一种迭代收缩非线性状态约束滤波算法

doi:10.3969/j.issn.1001-2400.2011.01.017

J4 ›› 2011, Vol. 38 ›› Issue (1): 104-109.doi: 10.3969/j.issn.1001-2400.2011.01.017

一种迭代收缩非线性状态约束滤波算法

陈金广^1,2;李洁¹;高新波¹

(1. 西安电子科技大学电子工程学院，陕西西安 710071；
2. 西安工程大学计算机科学学院，陕西西安 710048)

收稿日期:2009-12-30 出版日期:2011-02-20 发布日期:2011-04-08
作者简介:陈金广(1977-)，男，西安电子科技大学博士研究生，E-mail: xacjg@163.com．
基金资助:
国家自然科学基金资助项目(60832005,60702061);陕西省教育厅自然科学专项资助项目(2010JK565)

Iterative shrinking filtering algorithm with nonlinear state constraints

CHEN Jinguang^1,2;LI Jie¹;GAO Xinbo¹

(1. School of Electronic Engineering, Xidian Univ., Xi'an 710071， China;
2. School of Computer Sci., Xi'an Polytechnic Univ., Xi'an 710048， China)

Received:2009-12-30 Online:2011-02-20 Published:2011-04-08

摘要/Abstract

摘要：

在滤波过程中有效地利用状态约束条件，能够提高滤波精度．当状态约束为非线性函数时，可以通过泰勒级数展开法进行线性化处理．然而该方法在非线性约束函数的雅可比矩阵不存在时失效，而使用水平滑动估计算法所需要的计算量很大．为此，采用基于U变换的最佳量测方法解决该问题．为了降低U变换过程中基点误差对估计性能带来的影响，将非线性约束看作具有多个大小不等的噪声方差的量测值，在量测更新阶段逐步收缩噪声方差，从而不断增强约束条件．经过多次迭代，改善了状态估计的误差性能．仿真结果表明，该算法在保证较高的滤波精度的条件下，运算时间是窗口尺寸为2的水平滑动估计算法的1/27．

关键词: 非线性状态约束, U变换, 状态估计, 滤波, 信息融合

Abstract:

In the process of filtering, the filtering accuracy can be improved if the state constraints are used in an effective manner. The nonlinear constrained function can be linearized by the Taylor series expansion. However, if the Jacobian matrix of the nonlinear constrained function is nonexistent, this method will not work anymore. Moreover, the moving horizon estimation (MHE) algorithm needs a heavy computational burden in this condition. So a perfect measurement method is proposed based on the unscented transform to solve this problem. Furthermore, in order to reduce the negative effect from the base point error, the nonlinear constraints can be treated as measurements with different noise covariance. The noise covariance shrinks in the measurement update stage, and the constrained conditions are enhanced step by step. The state estimation error is improved after some iterations. Simulation results show that the proposed algorithm can obtain a higher filtering accuracy, and that its computational time is 1/27 of that of the moving horizon estimation algorithm even if the window size is 2.

Key words: nonlinear state constraints, unscented transform, state estimation, filtering, information fusion

陈金广;李洁;高新波. 一种迭代收缩非线性状态约束滤波算法[J]. J4, 2011, 38(1): 104-109.

CHEN Jinguang;LI Jie;GAO Xinbo. Iterative shrinking filtering algorithm with nonlinear state constraints[J]. J4, 2011, 38(1): 104-109.

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一种迭代收缩非线性状态约束滤波算法

Iterative shrinking filtering algorithm with nonlinear state constraints

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