基于不完全量测下离散线性滤波的修正Riccati方程

许志刚; 盛安冬; 郭  治

引用本文:	许志刚,盛安冬,郭治.基于不完全量测下离散线性滤波的修正Riccati方程[J].控制理论与应用,2009,26(6):673~677.[点击复制]
	XU Zhi-gang,SHENG An-dong,GUO Zhi.The modified Riccati equation for discrete-time linear filtering with incomplete measurements[J].Control Theory and Technology,2009,26(6):673~677.[点击复制]

基于不完全量测下离散线性滤波的修正Riccati方程

The modified Riccati equation for discrete-time linear filtering with incomplete measurements

摘要点击 1641 全文点击 1255 投稿时间：2007-11-22 修订日期：2008-09-19

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DOI编号 10.7641/j.issn.1000-8152.2009.6.018

2009,26(6):673-677

中文关键词线性滤波不完全量测修正Riccati差分方程(MRDE) 数据丢失位置

英文关键词 linear filtering incomplete measurements modified Riccati difference equation(MRDE) location of missing data

基金项目国家自然科学基金资助项目(60804019); 2004年度江苏省高校“青蓝工程”优秀青年骨干教师培养人选资金资助项目; 淮海工学院自然科学基金资助项目(Z2007021).

作者	单位	E-mail
许志刚	南京理工大学自动化学院, 江苏南京 210094 淮海工学院理学院, 江苏连云港 222005	xuzhigang@126.com
盛安冬	南京理工大学自动化学院, 江苏南京 210094	shengandong@mail.njust.edu.cn
郭治	南京理工大学自动化学院, 江苏南京 210094	guozhi@mail.njust.edu.cn

中文摘要

在量测数据丢失下滤波方程和Riccati方程出现一些新的性质变化．探测概率小于1的不完全量测条件下,利用正定矩阵性质和Lyapunov不等式, 研究了离散系统修正Riccati差分方程(MRDE)与数据丢失位置之间的关系．结果表明在一定条件下MRDE解与丢失数据位置满足单调递减的函数系．由于统计意义下的理论MRDE模型求解计算量随丢失/探测数量增加而呈指数型递增, 本文最后给出了一组便于工程应用的期望状态误差协方差上下界算法, 算法复杂度为O(k²).

英文摘要

There are some changes of property in the filter equation and Riccati equation when missing measurements occur．When the probability of detection is less than unity, by utilizing the properties of a positive-definite matrix and the Lyapunov inequality, we investigate the relation between the modified Riccati difference equation(MRDE) and the location of missing data in incomplete measurements for a discrete-time system．It is shown that under certain conditions the MRDE is a monotonically decreasing function of the location of missing data．Because the computation load for a theoretical MRDE statistically grows exponentially with respect to the number of possible miss/detection sequences, we give the upper and lower bounds of the covariance for the state-error for practical applications. The calculation complexity is O(k²).