Gaussian Sum High Order Unscented Kalman Filtering Algorithm

WANG Lei; CHENG Xiang-hong; LI Shuang-xi

doi:10.3969/j.issn.0372-2112.2017.02.022

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Gaussian Sum High Order Unscented Kalman Filtering Algorithm

更新时间：2025-07-16

- Gaussian Sum High Order Unscented Kalman Filtering Algorithm
- Acta Electronica Sinica Vol. 45, Issue 2, Pages: 424-430(2017)
- 作者机构：
  
  1. 安徽科技学院电气与电子工程学院,安徽,蚌埠,233100
  2. 东南大学仪器科学与工程学院,江苏,南京,210096
  3. 安徽科技学院电气与电子工程学院,安徽,蚌埠,233100
  4. 东南大学仪器科学与工程学院,江苏,南京,210096
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.61374215);Talents XXXX Project of Anhui Science And Technology University;Key Discipline Construction Plan of Anhui Science And Technology University (No.AKZDXK2015C02)
- DOI：10.3969/j.issn.0372-2112.2017.02.022
  CLC： TN713
- Published Online：25 February 2017，
  
  Published：2017
- 稿件说明：
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WANG Lei, CHENG Xiang-hong, LI Shuang-xi. Gaussian Sum High Order Unscented Kalman Filtering Algorithm[J]. Acta Electronica Sinica, 2017, 45(2): 424-430.
DOI：

WANG Lei, CHENG Xiang-hong, LI Shuang-xi. Gaussian Sum High Order Unscented Kalman Filtering Algorithm[J]. Acta Electronica Sinica, 2017, 45(2): 424-430. DOI： 10.3969/j.issn.0372-2112.2017.02.022.

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 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.

Abstract

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.

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