{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T10:26:05Z","timestamp":1766485565115,"version":"3.41.2"},"reference-count":37,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2023,6,7]],"date-time":"2023-06-07T00:00:00Z","timestamp":1686096000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Robot. AI"],"abstract":"<jats:p>In this paper, a distributed cooperative filtering strategy for state estimation has been developed for mobile sensor networks in a spatial\u2013temporal varying field modeled by the advection\u2013diffusion equation. Sensors are organized into distributed cells that resemble a mesh grid covering a spatial area, and estimation of the field value and gradient information at each cell center is obtained by running a constrained cooperative Kalman filter while incorporating the sensor measurements and information from neighboring cells. Within each cell, the finite volume method is applied to discretize and approximate the advection\u2013diffusion equation. These approximations build the weakly coupled relationships between neighboring cells and define the constraints that the cooperative Kalman filters are subjected to. With the estimated information, a gradient-based formation control law has been developed that enables the sensor network to adjust formation size by utilizing the estimated gradient information. Convergence analysis has been conducted for both the distributed constrained cooperative Kalman filter and the formation control. Simulation results with a 9-cell 12-sensor network validate the proposed distributed filtering method and control law.<\/jats:p>","DOI":"10.3389\/frobt.2023.1175418","type":"journal-article","created":{"date-parts":[[2023,6,7]],"date-time":"2023-06-07T08:48:40Z","timestamp":1686127720000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["Distributed cooperative Kalman filter constrained by advection\u2013diffusion equation for mobile sensor networks"],"prefix":"10.3389","volume":"10","author":[{"given":"Ziqiao","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Scott T.","family":"Mayberry","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wencen","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fumin","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1965","published-online":{"date-parts":[[2023,6,7]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"3439","DOI":"10.1109\/tac.2018.2882172","article-title":"A gradient-free three-dimensional source seeking strategy with robustness analysis","volume":"64","author":"Al-Abri","year":"2018","journal-title":"IEEE Trans. Automatic Control"},{"key":"B2","doi-asserted-by":"publisher","first-page":"741","DOI":"10.3390\/jmse9070741","article-title":"Energy-efficient collision avoidance mac protocols for underwater sensor networks: Survey and challenges","volume":"9","author":"Alfouzan","year":"2021","journal-title":"J. Mar. Sci. Eng."},{"volume-title":"Oil transport following the deepwater Horizon blowout","year":"2022","author":"Boufadel","key":"B3"},{"key":"B4","doi-asserted-by":"crossref","first-page":"5307","DOI":"10.23919\/ACC45564.2020.9147359","article-title":"Distributed and collision-free coverage control of a team of mobile sensors using the convex uncertain voronoi diagram","volume-title":"2020 American control conference (ACC)","author":"Chen","year":"2020"},{"key":"B5","doi-asserted-by":"crossref","first-page":"2775","DOI":"10.23919\/ACC50511.2021.9483372","article-title":"Employing mobile sensor density to approximate state feedback kernels in static output feedback control of pdes","volume-title":"2021 American control conference (ACC)","author":"Demetriou","year":"2021"},{"key":"B6","doi-asserted-by":"publisher","first-page":"1575","DOI":"10.1142\/s0218202514400041","article-title":"Finite volume schemes for diffusion equations: Introduction to and review of modern methods","volume":"24","author":"Droniou","year":"2014","journal-title":"Math. Models Methods Appl. Sci."},{"key":"B7","doi-asserted-by":"crossref","DOI":"10.2514\/6.2010-8178","article-title":"Evaluation of UAS concepts of operation for severe storm penetration using hardware-in-the-loop simulations","volume-title":"AIAA guidance, navigation, and control conference","author":"Elston","year":"2010"},{"key":"B8","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/s40860-018-0066-1","article-title":"An approach for safer navigation under severe hurricane damage","volume":"4","author":"Eshghi","year":"2018","journal-title":"J. Reliab. Intelligent Environ."},{"key":"B9","doi-asserted-by":"publisher","first-page":"87","DOI":"10.11591\/ijra.v5i2.pp87-97","article-title":"Using a mobile robot with interpolation and extrapolation method for chemical source localization in dynamic advection-diffusion environment","volume":"5","author":"Gao","year":"2016","journal-title":"Int. J. Robotics Automation (IJRA)"},{"key":"B10","doi-asserted-by":"publisher","first-page":"1306","DOI":"10.1109\/tcyb.2019.2917179","article-title":"Distributed event-triggered estimation over sensor networks: A survey","volume":"50","author":"Ge","year":"2019","journal-title":"IEEE Trans. Cybern."},{"key":"B11","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3361-7","volume-title":"Diffusion phenomena: Cases and studies","author":"Ghez","year":"2001"},{"key":"B12","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1007\/s10846-013-9897-4","article-title":"Multiple uav formations for cooperative source seeking and contour mapping of a radiative signal field","volume":"74","author":"Han","year":"2014","journal-title":"J. Intelligent Robotic Syst."},{"key":"B13","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1109\/tac.2019.2906462","article-title":"Distributed kalman filters with state equality constraints: Time-based and event-triggered communications","volume":"65","author":"He","year":"2020","journal-title":"IEEE Trans. Automatic Control"},{"key":"B14","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1006\/jcph.2000.6466","article-title":"A finite volume method for the approximation of diffusion operators on distorted meshes","volume":"160","author":"Hermeline","year":"2000","journal-title":"J. Comput. Phys."},{"key":"B15","doi-asserted-by":"publisher","first-page":"110109","DOI":"10.1016\/j.automatica.2021.110109","article-title":"Hybrid domain decomposition filters for advection\u2013diffusion pdes with mobile sensors","volume":"138","author":"Hu","year":"2022","journal-title":"Automatica"},{"key":"B16","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1016\/j.automatica.2016.11.014","article-title":"Distributed information-weighted kalman consensus filter for sensor networks","volume":"77","author":"Ji","year":"2017","journal-title":"Automatica"},{"key":"B17","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1016\/j.arcontrol.2008.05.001","article-title":"Adaptive control of pdes","volume":"32","author":"Krstic","year":"2008","journal-title":"Annu. Rev. Control"},{"key":"B18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.inffus.2018.09.013","article-title":"Machine learning algorithms for wireless sensor networks: A survey","volume":"49","author":"Kumar","year":"2019","journal-title":"Inf. Fusion"},{"key":"B19","doi-asserted-by":"publisher","first-page":"5242","DOI":"10.1109\/tcyb.2020.3029007","article-title":"Distributed kalman consensus filter for estimation with moving targets","volume":"52","author":"Lian","year":"2020","journal-title":"IEEE Trans. Cybern."},{"key":"B20","doi-asserted-by":"publisher","first-page":"109012","DOI":"10.1016\/j.automatica.2020.109012","article-title":"Stochastic predictive control under intermittent observations and unreliable actions","volume":"118","author":"Mishra","year":"2020","journal-title":"Automatica"},{"key":"B21","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1016\/j.compfluid.2014.11.006","article-title":"One-dimensional linear advection\u2013diffusion equation: Analytical and finite element solutions","volume":"107","author":"Mojtabi","year":"2015","journal-title":"Comput. Fluids"},{"key":"B22","doi-asserted-by":"publisher","first-page":"424","DOI":"10.1016\/j.automatica.2014.10.022","article-title":"A survey of multi-agent formation control","volume":"53","author":"Oh","year":"2015","journal-title":"Automatica"},{"key":"B23","doi-asserted-by":"crossref","first-page":"7036","DOI":"10.1109\/CDC.2009.5399678","article-title":"Kalman-consensus filter: Optimality, stability, and performance","volume-title":"Proceedings of the 48h IEEE conference on decision and control (CDC) held jointly with 2009 28th Chinese control conference","author":"Olfati-Saber","year":"2009"},{"key":"B24","doi-asserted-by":"publisher","first-page":"9457","DOI":"10.1109\/jsen.2021.3054943","article-title":"Dekcs: A dynamic clustering protocol to prolong underwater sensor networks","volume":"21","author":"Omeke","year":"2021","journal-title":"IEEE Sensors J."},{"key":"B25","doi-asserted-by":"crossref","first-page":"2395","DOI":"10.1109\/ICRA.2018.8461034","article-title":"Robust environmental mapping by mobile sensor networks","volume-title":"2018 IEEE international conference on Robotics and automation (ICRA)","author":"Park","year":"2018"},{"key":"B26","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1016\/j.cja.2020.11.002","article-title":"PDE solution to UAV\/UGV trajectory planning problem by spatio-temporal estimation during wildfires","volume":"34","author":"Radmanesh","year":"2021","journal-title":"Chin. J. Aeronautics"},{"key":"B27","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1109\/7.993234","article-title":"Kalman filtering with state equality constraints","volume":"38","author":"Simon","year":"2002","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"B28","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1016\/j.automatica.2019.03.029","article-title":"Event-triggered cooperative unscented kalman filtering and its application in multi-uav systems","volume":"105","author":"Song","year":"2019","journal-title":"Automatica"},{"key":"B29","doi-asserted-by":"publisher","first-page":"155014771983958","DOI":"10.1177\/1550147719839581","article-title":"An intelligent data gathering schema with data fusion supported for mobile sink in wireless sensor networks","volume":"15","author":"Wang","year":"2019","journal-title":"Int. J. Distributed Sens. Netw."},{"key":"B30","doi-asserted-by":"crossref","first-page":"4012","DOI":"10.23919\/ACC.2019.8814995","article-title":"Low-range interaction periodic rendezvous along Lagrangian coherent structures","volume-title":"2019 American control conference (ACC)","author":"Wei","year":"2019"},{"key":"B31","doi-asserted-by":"publisher","first-page":"842","DOI":"10.1017\/s0263574720000788","article-title":"Parameter identification of spatial\u2013temporal varying processes by a multi-robot system in realistic diffusion fields","volume":"39","author":"Wu","year":"2021","journal-title":"Robotica"},{"key":"B32","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1109\/tcns.2015.2459414","article-title":"A speeding-up and slowing-down strategy for distributed source seeking with robustness analysis","volume":"3","author":"Wu","year":"2015","journal-title":"IEEE Trans. Control Netw. Syst."},{"key":"B33","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1109\/tcst.2022.3183585","article-title":"Cooperative filtering and parameter identification for advection\u2013diffusion processes using a mobile sensor network","volume":"31","author":"You","year":"2022","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"B34","doi-asserted-by":"publisher","first-page":"650","DOI":"10.1109\/tac.2009.2039240","article-title":"Cooperative filters and control for cooperative exploration","volume":"55","author":"Zhang","year":"2010","journal-title":"IEEE Trans. Automatic Control"},{"key":"B35","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1109\/CACRE50138.2020.9230272","article-title":"Level curve tracking without localization enabled by recurrent neural networks","volume-title":"2020 5th international conference on automation, control and Robotics engineering (CACRE)","author":"Zhang","year":"2020"},{"key":"B36","doi-asserted-by":"crossref","DOI":"10.23919\/ACC55779.2023.10156161","article-title":"Distributed cooperative kalman filter constrained by discretized Poisson equation for mobile sensor networks","volume-title":"2023 American control conference (ACC)","author":"Zhang","year":"2023"},{"key":"B37","doi-asserted-by":"crossref","first-page":"982","DOI":"10.23919\/ACC53348.2022.9867676","article-title":"Cooperative filtering and parameter estimation for polynomial pdes using a mobile sensor network","volume-title":"2022 American control conference (ACC)","author":"Zhang","year":"2022"}],"container-title":["Frontiers in Robotics and AI"],"original-title":[],"link":[{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/frobt.2023.1175418\/full","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,14]],"date-time":"2023-12-14T19:37:45Z","timestamp":1702582665000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/frobt.2023.1175418\/full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,7]]},"references-count":37,"alternative-id":["10.3389\/frobt.2023.1175418"],"URL":"https:\/\/doi.org\/10.3389\/frobt.2023.1175418","relation":{},"ISSN":["2296-9144"],"issn-type":[{"type":"electronic","value":"2296-9144"}],"subject":[],"published":{"date-parts":[[2023,6,7]]},"article-number":"1175418"}}