How to Utilize Sensor Network Data to Efficiently Perform Model Calibration and Spatial Field Reconstruction

Abstract

This chapter provides a tutorial overview of some modern applications of the statistical modeling that can be developed based upon spatial wireless sensor network data. We then develop a range of new results relating to two important problems that arise in spatial field reconstructions from wireless sensor networks. The first new result allows one to accurately and efficiently obtain a spatial field reconstruction which is optimal in the sense that it is the Spatial Best Linear Unbiased Estimator for the field reconstruction. This estimator is obtained under three different system model configurations that represent different types of heterogeneous and homogeneous wireless sensor networks. The second novelty presented in this chapter relates to development of a framework that allows one to incorporate multiple sensed modalities from related spatial processes into the spatial field reconstruction. This is of practical significance for instance, if there are d spatial physical processes that are all being monitored by a wireless sensor network and it is believed that there is a relationship between the variability in the target spatial process to be reconstructed and the other spatial processes being monitored. In such settings it should be beneficial to incorporate these other spatial modalities into the estimation and spatial reconstruction of the target process. In this chapter we develop a spatial covariance regression framework to provide such estimation functionality. In addition, we develop a highly efficient estimation procedure for the model parameters via an Expectation Maximization algorithm. Results of the estimation and spatial field reconstructions are provided for two different real-world applications related to modeling the spatial relationships between coastal wind speeds and ocean height bathymetry measurements based on sensor network observations.