摘要翻译：
在某些估计问题中，并不是所有的参数都能被识别，这就导致了Fisher信息矩阵(FIM)的奇异性。CRM界(CRB)是FIM的逆，因此没有定义。为了正则化估计问题，可以对参数施加约束，并导出相应的CRBS。本文研究了局部可识别性与FIM正则性之间的对应关系。此外，FIM奇异点的个数等于具有良好定义的约束CRB和局部可辨识性所必需的独立约束的个数。通常，许多约束集可以使参数可识别，为CRB提供不同的值，这些值并不总是相关的。当约束条件可以选择时，我们提出了一个约束CRB，即FIM的伪逆，它给出了对于最小数目的约束条件，均方估计误差的最低界。这些结果被应用于盲FIR多信道估计的两种方法，这两种方法允许将信道识别到一个尺度或相位因子。对于未知的信道输入，这两种方法分别对应于确定性模型和高斯模型。研究了FIMs的奇异性和局部可辨识性，推导并解释了相应的约束CRBs。
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英文标题：
《Cram\'er-Rao Bounds for Blind Multichannel Estimation》
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作者：
Elisabeth de Carvalho and Dirk Slock
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最新提交年份：
2017
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Information Theory        信息论
分类描述：Covers theoretical and experimental aspects of information theory and coding. Includes material in ACM Subject Class E.4 and intersects with H.1.1.
涵盖信息论和编码的理论和实验方面。包括ACM学科类E.4中的材料，并与H.1.1有交集。
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一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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一级分类：Mathematics        数学
二级分类：Information Theory        信息论
分类描述：math.IT is an alias for cs.IT. Covers theoretical and experimental aspects of information theory and coding.
它是cs.it的别名。涵盖信息论和编码的理论和实验方面。
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英文摘要：
  In some estimation problems, not all the parameters can be identified, which results in singularity of the Fisher Information Matrix (FIM). The Cram\'er-Rao Bound (CRB), which is the inverse of the FIM, is then not defined. To regularize the estimation problem, one can impose constraints on the parameters and derive the corresponding CRBs. The correspondence between local identifiability and FIM regularity is studied here. Furthermore the number of FIM singularities is shown to be equal to the number of independent constraints necessary to have a well-defined constrained CRB and local identifiability. In general, many sets of constraints can render the parameters identifiable, giving different values for the CRB, that are not always relevant. When the constraints can be chosen, we propose a constrained CRB, the pseudo-inverse of the FIM, which gives, for a minimum number of constraints, the lowest bound on the mean squared estimation error. These results are applied to two approaches to blind FIR multichannel estimation which allow identification of the channel up to a scale or phase factor. These two approaches correspond to deterministic and Gaussian models for the unknown channel inputs. The singularities of the FIMs and local identifiability are studied and the corresponding constrained CRBs are derived and interpreted.
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PDF链接：
https://arxiv.org/pdf/1710.01605