{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:17:59Z","timestamp":1760242679265,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2016,2,19]],"date-time":"2016-02-19T00:00:00Z","timestamp":1455840000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"CEMEE","award":["CEMEE2014K0102A"],"award-info":[{"award-number":["CEMEE2014K0102A"]}]},{"DOI":"10.13039\/501100001809","name":"NSF of China","doi-asserted-by":"publisher","award":["61221003"],"award-info":[{"award-number":["61221003"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Heterogeneous wireless sensor networks (HWSNs) can achieve more tasks and prolong the network lifetime. However, they are vulnerable to attacks from the environment or malicious nodes. This paper is concerned with the issues of a consensus secure scheme in HWSNs consisting of two types of sensor nodes. Sensor nodes (SNs) have more computation power, while relay nodes (RNs) with low power can only transmit information for sensor nodes. To address the security issues of distributed estimation in HWSNs, we apply the heterogeneity of responsibilities between the two types of sensors and then propose a parameter adjusted-based consensus scheme (PACS) to mitigate the effect of the malicious node. Finally, the convergence property is proven to be guaranteed, and the simulation results validate the effectiveness and efficiency of PACS.<\/jats:p>","DOI":"10.3390\/s16020252","type":"journal-article","created":{"date-parts":[[2016,2,19]],"date-time":"2016-02-19T11:29:39Z","timestamp":1455881379000},"page":"252","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Secure Scheme for Distributed Consensus Estimation against Data Falsification in Heterogeneous Wireless Sensor Networks"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7027-2034","authenticated-orcid":false,"given":"Shichao","family":"Mi","sequence":"first","affiliation":[{"name":"Luoyang Electronic Equipment Test Center (LEETC), Luoyang 471003, China"},{"name":"Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai 200240, China"}]},{"given":"Hui","family":"Han","sequence":"additional","affiliation":[{"name":"Luoyang Electronic Equipment Test Center (LEETC), Luoyang 471003, China"}]},{"given":"Cailian","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai 200240, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3784-3952","authenticated-orcid":false,"given":"Jian","family":"Yan","sequence":"additional","affiliation":[{"name":"Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai 200240, China"}]},{"given":"Xinping","family":"Guan","sequence":"additional","affiliation":[{"name":"Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai 200240, China"}]}],"member":"1968","published-online":{"date-parts":[[2016,2,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/S1389-1286(01)00302-4","article-title":"Wireless sensor networks: A survey","volume":"38","author":"Akyildiz","year":"2002","journal-title":"Comput. Netw."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2292","DOI":"10.1016\/j.comnet.2008.04.002","article-title":"Wireless sensor network survey","volume":"52","author":"Yick","year":"2008","journal-title":"Comput. Netw."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1109\/TBCAS.2007.910901","article-title":"The advanced health and disaster aid network: A light-weight wireless medical system for triage","volume":"1","author":"Gao","year":"2007","journal-title":"IEEE Trans. Biomed. Circuits Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1109\/TVT.2009.2031181","article-title":"A distributed consensus-based cooperative spectrum-sensing scheme in cognitive radios","volume":"59","author":"Li","year":"2010","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"6869","DOI":"10.3390\/s90906869","article-title":"An overview on wireless sensor networks technology and evolution","volume":"9","author":"Buratti","year":"2009","journal-title":"Sensors"},{"key":"ref_6","first-page":"145","article-title":"Relay Node Deployment Strategies in Heterogeneous Wireless Sensor Networks","volume":"9","author":"Xu","year":"2009","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/s11276-006-0724-8","article-title":"Relay sensor placement in wireless sensor networks","volume":"14","author":"Cheng","year":"2008","journal-title":"Wirel. Netw."},{"key":"ref_8","first-page":"018901:1","article-title":"Consensus protocol for heterogeneous multi-agent systems: A Markov chain approach","volume":"22","author":"Zhu","year":"2013","journal-title":"Chin. Phys. B"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1963","DOI":"10.1109\/TSMCB.2012.2236647","article-title":"Distributed optimal consensus filter for target tracking in heterogeneous sensor networks","volume":"42","author":"Zhu","year":"2013","journal-title":"IEEE Trans. Cybern."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2000","DOI":"10.1109\/TSP.2009.2014812","article-title":"Distributed sensor localization in random environments using minimal number of anchor nodes","volume":"57","author":"Khan","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"19047","DOI":"10.3390\/s150819047","article-title":"Distributed Density Estimation Based on a Mixture of Factor Analyzers in a Sensor Network","volume":"15","author":"Wei","year":"2015","journal-title":"Sensors"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3456","DOI":"10.1109\/TSP.2007.893921","article-title":"Decentralized maximum-likelihood estimation for sensor networks composed of nonlinearly coupled dynamical systems","volume":"55","author":"Barbarossa","year":"2007","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1109\/JPROC.2006.887293","article-title":"Consensus and cooperation in networked multi-agent systems","volume":"95","author":"Fax","year":"2007","journal-title":"IEEE Proc."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1109\/TAC.2005.864190","article-title":"Flocking for multi-agent dynamic system: Algorithms and theory","volume":"51","year":"2006","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Mi, S., Zhu, S., Chen, C., and Guan, X. (2013, January 7\u201310). TWGS: A Tree Decomposition Based Indoor Pursuit-Evasion Game for Robotic Networks. Proceedings of the 13th IFAC Symposium on Large Scale Complex Systems: Theory and Applications, Shanghai, China.","DOI":"10.3182\/20130708-3-CN-2036.00059"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Chen, C., Zhu, S., Guan, X., and Shen, X. (2014). Wireless Sensor Networks: Distributed Consensus Estimation, Springer.","DOI":"10.1007\/978-3-319-12379-0"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/COMST.2006.315852","article-title":"A Survey of Security Issues In Wireless Sensor Networks","volume":"8","author":"Wang","year":"2006","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Pathan, A.K., Lee, H., and Hong, C.S. (2006, January 20\u201322). Security in wireless sensor networks: Issues and challenges. Proceedings of the 8th International Conference Advanced Communication Technology (ICACT\u201906), Phoenix Park, UK.","DOI":"10.1109\/ICACT.2006.206151"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1145\/1952982.1952995","article-title":"False data injection attacks against state estimation in electric power grids","volume":"14","author":"Liu","year":"2011","journal-title":"ACM Trans. Inf. Syst. Secur."},{"key":"ref_20","unstructured":"Yan, Q., Li, M., Jiang, T., Lou, W., and Thomas Hou, Y. (2012, January 25\u201330). Vulnerability and protection for distributed consensus-based spectrum sensing in cognitive radio networks. Proceedings of the International Conference on Computer Communications(INFOCOM\u201912), Orlando, FL, USA."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1109\/JPROC.2011.2161428","article-title":"Cyberphysical security of a smart grid infrastructure","volume":"100","author":"Mo","year":"2012","journal-title":"IEEE Proc."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1109\/TAC.2011.2158130","article-title":"Consensus computation in unreliable networks: A system theoretic approach","volume":"57","author":"Pasqualetti","year":"2012","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"766","DOI":"10.1109\/JSAC.2013.130413","article-title":"Resilient asymptotic consensus in robust networks","volume":"31","author":"LeBlanc","year":"2013","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1109\/TWC.2008.060603","article-title":"A framework for a distributed key management scheme in heterogeneous wireless sensor networks","volume":"7","author":"Lu","year":"2008","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.adhoc.2006.05.012","article-title":"An effective key management scheme for heterogeneous sensor networks","volume":"5","author":"Du","year":"2007","journal-title":"Ad Hoc Netw."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2723","DOI":"10.3390\/s140202732","article-title":"An Efficient and Adaptive Mutual Authentication Framework for Heterogeneous Wireless Sensor Network-Based Applications","volume":"14","author":"Kumar","year":"2014","journal-title":"Sensors"},{"key":"ref_27","unstructured":"Mi, S., Han, H., Zhu, S., Chen, C., Yang, B., and Guan, X. (July, January 29). A Secure Distributed Consensus Scheme for Wireless Sensor Networks Against Data Falsification. Proceedings of the 11th World Congress on Intelligent Controland Automation (WCICA), Shenyang, China."},{"key":"ref_28","unstructured":"Liu, S., Zhu, H., Li, S., Li, X., Chen, C., and Guan, X. (2012, January 3\u20137). An adaptive deviation-tolerant secure scheme for distributed cooperative spectrum Sensing. Proceedings of the Global Communications Conference (GLOBECOM\u201912), Anaheim, CA, USA."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Horn, R.A., and Johnson, C.R. (1985). Matrix Analysis, Cambridge Univercity Press.","DOI":"10.1017\/CBO9780511810817"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/2\/252\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:19:23Z","timestamp":1760210363000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/2\/252"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,19]]},"references-count":29,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,2]]}},"alternative-id":["s16020252"],"URL":"https:\/\/doi.org\/10.3390\/s16020252","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2016,2,19]]}}}