Particle Filter Using Second-Order Central Difference

石勇; 韩崇昭

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Particle Filter Using Second-Order Central Difference

更新时间：2025-12-08

- Particle Filter Using Second-Order Central Difference
- Vol. 42, Issue 4, Pages: 409-413(2008)
- 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 April 2008，
  
  Published：2008
- 稿件说明：
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石勇, 韩崇昭. Particle Filter Using Second-Order Central Difference[J]. 2008, 42(4): 409-413.
DOI：

石勇, 韩崇昭. Particle Filter Using Second-Order Central Difference[J]. 2008, 42(4): 409-413. DOI：

摘要

为了改善非线性系统状态估计问题中粒子滤波算法的估计精度

提出采用二阶中心差分滤波方法来产生建议分布函数的新算法.新算法对非线性系统方程作中心差分的二阶Stirling插值公式进行展开

不需要计算雅克比矩阵

易于实现

并且采用Cholesky分解技术保证了协方差的正定性

在一定程度上减小了局部线性化近似的截断误差

并且在系统状态转移概率的基础上融合了最新的量测数据

提高了建议分布对系统状态后验概率的逼近程度.仿真实验表明

与无迹粒子滤波算法相比

新算法的计算量更小

估计精度提高了20%以上.

Abstract

To improve the filtering precision when dealing with the state estimation problem of nonlinear systems

a new particle filter is proposed. The particle filter uses second-order central difference filter to generate the proposal distribution. The second-order central difference based on Stirling's interpolation formula is used to generate approximations to nonlinear dynamics

which avoids the evaluation of the Jacobian derivative matrix and is easy to implement. Cholesky factorization is employed to ensure the positive definiteness of the covariance matrix. The truncated errors of the local linearization are reduced in certain extent

and the latest measurements are integrated into the system state transition density so that the approximation to the system posterior density is improved. Simulation results indicate that the state estimation accuracy of new particle filter is improved more than 20%and the calculation cost is decreased

compared with the unscented particle filter.

关键词

Keywords

references

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AMLAMLALAM S, MASKELL S, GORDON N J. A tutorial on particle filters for online non-linear/non-Gaussian bayesian tracking [J].IEEE Transactions on Signal Processing, 2002, 50(2):174-188.

KOTECHA, J H, DJURIC, P M. Gaussian particle filtering [J].IEEE Transactions on Signal Processing, 2003, 51(10):2592-2601.

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van der MERWE R, DOUCET A, de FREITAS N, et al. The unscented particle filter [R]. Technical Report of the Cambridge University Engineering Department CUED/F-INFENG/TR, 380. Cambridge, UK: Cambridge University Press,2000:1-45.

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STEFFENSEN J F. Interpolation [M]. Baltimore, USA: Williams Wilkins,1927.

SAULSON B G., CHANG K C. Nonlinear estimation comparison for ballistic missile tracking [J]. Automatica, 2004, 43(6):1424-1438.

邓建中,刘之行.计算方法[M]. 西安:西安交通大学出版社,2001.

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