基于非高斯非均匀时间序列观测的二值空间随机场重构
Binary Spatial Random Field Reconstruction from Non-Gaussian Inhomogeneous Time-series Observations
AI总结：
针对非高斯非均匀时间序列观测下的二值空间随机场重构问题，提出基于近似似然比检验的单比特压缩与S-BLUE两步推断方法，并通过仿真和NEA天气数据集验证其有效性。
摘要：
我们开发了一种用于二值空间现象空间随机场重构的新模型。在该模型中，传感器部署在覆盖广阔地理区域的无线传感器网络中。每个传感器测量一个依赖于该空间现象的非高斯、非均匀时间过程。系统采用两类传感器：一类在特定时间点收集点观测，另一类在时间区间上收集积分观测。随后，传感器将这些时间序列观测发送至融合中心（Fusion Center，FC），由FC根据这些观测推断空间现象。我们证明所得后验预测分布难以处理，并提出一种可处理的两步推断流程。首先，我们开发算法对时间序列观测执行近似似然比检验，将点传感器和积分传感器的观测均压缩为单个比特。其次，压缩观测发送至FC后，我们利用空间最佳线性无偏估计器（Spatial Best Linear Unbiased Estimator，S-BLUE）在任意所需空间位置重构二值空间随机场。通过仿真研究了所提方法的性能。我们还使用新加坡国家环境局（National Environment Agency，NEA）的天气数据集进一步验证了方法的有效性，该数据集包含温度和相对湿度等场。
英文摘要：
We develop a new model for spatial random field reconstruction of a binary-valued spatial phenomenon. In our model, sensors are deployed in a wireless sensor network across a large geographical region. Each sensor measures a non-Gaussian inhomogeneous temporal process which depends on the spatial phenomenon. Two types of sensors are employed: one collects point observations at specific time points, while the other collects integral observations over time intervals. Subsequently, the sensors transmit these time-series observations to a Fusion Center (FC), and the FC infers the spatial phenomenon from these observations. We show that the resulting posterior predictive distribution is intractable and develop a tractable two-step procedure to perform inference. Firstly, we develop algorithms to perform approximate Likelihood Ratio Tests on the time-series observations, compressing them to a single bit for both point sensors and integral sensors. Secondly, once the compressed observations are transmitted to the FC, we utilize a Spatial Best Linear Unbiased Estimator (S-BLUE) to reconstruct the binary spatial random field at any desired spatial location. The performance of the proposed approach is studied using simulation. We further illustrate the effectiveness of our method using a weather dataset from the National Environment Agency (NEA) of Singapore with fields including temperature and relative humidity.
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。
