Multivariate versus Univariate Sensor Selection for Spatial Field Estimation

The paper discusses the sensor selection problem in estimating spatial fields. It is demonstrated that selecting a subset of sensors depends on modelling spatial processes. It is first proposed to exploit Gaussian process (GP) to model a univariate spatial field and multivariate GP (MGP) to jointly represent multivariate spatial phenomena. A Mat\'ern cross-covariance function is employed in the MGP model to guarantee its cross-covariance matrices to be positive semi-definite. We then consider two corresponding \textit{univariate} and \textit{multivariate sensor selection} problems in effectively monitoring multiple spatial random fields. The sensor selection approaches were implemented in the real-world experiments and their performances were compared. Difference of results obtained by the univariate and multivariate sensor selection techniques is insignificant; that is, either of the methods can be efficiently used in practice.