| 基于量化测量值的实时状态估计的PCRLB |
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| 引用本文： | 胡斌,沈志萍,苏为洲.基于量化测量值的实时状态估计的PCRLB[J].控制与决策,2018,33(10):1820-1824. |
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| 作者姓名： | 胡斌 沈志萍 苏为洲 |
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| 作者单位： | 华南理工大学自动化科学与工程学院，广州510640,河南师范大学数学与信息科学学院，河南新乡453007;河南师范大学大数据统计分析与优化控制河南省工程实验室，河南新乡453007,华南理工大学自动化科学与工程学院，广州510640 |
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| 基金项目： | 国家自然科学基金项目(61273109,61673183). |
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| 摘 要： | 针对网络化系统中的实时量化估计问题,研究基于量化测量值的离散时间系统实时状态估计均方误差的后验克拉美罗下界(PCRLB).给出量化律的最优实时重构值和最小实时均方失真函数.利用系统模型和量化律的最小实时均方失真函数,得到实时状态估计的PCRLB.所得到的PCRLB反映量化效应,尤其是量化律的实时均方失真函数对实时状态估计性能的影响.仿真算例表明,当基于通信网络的系统具有不稳定特征根时,在低比特率量化律的情形下,实时状态估计的PCRLB可能不是有界的.
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| 关 键 词： | 状态估计 量化 后验克拉美罗下界 失真函数 |
PCRLB in real-time state estimation with quantized measurements |
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| HU Bin,SHEN Zhi-ping and SU Wei-zhou.PCRLB in real-time state estimation with quantized measurements[J].Control and Decision,2018,33(10):1820-1824. |
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| Authors: | HU Bin SHEN Zhi-ping and SU Wei-zhou |
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| Affiliation: | College of Automation Science and Technology,South China University of Technology,Guangzhou510640,China,College of Mathematics and Information Science,He''nan Normal University,Xinxiang 453007,China;He''nan Engineering Laboratory for Big Data Statistical Analysis and Optimization Control,He''nan Normal University,Xinxiang453007,China and College of Automation Science and Technology,South China University of Technology,Guangzhou510640,China |
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| Abstract: | This paper studies the posterior Cramér-Rao lower bound(PCRLB) of the mean-square error in real-time state estimation for a discrete-time system with quantized measurements in the area of networked systems. The optimal real-time reconstruction and the minimum real-time mean-square distortion function of quantization law are presented. Then the PCRLB is obtained in terms of the model of the system and the minimum real-time mean-square distortion function of the quantization law adapted in the system. The proposed PCRLB shows the quantization effect, especially the influence of the real-time mean-square distortion function on the performance of the state estimation. It is found that in the case when the system with a communication network is unstable, the PCRLB may not be bounded for a quantization law with a low bit-rate. |
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