一般相关噪声下线性系统定区间平滑估计算法

陈嘉鸿 1; 2; 韩九强 1; 张忠华 2; 张新曼 1

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一般相关噪声下线性系统定区间平滑估计算法

专题研究 | 更新时间：2025-12-08

- 一般相关噪声下线性系统定区间平滑估计算法
- A Fixed-Interval Smoothing Algorithm for Linear Systems with General Correlated Noises
- 西安交通大学学报 2008年42卷第8期页码：954-957+1039
- 作者机构：
  
  1. 西安交通大学电子与信息工程学院,西安,710049
  2. 中国卫星海上测控部, 214431, 江苏江阴
- 作者简介：
- 基金信息：
  
  : 2007-12-10. 作者简介: 陈嘉鸿(1971-),男,博士生;韩九强(联系人),男,教授,博士生导师. 基金项目: 国家自然科学基金资助项目(60602025)
- DOI：
  中图分类号： TP271.8
- 网络首发：2008-08-10，
  
  纸质出版：2008
- 稿件说明：
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陈嘉鸿 1, 2, 韩九强 1, 等. 一般相关噪声下线性系统定区间平滑估计算法[J]. 西安交通大学学报, 2008,42(8):954-957+1039.

陈嘉鸿 1, 2, 韩九强 1, et al. A Fixed-Interval Smoothing Algorithm for Linear Systems with General Correlated Noises[J]. 2008, 42(8): 954-957+1039.
陈嘉鸿 1, 2, 韩九强 1, 等. 一般相关噪声下线性系统定区间平滑估计算法[J]. 西安交通大学学报, 2008,42(8):954-957+1039. DOI：

陈嘉鸿 1, 2, 韩九强 1, et al. A Fixed-Interval Smoothing Algorithm for Linear Systems with General Correlated Noises[J]. 2008, 42(8): 954-957+1039. DOI：

摘要

针对机动目标跟踪中固定区间平滑估计算法对噪声相关性考虑不完全的问题

提出了一种具有一般相关过程噪声与量测噪声的离散线性系统最优固定区间平滑估计算法.该算法通过将固定区间内全部量测进行集中式扩维

并对误差传递进行分析

从而精确给出了误差间的相关性

在线性无偏最小方差意义下对系统状态进行递推估计.与不考虑相关性的卡尔曼平滑算法以及仅考虑量测相关性的正、逆向滤波融合平滑估计算法相比

新算法在噪声的高斯分布假设下是最优的

且随噪声相关性增强其优越性越明显.仿真结果表明

在相关系数为0.36时

新算法的位置跟踪均方根误差比不考虑相关性和仅考虑量测相关性的平滑估计算法可降低38%.

Abstract

In view of on the incomplete consideration of noise correlation in the fixed-interval smoothing algorithm for maneuvering target tracking

an optimal fixed-interval smoothing algorithm is proposed for discrete-time linear system with general correlated measurement noises and process noises. Based on the linear unbiased minimum variance estimation theory

the new algorithm estimates the system states recursively by using the centralized expanding-dimension method with all measurements in the fixed interval

and calculates the correlations between the errors precisely using analysis of the error transfer property. Compared with the uncorrelated Kalman smoothing algorithm and the forward-backward filtering based fusion-smoothing algorithm in which only the measurement noises correlation is considered

the new algorithm is the best one under the hypothesis of Gauss distribution. Bigger the correlation coefficient is

more obvious the superiority of the new algorithm is. Simulation results show that when the correlation coefficient is 0.36

the root mean square error of position tracking of the new algorithm is decreased 38% or more compared with the uncorrelated and measurement correlated Kalman smoothing algorithm.

关键词

Keywords

references

MIRKIN L,TADMDR G. Fixed-lag smoothing as a constrained version of the fixed-interval case [C]∥Proceedings of the 2004 American Control Conference. Boston, Massachusetts, USA: American Automatic Control Council, 2004: 4165-4170.

DONALD C F, JAMES E P. The optimum linear smoother as a combination of two optimum linear filters [J]. IEEE Transactions on Automatic Control, 1969, 14(8): 387-390.

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韩崇昭,王洁,李晓榕.一般相关量测噪声下线性系统的平滑估计算法[J]. 西安交通大学学报, 2000, 34(9): 1-4.

HAN Chongzhao, WANG Jie, LI Xiaorong. Smoothing algorithm for linear systems with general correlated measurement noises [J]. Journal of Xi'an Jiaotong University, 2000, 34(9): 1-4.

左东广,韩崇昭,魏瑞轩,等.相关噪声情况下航迹的关联及融合算法[J].电子学报, 2002, 30(8): 1117-1120.

ZUO Dongguang, HAN Chongzhao, WEI Ruixuan,et al. Tracks association and fusion in case of correlated noises [J]. Acta Electronica Sinica, 2002, 30(8): 1117-1120.

LI Xiaorong, ZHU Yunmin, WANG Jie, et al. Optimal linear estimation fusion, part I: unified fusion rules [J]. IEEE Transactions on Information Theory, 2003, 49(9): 2192-2208.

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