| 引用本文: | 刘锐,戚国庆,陈黎,盛安冬.不完全量测下随机有偏离散系统的Cramér-Rao下界[J].控制理论与应用,2010,27(7):927~932.[点击复制] |
| LIU Rui,QI Guo-qing,CHEN Li,SHENG An-dong.Cramér-Rao lower bounds for stochastic-bias discrete-time system with incomplete measurements[J].Control Theory and Technology,2010,27(7):927~932.[点击复制] |
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| 不完全量测下随机有偏离散系统的Cramér-Rao下界 |
| Cramér-Rao lower bounds for stochastic-bias discrete-time system with incomplete measurements |
| 摘要点击 2830 全文点击 1511 投稿时间：2009-03-12 修订日期：2009-10-15 |
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| DOI编号 10.7641/j.issn.1000-8152.2010.7.CCTA090248 |
| 2010,27(7):927-932 |
| 中文关键词 状态估计 不完全量测 随机有偏 Cramér-Rao下界 |
| 英文关键词 state estimation incomplete measurements stochastic-bias Cramér-Rao lower bound |
| 基金项目 国家自然科学基金资助项目(60804019, 60874118); 南京理工大学科技发展基金资助项目(XKF09020). |
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| 中文摘要 |
| 针对含有不完全随机有偏测量序列的状态估计问题, 给出了统计意义下的修正递推估计误差方差Cramér-Rao下界(CRLB)求解算法. 首先建立了不完全随机有偏量测离散系统的数学模型, 进而推导了枚举的CRLB和统计意义的CRLB计算式, 该统计意义的CRLB为枚举CRLB的下界, 其计算量远小于枚举CRLB求解的计算量. 最后, 以给定探测概率和偏差发生率下的一类光电跟踪系统为例, 进行了数字仿真. |
| 英文摘要 |
| A modified recursive Cramér-Rao lower bound(CRLB) of the statistical estimation error variance is derived for the state estimation with incomplete and stochastic-biased measurement sequences. Firstly, a mathematical model of the discrete-time system with incomplete and stochastic-biased measurements is built; and then, the enumeration CRLB and the statistical CRLB are derived, respectively. The proposed statistical CRLB is a lower bound of the enumeration CRLB, but its calculation complexity is far lower than that of the enumeration CRLB. Simulation is performed in an optical-electrical tracking system with pre-specified detection probability and biased occurrence probability. |