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It is proposed to employ Gaussian Markov random field (GMRF) represented on an irregular discrete lattice by using the stochastic partial differential equations method to model the physical spatial field. It then derives a GMRF-based approach to effectively predict the field at unmeasured locations, given available observations, in both centralized and distributed manners. Furthermore, a novel but efficient optimality criterion is then proposed to design centralized and distributed adaptive sampling strategies for the mobile robotic sensors to find the most informative sampling paths in taking future measurements. By taking advantage of conditional independence property in the GMRF, the adaptive sampling optimization problem is proven to be resolved in a deterministic time. The effectiveness of the proposed approach is compared and demonstrated using pre-published data sets with appealing results.<\/jats:p>","DOI":"10.1017\/s026357472000079x","type":"journal-article","created":{"date-parts":[[2020,9,1]],"date-time":"2020-09-01T08:21:35Z","timestamp":1598948495000},"page":"862-884","source":"Crossref","is-referenced-by-count":25,"title":["Mobile Robotic Sensors for Environmental Monitoring using Gaussian Markov Random Field"],"prefix":"10.1017","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5360-886X","authenticated-orcid":false,"given":"Linh","family":"Nguyen","sequence":"first","affiliation":[]},{"given":"Sarath","family":"Kodagoda","sequence":"additional","affiliation":[]},{"given":"Ravindra","family":"Ranasinghe","sequence":"additional","affiliation":[]},{"given":"Gamini","family":"Dissanayake","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2020,9,1]]},"reference":[{"key":"S026357472000079X_ref10","first-page":"2816","article-title":"Distributed Kriged Kalman filter for spatial estimation","volume":"54","author":"Cort\u00e9s","year":"2009","journal-title":"Control"},{"key":"S026357472000079X_ref13","doi-asserted-by":"publisher","DOI":"10.1177\/0278364913488427"},{"key":"S026357472000079X_ref19","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA.2012.6224765"},{"key":"S026357472000079X_ref30","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2007.10.008"},{"key":"S026357472000079X_ref22","unstructured":"22. 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