Quadrature Kalman Particle Filter

巫春玲; 韩崇昭

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Quadrature Kalman Particle Filter

更新时间：2025-12-08

- Quadrature Kalman Particle Filter
- Vol. 43, Issue 2, Pages: 25-28+42(2009)
- 作者机构：
  
  西安交通大学电子与信息工程学院,西安,710049
- 作者简介：
- 基金信息：
- DOI：
  CLC： TP391
- Online First：10 February 2009，
  
  Published：2009
- 稿件说明：
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巫春玲, 韩崇昭. Quadrature Kalman Particle Filter[J]. 2009, 43(2): 25-28+42.
DOI：

巫春玲, 韩崇昭. Quadrature Kalman Particle Filter[J]. 2009, 43(2): 25-28+42. DOI：

摘要

针对非线性/非高斯系统的状态估计问题

提出一种采用求积分卡尔曼滤波(QKF)算法来产生重要性密度函数的粒子滤波新算法——PF-QKF算法. 新算法使用统计线性回归的方法

通过一套高斯-厄米特积分点来线性化非线性函数

不需要计算雅可比矩阵

易于实现

而且所产生的重要性密度函数在系统状态转移概率密度的基础上

融入最新的观测数据

提高了对系统状态后验概率的逼近程度. 理论分析和实验结果表明

PF-QKF算法的估计精度比无味粒子滤波(PF-UF)算法提高了约18%

其计算复杂度比PF-UF算法稍有降低

表明PF-QKF算法是一种很有效的非线性滤波算法.

Abstract

A new kind of quadrature Kalman particle filter is proposed for the state estimation of nonlinear/non-Gaussian systems. The new algorithm uses the quadrature Kalman filter(QKF)to generate the importance density function

and linearizes the nonlinear functions using the statistical linear regression method through a set of Gaussian-Hermite quadrature points. The algorithm does not evaluate the Jacobian matrix

and is easy to implement. Moreover

the importance density function integrates the latest observations into the system state transition density

so that the approximation to the system posterior density is improved. Theoretical analysis and experimental results show that

compared with the unscented particle filter(PF-UF)

the estimation accuracy of the new particle filter is improved by almost 18%

and its calculation cost is slightly reduced

which indicates the PF-QKF to be an effective nonlinear filtering algorithm.

关键词

Keywords

references

COSTA P. Adaptive model architecture and extended Kalman-Bucy filters [J]. IEEE Transactions on Aerospace and Electronic Systems, 1994, 30(2): 525-533.

GORDON N J, SALMOND D J, SMITH A F M. Novel approach to nonlinear/non-Gaussian Bayesian state estimation [J]. IEE Proceedings on Radar and Signal Processing, 1993, 140(2): 107-113.

Doucet A. On sequential simulation-based methods for Bayesian filtering, CUED/F-INFENG/TR.310 [R]. Cambridge,UK:Cambridge University Press, 1998: 1-26.

VAN DER MERWE R, DOUCET A, DE FREITAS N, et al. The unscented particle filter, CUED/F-INFEN G/TR, 380 [R]. Cambridge, UK: Cambridge University Press, 2000:1-45.

JULIER S J, UHLMANN J K. Unscented filtering and nonlinear estimation [J]. Proceedings of the IEEE, 2004, 92(3): 401-422.

ARASARATNAM I, HAYKIN S, ELLIOTT R J. Discrete-time nonlinear filtering algorithms using Gauss-Hermite quadrature [J]. Proceedings of the IEEE, 2007, 95(5): 953-977.

ITO K, XIONG K. Gaussian filters for nonlinear filtering problems [J]. IEEE Transactions on Automatic Control, 2000, 45(5): 910-927.

GOLUB G H, WELSCH J H. Calculation of Gauss Quadrature rules [J]. Math Comput, 1969, 23(106): 221-230.

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