摘要翻译：
我们研究了由在资源约束下运行的传感器网络收集的观测数据估计随机过程的问题。当过程的动力学和传感器观测由状态空间模型描述且资源无限时，常规的Kalman滤波器提供最小均方误差(MMSE)估计。然而，在任何给定时间，对可用通信带宽和计算能力和/或功率的限制对其观测可用于计算估计的网络节点的数量施加限制。我们将传感器信息最丰富子集的选择问题归结为一致拟阵约束下单调集函数最大化的组合问题。对于MMSE估计准则，我们证明了目标函数的最大元素曲率满足一定的上界约束，因此是弱子模的。我们开发了一个高效的随机贪婪算法来选择传感器，并在这种情况下建立了估计器性能的保证。大量的仿真结果表明，与最先进的贪婪和半定规划松弛方法相比，随机贪婪算法的有效性。
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英文标题：
《Randomized Greedy Sensor Selection: Leveraging Weak Submodularity》
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作者：
Abolfazl Hashemi, Mahsa Ghasemi, Haris Vikalo, and Ufuk Topcu
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最新提交年份：
2018
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分类信息：

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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英文摘要：
  We study the problem of estimating a random process from the observations collected by a network of sensors that operate under resource constraints. When the dynamics of the process and sensor observations are described by a state-space model and the resource are unlimited, the conventional Kalman filter provides the minimum mean-square error (MMSE) estimates. However, at any given time, restrictions on the available communications bandwidth and computational capabilities and/or power impose a limitation on the number of network nodes whose observations can be used to compute the estimates. We formulate the problem of selecting the most informative subset of the sensors as a combinatorial problem of maximizing a monotone set function under a uniform matroid constraint. For the MMSE estimation criterion we show that the maximum element-wise curvature of the objective function satisfies a certain upper-bound constraint and is, therefore, weak submodular. We develop an efficient randomized greedy algorithm for sensor selection and establish guarantees on the estimator's performance in this setting. Extensive simulation results demonstrate the efficacy of the randomized greedy algorithm compared to state-of-the-art greedy and semidefinite programming relaxation methods.
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PDF链接：
https://arxiv.org/pdf/1807.08627