稀疏网格平方根求积分非线性滤波器

doi:10.3969/j.issn.0372-2112.2012.07.002

电子学报

稀疏网格平方根求积分非线性滤波器

伍宗伟^1,2, 姚敏立¹, 马红光¹, 贾维敏¹, 田方浩¹

1. 第二炮兵工程大学, 陕西西安 710025;
2. 解放军96265部队, 河南南阳 473000

收稿日期:2011-10-13 修回日期:2012-02-27 出版日期:2012-07-25
- 作者简介:
- 伍宗伟男,1985年11月出生于湖北十堰.现为第二炮兵工程大学博士生,从事姿态估计、信息融合方面的有关研究工作. E-mail:wzw_submit@163.com 姚敏立男,1966出生于山西运城,第二炮兵工程大学教授、博士生导师,主要从事信号与信息处理、智能天线、移动卫星通信等方面的教学和研究工作.近年来致力于开发低成本动中通的理论与工程研究. E-mail:yaominli@sohu.com
- 基金资助:
- 国家自然科学基金 (No.61179004,No.61179005)

Sparse-Grid Square-Root Quadrature Nonlinear Filter

WU Zong-wei^1,2, YAO Min-li¹, MA Hong-guang¹, JIA Wei-min¹, TIAN Fang-hao¹

1. The Second Artillery Engineering University, Xi’an, Shaanxi 710025, China;
2. The 96265^th Unit of PLA, Nanyang, Henan 473000, China

Received:2011-10-13 Revised:2012-02-27 Online:2012-07-25 Published:2012-07-25
- Supported by:
- National Natural Science Foundation of China (No.61179004, No.61179005)

摘要/Abstract

摘要： 针对具有加性噪声的非线性高斯动态系统的状态估计问题,本文提出一种新的基于稀疏网格法的平方根求积分滤波器(SSRQF),该滤波器通过稀疏网格取点来近似计算多维积分并进行平方根滤波.与常规QF的积分点数随着维数呈指数增长相比,该方法的积分点数随着维数呈多项式增长,减少了计算量;理论分析表明,无味卡尔曼滤波器(UKF)只是稀疏网格求积分滤波器(SQF)的一个特例,因此SSRQF在精度和取点上比UKF更为灵活.仿真实验表明,SSRQF的滤波精度均高于UKF和扩展卡尔曼滤波器(EKF),是一种效率较高的高精度非线性滤波算法.

关键词: 非线性滤波器, 稀疏网格, 高斯-厄米特积分, 求积分滤波器, 无味卡尔曼滤波器

Abstract: For nonlinear estimation with additive noise,we utilized the sparse-grid theory to propose a novel nonlinear filter,Sparse-grid Square-Root Quadrature Filter (SSRQF).The quadrature points for the conventional QF increases exponentially with the dimension.However,the new filter SSRQF uses the sparse-grid theory to reduce the number of quadrature points to a polynomial with the dimension,which alleviates the computation burden greatly.Through the theoretical analysis,we proposed that Unscented Kalman Filter (UKF) is only a special case for Sparse-grid Quadrature Filter (SQF),thus SSRQF is more flexible in terms of choosing points and controlling accuracy.The simulation results show that the SSRQF achieves higher accuracy than the UKF and the Extended Kalman Filter (EKF).Thus,it is a high accuracy nonlinear filter algorithm with computationally efficient.

Key words: nonlinear filter, sparse grid, Gauss-Hermite quadrature, quadrature filter, unscented Kalman filter

中图分类号:

TP391

伍宗伟, 姚敏立, 马红光, 等. 稀疏网格平方根求积分非线性滤波器[J]. 电子学报, DOI: 10.3969/j.issn.0372-2112.2012.07.002.

WU Zong-wei, YAO Min-li, MA Hong-guang, et al. Sparse-Grid Square-Root Quadrature Nonlinear Filter[J]. Acta Electronica Sinica, DOI: 10.3969/j.issn.0372-2112.2012.07.002.

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稀疏网格平方根求积分非线性滤波器

Sparse-Grid Square-Root Quadrature Nonlinear Filter

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