Estimation of Spatially Correlated Random Fields in Heterogeneous Wireless Sensor Networks

Abstract

We develop new algorithms for spatial field reconstruction, exceedance level estimation and classification in heterogeneous (mixed analog & digital sensors) Wireless Sensor Networks (WSNs). We consider spatial physical phenomena which are observed by a heterogeneous WSN, meaning that it consists partially of sparsely deployed high-quality sensors and partially of low-quality sensors. The high-quality sensors transmit their (continuous) noisy observations to the Fusion Centre (FC), while the low-quality sensors first perform a simple thresholding operation and then transmit their binary values over imperfect wireless channels to the FC. The resulting observations are mixed continuous and discrete (1-bit decisions) observations, and are combined in the FC to solve the inference problems. We first formulate the problem of spatial field reconstruction, exceedance level estimation and classification in such heterogeneous networks. We show that the resulting posterior predictive distribution, which is key in fusing such disparate observations, involves intractable integrals. To overcome this problem, we develop an algorithm that is based on a multivariate series expansion approach resulting in a Saddle-point type approximation. We then present comprehensive study of the performance gain that can be obtained by augmenting the high-quality sensors with low-quality sensors using real data of insurance storm surge database known as the Extreme Wind Storms Catalogue.