{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T04:24:59Z","timestamp":1769833499942,"version":"3.49.0"},"reference-count":32,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2018,6,1]],"date-time":"2018-06-01T00:00:00Z","timestamp":1527811200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>We propose a sensor placement method for spatio-temporal field estimation based on a kriged Kalman filter (KKF) using a network of static or mobile sensors. The developed framework dynamically designs the optimal constellation to place the sensors. We combine the estimation error (for the stationary as well as non-stationary component of the field) minimization problem with a sparsity-enforcing penalty to design the optimal sensor constellation in an economic manner. The developed sensor placement method can be directly used for a general class of covariance matrices (ill-conditioned or well-conditioned) modelling the spatial variability of the stationary component of the field, which acts as a correlated observation noise, while estimating the non-stationary component of the field. Finally, a KKF estimator is used to estimate the field using the measurements from the selected sensing locations. Numerical results are provided to exhibit the feasibility of the proposed dynamic sensor placement followed by the KKF estimation method.<\/jats:p>","DOI":"10.3390\/s18061778","type":"journal-article","created":{"date-parts":[[2018,6,4]],"date-time":"2018-06-04T08:52:03Z","timestamp":1528102323000},"page":"1778","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Spatio-Temporal Field Estimation Using Kriged Kalman Filter (KKF) with Sparsity-Enforcing Sensor Placement"],"prefix":"10.3390","volume":"18","author":[{"given":"Venkat","family":"Roy","sequence":"first","affiliation":[{"name":"NXP Semiconductors, High Tech Campus 46, 5656 AE Eindhoven, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrea","family":"Simonetto","sequence":"additional","affiliation":[{"name":"Optimisation and Control group, IBM Research Ireland, Dublin 15, Ireland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Geert","family":"Leus","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,6,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"143","DOI":"10.4304\/jcm.6.2.143-151","article-title":"Wireless sensor networks: A survey on environmental monitoring","volume":"6","author":"Oliveira","year":"2011","journal-title":"J. Commun."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.earscirev.2006.05.001","article-title":"Environmental sensor networks: A revolution in the earth system science?","volume":"78","author":"Hart","year":"2006","journal-title":"Earth-Sci. Rev."},{"key":"ref_3","unstructured":"Cressie, N., and Wikle, K. (2011). Statistics for Spatio-Temporal Data, John Wiley & Sons."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/BF02565111","article-title":"The kriged Kalman filter","volume":"7","author":"Mardia","year":"1998","journal-title":"Test"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1093\/biomet\/86.4.815","article-title":"A dimension-reduced approach to space-time Kalman filtering","volume":"86","author":"Wikle","year":"1999","journal-title":"Biometrika"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1109\/JSTSP.2010.2053016","article-title":"Cooperative spectrum sensing for cognitive radios using kriged Kalman filtering","volume":"5","author":"Kim","year":"2011","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2910","DOI":"10.1109\/TIT.2014.2311802","article-title":"Dynamic network delay cartography","volume":"60","author":"Rajawat","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1111\/j.1467-9876.2005.00480.x","article-title":"A Bayesian kriged Kalman model for short term forecasting of air pollution levels","volume":"54","author":"Sahu","year":"2005","journal-title":"J. R. Stat. Soc. Ser. C (Appl. Stat.)"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2816","DOI":"10.1109\/TAC.2009.2034192","article-title":"Distributed Kriged Kalman filter for spatial estimation","volume":"54","author":"Cortes","year":"2009","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_10","first-page":"235","article-title":"Near-optimal sensor placements in Gaussian processes: Theory, efficient algorithms and empirical studies","volume":"9","author":"Krause","year":"2008","journal-title":"J. Mach. Learn. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.1109\/TSP.2014.2299518","article-title":"Near-optimal sensor placement for linear inverse problems","volume":"62","author":"Ranieri","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Carmi, A. (2010, January 26\u201329). Sensor scheduling via compressed sensing. Proceedings of the 13th Conference on Information Fusion (FUSION), Edinburgh, UK.","DOI":"10.1109\/ICIF.2010.5712027"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3538","DOI":"10.1109\/TAES.2012.6324736","article-title":"Distributed sensor allocation for multi-target tracking in wireless sensor networks","volume":"48","author":"Fu","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Patan, M. (2012). Optimal Sensor Networks Scheduling in Identification of Distributed Parameter Systems, Springer Science & Business Media.","DOI":"10.1007\/978-3-642-28230-0"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3055","DOI":"10.1109\/TSP.2014.2320455","article-title":"Optimal periodic sensor scheduling in networks of dynamical systems","volume":"62","author":"Liu","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1330","DOI":"10.1016\/j.automatica.2011.02.001","article-title":"Sensor selection strategies for state estimation in energy constrained wireless sensor networks","volume":"47","author":"Mo","year":"2011","journal-title":"Automatica"},{"key":"ref_17","unstructured":"Akyildiz, I.F., Vuran, M.C., and Akan, O.B. (, January March). On exploiting spatial and temporal correlation in wireless sensor networks. Proceedings of the WiOpt, Cambridge, UK."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1109\/TSP.2008.2007095","article-title":"Sensor selection via convex optimization","volume":"57","author":"Joshi","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5951","DOI":"10.1109\/TSP.2015.2460224","article-title":"Distributed sparsity-aware sensor selection","volume":"63","author":"Simonetto","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1109\/TSP.2014.2379662","article-title":"Sparsity-promoting sensor selection for non-linear measurement models","volume":"63","author":"Chepuri","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Liu, S., Cao, N., and Varshney, P.K. (2016, January 7\u20139). Sensor placement for field estimation via poisson disk sampling. Proceedings of the 2016 IEEE Global Conference on Signal and Information Processing (GlobalSIP), Washington, DC, USA.","DOI":"10.1109\/GlobalSIP.2016.7905896"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/j.sigpro.2016.05.011","article-title":"Spatio-temporal sensor management for environmental field estimation","volume":"128","author":"Roy","year":"2016","journal-title":"Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1145\/1218556.1218558","article-title":"Modeling spatially correlated data in sensor networks","volume":"2","author":"Jindal","year":"2006","journal-title":"ACM Trans. Sens. Netw."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3509","DOI":"10.1109\/TSP.2016.2550005","article-title":"Sensor selection for estimation with correlated measurement noise","volume":"64","author":"Liu","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/BF02065878","article-title":"On the condition number of covariance matrices in kriging, estimation, and simulation of random fields","volume":"26","author":"Ababou","year":"1994","journal-title":"Math. Geol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1452","DOI":"10.1214\/12-AOAS564","article-title":"A dynamic nonstationary spatio-temporal model for short term prediction of precipitation","volume":"6","author":"Sigrist","year":"2012","journal-title":"Ann. Appl. Stat."},{"key":"ref_27","unstructured":"Kay, S.M. (1993). Fundamentals of Statistical Signal Processing: Estimation Theory, PTR Prentice-Hall."},{"key":"ref_28","unstructured":"Boyd, S., and Vandenberghe, S. (2009). Convex Optimization, Cambridge University Press."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1007\/s00041-008-9045-x","article-title":"Enhancing sparsity by reweighted \u21131 minimization","volume":"14","author":"Candes","year":"2008","journal-title":"J. Fourier Anal. Appl."},{"key":"ref_30","unstructured":"Grant, M., Boyd, S., and Ye, Y. (CVX, Matlab Software for Disciplined Convex Programming, 2008). CVX, Matlab Software for Disciplined Convex Programming."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1080\/10556789908805766","article-title":"Using sedumi 1.02, a matlab toolbox for optimization over symmetric cones","volume":"11","author":"Sturm","year":"1999","journal-title":"Optim. Methods Softw."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"5481","DOI":"10.1109\/TSP.2017.2728498","article-title":"Prediction-correction algorithms for time-varying constrained optimization","volume":"65","author":"Simonetto","year":"2017","journal-title":"IEEE Trans. Signal Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/6\/1778\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:06:53Z","timestamp":1760195213000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/6\/1778"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,1]]},"references-count":32,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2018,6]]}},"alternative-id":["s18061778"],"URL":"https:\/\/doi.org\/10.3390\/s18061778","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,6,1]]}}}