{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T17:08:36Z","timestamp":1774890516454,"version":"3.50.1"},"reference-count":40,"publisher":"Elsevier BV","issue":"6","license":[{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["25ZR1401149"],"award-info":[{"award-number":["25ZR1401149"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of the Franklin Institute"],"published-print":{"date-parts":[[2026,4]]},"DOI":"10.1016\/j.jfranklin.2026.108498","type":"journal-article","created":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T07:47:45Z","timestamp":1770709665000},"page":"108498","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"title":["Distributed maximum correntropy Kalman filtering for stochastic discrete time system: A encoding-decoding-based approach"],"prefix":"10.1016","volume":"363","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-6345-2189","authenticated-orcid":false,"given":"Xinyi","family":"Xu","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1586-8702","authenticated-orcid":false,"given":"Xiu","family":"Kan","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0005-9129-4685","authenticated-orcid":false,"given":"Weiwei","family":"Wang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0000-3037-3455","authenticated-orcid":false,"given":"Jiawei","family":"Chu","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"2","key":"10.1016\/j.jfranklin.2026.108498_bib0001","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1109\/MP.2003.1197877","article-title":"Sensor networks: an overview","volume":"22","author":"Tubaishat","year":"2003","journal-title":"IEEE Potent."},{"issue":"5","key":"10.1016\/j.jfranklin.2026.108498_bib0002","doi-asserted-by":"crossref","first-page":"3733","DOI":"10.1109\/TCYB.2020.3016093","article-title":"Distributed maximum correntropy filtering for stochastic nonlinear systems under deception attacks","volume":"52","author":"Song","year":"2020","journal-title":"IEEE Trans. Cybern."},{"key":"10.1016\/j.jfranklin.2026.108498_bib0003","doi-asserted-by":"crossref","DOI":"10.1016\/j.sigpro.2024.109438","article-title":"An improved two-phase robust distributed Kalman filter","volume":"220","author":"Luo","year":"2024","journal-title":"Signal Process."},{"issue":"4","key":"10.1016\/j.jfranklin.2026.108498_bib0004","doi-asserted-by":"crossref","first-page":"2490","DOI":"10.1109\/TAC.2022.3175925","article-title":"A distributed implementation of steady-state Kalman filter","volume":"68","author":"Yan","year":"2022","journal-title":"IEEE Trans. Autom. Contr."},{"key":"10.1016\/j.jfranklin.2026.108498_bib0005","doi-asserted-by":"crossref","first-page":"688","DOI":"10.1109\/LSP.2023.3283333","article-title":"High accuracy distributed Kalman filtering for synchronizing frequency and phase in distributed phased arrays","volume":"30","author":"Rashid","year":"2023","journal-title":"IEEE Signal Process. Lett."},{"issue":"2","key":"10.1016\/j.jfranklin.2026.108498_bib0006","doi-asserted-by":"crossref","first-page":"1268","DOI":"10.1109\/TSMC.2022.3195121","article-title":"Secure event-triggered distributed Kalman filters for state estimation over wireless sensor networks","volume":"53","author":"Mustafa","year":"2022","journal-title":"IEEE Trans. Syst. Man, and Cybern. Syst."},{"issue":"18","key":"10.1016\/j.jfranklin.2026.108498_bib0007","doi-asserted-by":"crossref","DOI":"10.1016\/j.jfranklin.2025.108175","article-title":"Deterministic learning based extended kalman filter for nonlinear dynamics modeling","volume":"362","author":"Wu","year":"2025","journal-title":"J. Frank. Inst."},{"issue":"13","key":"10.1016\/j.jfranklin.2026.108498_bib0008","doi-asserted-by":"crossref","first-page":"3396","DOI":"10.3390\/rs15133396","article-title":"Application of data sensor fusion using extended Kalman filter algorithm for identification and tracking of moving targets from LiDAR-radar data","volume":"15","author":"Monta\u00f1ez","year":"2023","journal-title":"Remote Sens."},{"key":"10.1016\/j.jfranklin.2026.108498_bib0009","series-title":"2020 International Conference on Emerging Trends in Communication, Control and Computing (ICONC3)","first-page":"1","article-title":"State estimation using extended kalman filter and unscented kalman filter","author":"Madhukar","year":"2020"},{"issue":"2","key":"10.1016\/j.jfranklin.2026.108498_bib0010","doi-asserted-by":"crossref","first-page":"5421","DOI":"10.1109\/LRA.2022.3153705","article-title":"Stein particle filter for nonlinear, non-gaussian state estimation","volume":"7","author":"Maken","year":"2022","journal-title":"IEEE Robot. Autom. Lett."},{"issue":"5","key":"10.1016\/j.jfranklin.2026.108498_bib0011","doi-asserted-by":"crossref","first-page":"3181","DOI":"10.1109\/TAC.2024.3496573","article-title":"Binary-encoding-based quantized kalman filter: an approximate MMSE approach","volume":"70","author":"Liu","year":"2025","journal-title":"IEEE Trans. Autom. Contr."},{"issue":"1","key":"10.1016\/j.jfranklin.2026.108498_bib0012","first-page":"21","article-title":"Gaussianity and the kalman filter: a simple yet complicated relationship","volume":"14","author":"Uhlmann","year":"2022","journal-title":"J. de Cienc. e Ing."},{"key":"10.1016\/j.jfranklin.2026.108498_bib0013","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2024.111895","article-title":"On vulnerability of Kalman filtering with holistic estimation performance loss","volume":"171","author":"Zhou","year":"2025","journal-title":"Autom."},{"issue":"15","key":"10.1016\/j.jfranklin.2026.108498_bib0014","doi-asserted-by":"crossref","DOI":"10.1016\/j.jfranklin.2025.108010","article-title":"Cauchy kernel-based maximum correntropy iterated unscented Kalman filter: the adaptive event-triggered case","volume":"362","author":"Liu","year":"2025","journal-title":"J. Frank Inst."},{"key":"10.1016\/j.jfranklin.2026.108498_bib0015","doi-asserted-by":"crossref","DOI":"10.1016\/j.sysconle.2023.105515","article-title":"Two efficient Kalman filter algorithms for measurement packet dropping systems under maximum correntropy criterion","volume":"175","author":"Zhang","year":"2023","journal-title":"Syst. Contr. Lett."},{"key":"10.1016\/j.jfranklin.2026.108498_bib0016","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2022.110410","article-title":"Robust stable iterated unscented Kalman filter based on maximum correntropy criterion","volume":"142","author":"Zhao","year":"2022","journal-title":"Autom."},{"key":"10.1016\/j.jfranklin.2026.108498_bib0017","doi-asserted-by":"crossref","first-page":"2792","DOI":"10.1109\/TSP.2023.3300631","article-title":"Maximum correntropy quaternion Kalman filter","volume":"71","author":"Lin","year":"2023","journal-title":"IEEE Trans. Signal Process."},{"issue":"3","key":"10.1016\/j.jfranklin.2026.108498_bib0018","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1002\/rnc.7686","article-title":"Robust maximum correntropy Kalman filter","volume":"35","author":"Saha","year":"2024","journal-title":"Int. J. Robust Nonlinear Contr."},{"key":"10.1016\/j.jfranklin.2026.108498_bib0019","first-page":"433","article-title":"An efficient distributed Kalman filter over sensor networks with maximum correntropy criterion","volume":"8","author":"Hu","year":"2022","journal-title":"IEEE Trans. Signal and Inf. Process. Over Netw."},{"issue":"2","key":"10.1016\/j.jfranklin.2026.108498_bib0020","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1080\/00207721.2022.2122905","article-title":"Distributed fusion filtering for uncertain systems with coupled noises, random delays and packet loss prediction compensation","volume":"54","author":"Caballero-\u00c1guila","year":"2022","journal-title":"Int. J. Syst. Sci."},{"issue":"8","key":"10.1016\/j.jfranklin.2026.108498_bib0021","doi-asserted-by":"crossref","first-page":"1729","DOI":"10.1080\/00207721.2023.2209887","article-title":"Distributed recursive filtering for multi-rate uniform sampling systems with packet losses in sensor networks","volume":"54","author":"Shen","year":"2023","journal-title":"Int. J. Syst. Sci."},{"key":"10.1016\/j.jfranklin.2026.108498_bib0022","doi-asserted-by":"crossref","DOI":"10.1016\/j.sigpro.2021.108306","article-title":"Distributed filtering for sensor networks with fading measurements and compensations for transmission delays and losses","volume":"190","author":"Jin","year":"2022","journal-title":"Signal Process."},{"issue":"1","key":"10.1016\/j.jfranklin.2026.108498_bib0023","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1080\/21642583.2022.2086183","article-title":"Joint state and fault estimation for nonlinear complex networks with mixed time-delays and uncertain inner coupling: non-fragile recursive method","volume":"10","author":"Feng","year":"2022","journal-title":"Syst. Sci. Contr. Eng."},{"key":"10.1016\/j.jfranklin.2026.108498_bib0024","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1016\/j.ins.2022.11.039","article-title":"H\u221e filtering for discrete-time switched fuzzy delayed systems with channel fading via improved state-dependent switching","volume":"619","author":"Sang","year":"2023","journal-title":"Inf. Sci."},{"key":"10.1016\/j.jfranklin.2026.108498_bib0025","doi-asserted-by":"crossref","DOI":"10.1016\/j.sigpro.2021.108387","article-title":"Optimal linear filtering for networked control systems under time correlated fading channel and noise","volume":"192","author":"Liu","year":"2022","journal-title":"Signal Process."},{"key":"10.1016\/j.jfranklin.2026.108498_bib0026","doi-asserted-by":"crossref","DOI":"10.1016\/j.dsp.2024.104529","article-title":"Identification and distributed fusion filter for multi-sensor networked systems with stochastic deception attacks","volume":"151","author":"He","year":"2024","journal-title":"Digit. Signal Process."},{"issue":"3","key":"10.1016\/j.jfranklin.2026.108498_bib0027","doi-asserted-by":"crossref","first-page":"1238","DOI":"10.1109\/TCNS.2022.3141026","article-title":"Relentless false data injection attacks against Kalman-filter-based detection in smart grid","volume":"9","author":"Liu","year":"2022","journal-title":"IEEE Trans. on Control of Netw. Syst."},{"key":"10.1016\/j.jfranklin.2026.108498_bib0028","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.neucom.2022.08.041","article-title":"Encoding-decoding-based secure filtering for neural networks under mixed attacks","volume":"508","author":"Yi","year":"2022","journal-title":"Neurocomputing"},{"issue":"5","key":"10.1016\/j.jfranklin.2026.108498_bib0029","doi-asserted-by":"crossref","DOI":"10.1007\/s11432-023-3905-1","article-title":"Linear-fitting-based recursive filtering for nonlinear systems under encoding-decoding mechanism","volume":"67","author":"Jiang","year":"2024","journal-title":"Sci. China Inf. Sci."},{"issue":"8","key":"10.1016\/j.jfranklin.2026.108498_bib0030","doi-asserted-by":"crossref","first-page":"2833","DOI":"10.1002\/acs.3833","article-title":"Outlier-resistant state estimation for complex networks with random false data injection attacks under encoding-decoding mechanism","volume":"38","author":"Liu","year":"2024","journal-title":"Int. J. of Adapt. Control and Signal Process."},{"issue":"3","key":"10.1016\/j.jfranklin.2026.108498_bib0031","doi-asserted-by":"crossref","first-page":"1359","DOI":"10.1109\/TCYB.2024.3524240","article-title":"Adaptive quantized iterative learning control using encoding-decoding strategy","volume":"55","author":"Liu","year":"2025","journal-title":"IEEE Trans. Cybern."},{"issue":"7","key":"10.1016\/j.jfranklin.2026.108498_bib0032","doi-asserted-by":"crossref","first-page":"1606","DOI":"10.1080\/00207721.2024.2428849","article-title":"Critical-information-based attack-defense strategy for nonlinear systems: an encoding-decoding scheme","volume":"56","author":"Wang","year":"2024","journal-title":"Int. J. Syst. Sci."},{"issue":"12","key":"10.1016\/j.jfranklin.2026.108498_bib0033","first-page":"4904","article-title":"Encoding-decoding-based distributed filtering for time-varying saturated systems with constrained bit rate","volume":"69","author":"Li","year":"2022","journal-title":"IEEE Trans. Circuits and Syst. II: Express Brief."},{"issue":"6","key":"10.1016\/j.jfranklin.2026.108498_bib0034","doi-asserted-by":"crossref","first-page":"1103","DOI":"10.1109\/JAS.2022.105644","article-title":"Encoding-decoding-based recursive filtering for fractional-order systems","volume":"9","author":"Jiang","year":"2022","journal-title":"IEEE\/CAA J. Autom. Sin."},{"issue":"2","key":"10.1016\/j.jfranklin.2026.108498_bib0035","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/0167-6911(92)90097-C","article-title":"Robust control of a class of uncertain nonlinear systems","volume":"19","author":"Wang","year":"1992","journal-title":"Syst. Contr. Lett."},{"issue":"2","key":"10.1016\/j.jfranklin.2026.108498_bib0036","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1109\/78.485915","article-title":"Robust discrete-time minimum-variance filtering","volume":"44","author":"Theodor","year":"1996","journal-title":"IEEE Trans. Signal Process."},{"issue":"3","key":"10.1016\/j.jfranklin.2026.108498_bib0037","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1109\/MSP.2021.3134635","article-title":"Kalman filtering in non-Gaussian model errors: a new perspective [tips & tricks]","volume":"39","author":"Roonizi","year":"2022","journal-title":"IEEE Signal Process. Mag."},{"key":"10.1016\/j.jfranklin.2026.108498_bib0038","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2021.110004","article-title":"Distributed filtering based on Cauchy-kernel-based maximum correntropy subject to randomly occurring cyber-attacks","volume":"135","author":"Song","year":"2022","journal-title":"Autom."},{"key":"10.1016\/j.jfranklin.2026.108498_bib0039","doi-asserted-by":"crossref","first-page":"5036","DOI":"10.1109\/TSP.2024.3473988","article-title":"Event-triggered multi-sensor scheduling for remote state estimation over packet-dropping networks","volume":"72","author":"Zhong","year":"2024","journal-title":"IEEE Trans. Signal Process."},{"issue":"3","key":"10.1016\/j.jfranklin.2026.108498_bib0040","doi-asserted-by":"crossref","first-page":"2144","DOI":"10.1109\/TCNS.2025.3554015","article-title":"State estimation of multisensor with out-of-order measurements","volume":"12","author":"Zhao","year":"2025","journal-title":"IEEE Trans. Control Netw. Syst."}],"container-title":["Journal of the Franklin Institute"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0016003226000980?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0016003226000980?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T16:12:06Z","timestamp":1774887126000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0016003226000980"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4]]},"references-count":40,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2026,4]]}},"alternative-id":["S0016003226000980"],"URL":"https:\/\/doi.org\/10.1016\/j.jfranklin.2026.108498","relation":{},"ISSN":["0016-0032"],"issn-type":[{"value":"0016-0032","type":"print"}],"subject":[],"published":{"date-parts":[[2026,4]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Distributed maximum correntropy Kalman filtering for stochastic discrete time system: A encoding-decoding-based approach","name":"articletitle","label":"Article Title"},{"value":"Journal of the Franklin Institute","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.jfranklin.2026.108498","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Published by Elsevier Inc. on behalf of The Franklin Institute.","name":"copyright","label":"Copyright"}],"article-number":"108498"}}