Binary Spatial Random Field Reconstruction from Non-Gaussian Inhomogeneous Time-series Observations

TL;DR

This paper introduces a novel method for reconstructing binary spatial fields from non-Gaussian, inhomogeneous time-series data collected by sensors, using a two-step inference process involving likelihood ratio tests and a spatial BLUE estimator.

Contribution

The paper presents a new model and algorithms for binary spatial field reconstruction from complex sensor data, including a tractable inference procedure and practical validation.

Findings

Effective binary field reconstruction demonstrated through simulations.

Successful application to weather data from Singapore.

Approximate likelihood ratio tests enable efficient data compression.

Abstract

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.