Binary spatial random field reconstruction from non-Gaussian inhomogeneous time-series observations

• Main Authors: Sheng, Shunan, Xiang, Qikun, Nevat, Ido, Neufeld, Ariel
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2024
• Subjects: Mathematical Sciences; Sensor networks; Warped Gaussian process
• Online Access: https://hdl.handle.net/10356/176210
• Institution: Nanyang Technological University

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.