高斯和高阶无迹卡尔曼滤波算法

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 order Unscented 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 Unscented Kalman 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.

Gaussian Sum High Order Unscented Kalman Filtering Algorithm

A novel high order unscented transform (HUT) mechanism is proposed to improve the approximation accuracy of the nonlinear transformation.The HUT is adopted to select the Sigma points which can be used to approximate the posterior probability density of state variable by numerical integration.Thus the high order unscented Kalman filtering (HUKF) algorithm can be made up.Further,to solve the state estimation problem for nonlinear/non-Gaussian system,Gaussian sum high order unscented Kalman filter (GS-HUKF) is proposed by combining the HUKF and Gaussian sum filter (GSF).The basic idea of the GS-HUKF is that a cluster of Gaussian distribution is used to approximate the posterior probability density of state variable.At the mean time,each separated Gaussian distribution is estimated by HUKF.Numerical simulation results demonstrate that the proposed HUT has higher estimation precision than ordinary unscented transform (UT) method.The GS-HUKF has integrated advantages with respect to estimation accuracy and computational complexity and its performance is superior to the existing Gaussian sum filters.