卡尔曼滤波原理来更新高斯项的均值和方差,同时引入衰减记忆因子克服由于模型失配导致的滤波结果发散问题,利用重采样解决由于载波相位测量值不确定导致的算法复杂度增加问题。理论分析和仿真结果表明,该文提出的方法不仅能够克服周跳对伪距估计的影响,而且可以获得更好的测距精度。
文摘通过将模型的状态噪声和观测噪声均表示成高斯和的形式,推导出非线性非高斯状态空间模型的高斯和递推算法,进一步提出了对应的扩展卡尔曼和滤波器(extended Kalman sum filter,EKSF)和高斯厄密特和滤波器(Gauss-Hermite sum filter,GHSF)。EKSF和GHSF分别用扩展卡尔曼滤波器(extended Kalman filter,EKF)和高斯厄密特滤波器(Gauss-Hermite filter,GHF)作为高斯子滤波器。分析的结果表明,现有的高斯和滤波算法是本文算法的特例;仿真结果表明,EKSF和GHSF能有效处理非线性非高斯模型的状态滤波问题,与高斯和粒子滤波器(Gaussian sum particle filter,GSPF)相比,EKSF和GHSF在保证精度的同时,大大降低了计算量,仿真时间分别约为GSPF的5%和6%。
文摘为了提高非线性变换的近似精度,提出了一种高阶无迹变换(High orderUnscented Transform,HUT)机制,利用HUT确定采样点并进行数值积分去近似状态的后验概率密度函数,建立了高阶无迹卡尔曼滤波(High-order UnscentedKalman Filter,HUKF)算法.进一步的为了解决非线性、非高斯系统的状态估计问题,将HUKF与高斯和滤波(Gaussian Sum Filter,GSF)相结合,提出了一种高斯和高阶无迹卡尔曼滤波算法(Gaussian Sum High order Unscented Kalman filter,GS-HUKF),该算法的核心思想是利用一组高斯分布的和去近似状态的后验概率密度,同时针对每一个高斯分布采用高阶无迹卡尔曼滤波算法进行估计.数值仿真实验结果表明,提出的HUT机制与普通的无迹变换(Unscented Transform,UT)相比,具有更高的近似精度;提出的GS-HUKF与传统的GSF以及高斯和粒子滤波器(Gaussian Sum Particle Filter,GS-PF)相比,兼容了二者的优点,即具有计算复杂度低和估计精度高的特性.
