使用随机部署的、有噪声的二元传感器的非参数场估计
Non-Parametric Field Estimation using Randomly Deployed, Noisy, Binary Sensors
摘要：
研究了由随机分布在场域上的传感器的二进制量化噪声观测值重建确定性数据场的问题。该研究的重点是在传感器部署中缺乏确定性控制，缺乏噪声分布的知识，以及缺乏传感精度和可靠性的极端。这样的不利条件是由可能的现实世界的情况下，大量的低成本，粗糙制造的传感器的集合被大规模部署在一个环境中，几乎可以假设的环境噪声。一个简单的估计，重建整个数据字段从这些不可靠的，二进制量化，噪声观测。技术条件几乎肯定和综合均方误差（MSE）收敛的估计的数据字段，传感器的数量趋于无穷大，推导和讨论它们的影响。对于有限维，有界变差，Sobolev可微函数类，具体的综合MSE衰减率。对于第一和第三功能类，这些速率被发现是最小最大顺序最优的无限精度传感和已知的噪声分布。
英文摘要：
The reconstruction of a deterministic data field from binary-quantized noisy observations of sensors which are randomly deployed over the field domain is studied. The study focuses on the extremes of lack of deterministic control in the sensor deployment, lack of knowledge of the noise distribution, and lack of sensing precision and reliability. Such adverse conditions are motivated by possible real-world scenarios where a large collection of low-cost, crudely manufactured sensors are mass-deployed in an environment where little can be assumed about the ambient noise. A simple estimator that reconstructs the entire data field from these unreliable, binary-quantized, noisy observations is proposed. Technical conditions for the almost sure and integrated mean squared error (MSE) convergence of the estimate to the data field, as the number of sensors tends to infinity, are derived and their implications are discussed. For finite-dimensional, bounded-variation, and Sobolev-differentiable function classes, specific integrated MSE decay rates are derived. For the first and third function classes these rates are found to be minimax order optimal with respect to infinite precision sensing and known noise distribution.
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。
