噪声能量有界线性离散系统状态观测能力的定义及解析表达式
Definition and Analytical Expression on State Observe Ability for Linear Discrete-time Systems with the Bounded Noise Energy
摘要：
本文系统地研究了线性离散时间（LDT）系统观测能力的定义及其与信号检测性能的关系。首先，为了定义和分析实际系统对测量噪声的观测能力，将有界噪声模型分为六类。在噪声能量有界的情况下，利用状态观测误差定义了LDT系统的可观测椭球和图像可观测椭球，并提出了观测能力的概念。在此基础上，给出并证明了观测能力和信号检测性能的一些定理和性质，从而建立了观测能力最大化就是信号检测性能最优的理由。其次，提出并证明了能观椭球与能控椭球之间的一种对偶关系，这两个椭球的体积和半径分别具有某种反比关系。在此基础上，得到了两个可观测椭球体积的解析计算公式，并解构了这两个椭球的一些解析形状因子。在此基础上，可以进行体积、半径和形状因子的有效计算，并对观测能力进行分析和优化。第三，为了合理比较不同系统或不同系统参数的状态观测能力，讨论了输出变量、状态变量和系统模型的归一化问题。最后，数值实验结果表明了观测能力计算和比较方法的有效性。
英文摘要：
In this article, the definition on the observe ability and its relation to the signal detecting performance are studied systematically for the linear discrete-time(LDT) systems. Firstly, to define and analyze the observe ability for the practical systems with the measured noise, six kinds of bounded noise models are classified. For the noise energy bounded case, the observability ellipsoid and the image observability ellipsoid are defined by the state observed error and then a novel concept on the LDT systems, called as the observe ability, is proposed. Based on that, some theorems and properties about the observe ability and the signal detecting performances are given and proven, and then the reason that to maximize the observe ability is to optimize the signal detecting performances is established. Secondly, a dual relation between the observability ellipsoid and the controllability ellipsoid, which volumes and radii are respectively with some inverse relations, is stated and proven. Accordingly, the analytical computing equations for the volume of the two observability ellipsoids are got and some analytical shape factors of these ellipsoids are deconstructed. Based on these effective compting for the volumes, radii, and shape factors, analyzing and optimizing for the observe ability can be carried out. Thirdly, to compare rationally the state observe ability between the different systems or different system parameters, the normalization of the output variables, the state variables, and the system models are discussed. Finally, some numerical experiments and their results show the effectiveness of the computing and comparing methods for the observe ability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
