Multivariate versus Univariate Sensor Selection for Spatial Field Estimation
preprintposted on 26.05.2021, 10:57 authored by Linh Nguyen, Karthick ThiyagarajanKarthick Thiyagarajan, Nalika UlapaneNalika Ulapane, sarath kodagoda
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 univariate and 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.