高斯和高阶无迹卡尔曼滤波算法

发布时间：2018-11-10 11:05

【摘要】：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.
[Abstract]:In order to improve the approximate accuracy of nonlinear transformation, a higher order unscented transformation (High orderUnscented Transform,HUT) mechanism is proposed, in which the sampling points are determined by HUT and the posterior probability density function of approximate state is obtained by numerical integration. A high order unscented Kalman filter (High-order UnscentedKalman Filter,HUKF) algorithm is established. In order to solve the nonlinear state estimation problem of non-Gao Si system, a novel state estimation algorithm (Gaussian Sum High order Unscented Kalman filter,GS-HUKF) is proposed, which combines HUKF with Gao Si and filtering (Gaussian Sum Filter,GSF, and has a high order unscented Kalman filter algorithm (Gaussian Sum High order Unscented Kalman filter,GS-HUKF). The core idea of the algorithm is to use a set of posterior probability densities of Gao Si distribution and de-approximation state, and to estimate each Gao Si distribution using high-order unscented Kalman filtering algorithm. The numerical simulation results show that the proposed HUT mechanism has a higher approximate accuracy than the conventional unscented transformation (Unscented Transform,UT). Compared with traditional GSF and Gao Si and particle filter (Gaussian Sum Particle Filter,GS-PF, the proposed GS-HUKF has the advantages of low computational complexity and high estimation accuracy.
【作者单位】：安徽科技学院电气与电子工程学院;东南大学仪器科学与工程学院;
【基金】：国家自然科学基金(No.61374215) 安徽科技学院人才稳定项目;安徽科技学院重点学科建设(No.AKZDXK2015C02)
【分类号】：TN713

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