{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:15:37Z","timestamp":1760188537285,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,5,8]],"date-time":"2019-05-08T00:00:00Z","timestamp":1557273600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61471383, 91538201, 61531020, 61790550, 61671463, 61790552"],"award-info":[{"award-number":["61471383, 91538201, 61531020, 61790550, 61671463, 61790552"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Owing to its high-fault tolerance and scalability, the consensus-based paradigm has attracted immense popularity for distributed state estimation. If a target is neither observed by a certain node nor by its neighbors, this node is naive about the target. Some existing algorithms have considered the presence of naive nodes, but it takes sufficient consensus iterations for these algorithms to achieve a satisfactory performance. In practical applications, because of constrained energy and communication resources, only a limited number of iterations are allowed and thus the performance of these algorithms will be deteriorated. By fusing the measurements as well as the prior estimates of each node and its neighbors, a local optimal estimate is obtained based on the proposed distributed local maximum a posterior (MAP) estimator. With some approximations of the cross-covariance matrices and a consensus protocol incorporated into the estimation framework, a novel distributed hybrid information weighted consensus filter (DHIWCF) is proposed. Then, theoretical analysis on the guaranteed stability of the proposed DHIWCF is performed. Finally, the effectiveness and superiority of the proposed DHIWCF is evaluated. Simulation results indicate that the proposed DHIWCF can achieve an acceptable estimation performance even with a single consensus iteration.<\/jats:p>","DOI":"10.3390\/s19092134","type":"journal-article","created":{"date-parts":[[2019,5,9]],"date-time":"2019-05-09T11:22:35Z","timestamp":1557400955000},"page":"2134","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A Novel Distributed State Estimation Algorithm with Consensus Strategy"],"prefix":"10.3390","volume":"19","author":[{"given":"Jun","family":"Liu","sequence":"first","affiliation":[{"name":"Research Institute of Information Fusion, Naval Aviation University, Yantai 264001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5216-3181","authenticated-orcid":false,"given":"Yu","family":"Liu","sequence":"additional","affiliation":[{"name":"Research Institute of Information Fusion, Naval Aviation University, Yantai 264001, China"},{"name":"School of Electronic and Information Engineering, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kai","family":"Dong","sequence":"additional","affiliation":[{"name":"Research Institute of Information Fusion, Naval Aviation University, Yantai 264001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ziran","family":"Ding","sequence":"additional","affiliation":[{"name":"Research Institute of Information Fusion, Naval Aviation University, Yantai 264001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"You","family":"He","sequence":"additional","affiliation":[{"name":"Research Institute of Information Fusion, Naval Aviation University, Yantai 264001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.sysconle.2018.04.005","article-title":"Distributed Kalman filter in a network of linear systems","volume":"116","author":"Marelli","year":"2018","journal-title":"Syst. Control Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.automatica.2018.03.005","article-title":"A distributed Kalman filter with event-triggered communication and guaranteed stability","volume":"93","author":"Battistelli","year":"2018","journal-title":"Automatica"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1115\/1.3662552","article-title":"A New Approach to Linear Filtering and Prediction Problems","volume":"82","author":"Kalman","year":"1960","journal-title":"J. Basic Eng."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Kamal, A.T., Ding, C., Song, B., Farrell, J.A., and Roy-Chowdhury, A.K. (2011, January 12\u201315). A Generalized Kalman Consensus Filter for Wide-Area Video Networks. Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, FL, USA.","DOI":"10.1109\/CDC.2011.6160333"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Olfati-Saber, R. (2007, January 12\u201314). Distributed Kalman Filtering for Sensor Networks. Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, LA, USA.","DOI":"10.1109\/CDC.2007.4434303"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Olfati-Saber, R. (2009, January 15\u201318). Kalman-Consensus Filter: Optimality, Stability, and Performance. Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly with 2009 28th Chinese Control Conference, Shanghai, China.","DOI":"10.1109\/CDC.2009.5399678"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1049\/iet-spr.2016.0388","article-title":"Generalised Kalman-consensus filter","volume":"11","author":"AminiOmam","year":"2017","journal-title":"IET Signal Process"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Deshmukh, R., Kwon, C., and Hwang, I. (2017, January 24\u201326). Optimal Discrete-Time Kalman Consensus Filter. Proceedings of the 2017 American Control Conference (ACC), Seattle, WA, USA.","DOI":"10.23919\/ACC.2017.7963859"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1002\/acs.2861","article-title":"Average information-weighted consensus filter for target tracking in distributed sensor networks with naivety issues","volume":"5","author":"Yao","year":"2018","journal-title":"Int. J. Adapt. Control"},{"key":"ref_10","unstructured":"Chong, C., Chang, K., and Mori, S. (2016, January 5\u20138). Comparison of Optimal Distributed Estimation and Consensus Filtering. Proceedings of the 19th International Conference on Information Fusion, Heidelberg, Germany."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Liu, Y., Liu, J., Xu, C., Qi, L., Sun, S., and Ding, Z. (2017, January 10\u201313). Consensus Algorithm for Distributed State Estimation in Multi-Clusters Sensor Network. Proceedings of the 20th International Conference on Information Fusion, Xi\u2019an, China.","DOI":"10.23919\/ICIF.2017.8009845"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"7611","DOI":"10.1109\/JSEN.2018.2859378","article-title":"Consensus-based distributed robust filtering for multisensor systems with stochastic uncertainties","volume":"18","author":"Rastgar","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_13","doi-asserted-by":"crossref","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":"ref_14","doi-asserted-by":"crossref","first-page":"2701","DOI":"10.1109\/TAC.2017.2774601","article-title":"On Kalman-consensus filtering with random link failures over sensor networks","volume":"63","author":"Liu","year":"2018","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1109\/TSIPN.2016.2626141","article-title":"Consensus-based algorithms for distributed network-state estimation and localization","volume":"3","author":"Soatti","year":"2017","journal-title":"IEEE Trans. Signal Inf. Proc. Over Netw."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3112","DOI":"10.1109\/TAC.2013.2277621","article-title":"Information weighted consensus filters and their application in distributed camera networks","volume":"58","author":"Kamal","year":"2013","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3113","DOI":"10.1049\/iet-com.2014.0338","article-title":"Information weighted consensus-based distributed particle filter for large-scale sparse wireless sensor networks","volume":"8","author":"Tang","year":"2014","journal-title":"IET Commun."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Kamal, A.T. (2013). Information Weighted Consensus for Distributed Estimation in Vision Networks. [Ph.D. Dissertation, University of California Riverside].","DOI":"10.1109\/CVPR.2013.311"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Liu, G., Tian, G., and Zhao, Y. (2016, January 27\u201329). Information Weighted Consensus Filtering with Improved Convergence Rate. Proceedings of the IEEE 35th Chinese Control Conference (CCC), Chengdu, China.","DOI":"10.1109\/ChiCC.2016.7554688"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1908","DOI":"10.1109\/TAES.2016.140506","article-title":"Cooperative space object tracking using space-based optical sensors via consensus-based filters","volume":"52","author":"Bin","year":"2016","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Jia, B., Pham, K.D., Blasch, E., Shen, D., and Chen, G. (2017, January 4\u201311). Consensus-Based Auction Algorithm for Distributed Sensor Management in Space Object Tracking. Proceedings of the 2017 IEEE Aerospace Conference, Big Sky, MT, USA.","DOI":"10.1109\/AERO.2017.7943708"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Kamal, A.T., Farrell, J.A., and Roy-Chowdhury, A.K. (2012, January 10\u201313). Information Weighted Consensus. Proceedings of the 51st IEEE Conference on Decision and Control, Maui, HI, USA.","DOI":"10.1109\/CDC.2012.6426886"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.sysconle.2018.10.001","article-title":"Resilient consensus of switched multi-agent systems","volume":"122","author":"Shang","year":"2018","journal-title":"Syst. Control Lett."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Shang, Y. (2018). Resilient Multiscale Coordination Control against Adversarial Nodes. Energies, 11.","DOI":"10.3390\/en11071844"},{"key":"ref_25","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_26","doi-asserted-by":"crossref","first-page":"1410","DOI":"10.1109\/TAC.2014.2357135","article-title":"Consensus-based linear and nonlinear filtering","volume":"60","author":"Battistelli","year":"2015","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Battistelli, G., Chisci, L., Mugnai, G., Farina, A., and Graziano, A. (2012, January 10\u201313). Consensus-Based Algorithms for Distributed Filtering. Proceedings of the IEEE 51st IEEE Conference on Decision and Control (CDC), Maui, HI, USA.","DOI":"10.1109\/CDC.2012.6426435"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1016\/j.automatica.2013.11.042","article-title":"Kullback\u2013Leibler average, consensus on probability densities, and distributed state estimation with guaranteed stability","volume":"50","author":"Battistelli","year":"2014","journal-title":"Automatica"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Julier, S.J., and Uhlmann, J.K. (1997, January 6). A Non-Divergent Estimation Algorithm in the Presence of Unknown Correlations. Proceedings of the 1997 American Control Conference, Albuquerque, NM, USA.","DOI":"10.1109\/ACC.1997.609105"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1300","DOI":"10.1109\/TCST.2017.2715849","article-title":"On the convergence conditions of distributed dynamic state estimation using sensor networks: A unified framework","volume":"26","author":"Wang","year":"2018","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"4561","DOI":"10.1109\/JSEN.2018.2823908","article-title":"Hybrid consensus-based cubature Kalman filtering for distributed state estimation in sensor networks","volume":"18","author":"Chen","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"580","DOI":"10.1109\/TSIPN.2016.2631944","article-title":"Convergence of Distributed Flooding and Its Application for Distributed Bayesian Filtering","volume":"3","author":"Li","year":"2017","journal-title":"IEEE Trans. Signal Inf. Proc. Over Netw."},{"key":"ref_33","unstructured":"Xiao, L., and Boyd, S. (2003, January 9\u201312). Fast Linear Iterations for Distributed Averaging. Proceedings of the 42nd IEEE International Conference on Decision and Control, Maui, HI, USA."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2615","DOI":"10.1109\/ACCESS.2016.2570518","article-title":"Finite-Time Weighted Average Consensus and Generalized Consensus Over a Subset","volume":"4","author":"Yilun","year":"2016","journal-title":"IEEE Access"},{"key":"ref_35","unstructured":"Ren, W., Beard, R.W., and Kingston, D.B. (2005, January 8\u201310). Multi-Agent Kalman Consensus with Relative Uncertainty. Proceedings of the American Control Conference, Portland, OR, USA."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"298","DOI":"10.2514\/1.34226","article-title":"Unbiased Kalman consensus algorithm","volume":"5","author":"Alighanbari","year":"2008","journal-title":"J. Aerosp. Comput. Inf. Commun."},{"key":"ref_37","unstructured":"Motion, L. (2001). General Decentralized Data Fusion with Covariance Intersection. Handbook of Multisensor Data Fusion, CRC Press."},{"key":"ref_38","unstructured":"Niehsen, W. (2002, January 8\u201316). Information Fusion Based on Fast Covariance Intersection Filtering. Proceedings of the Fifth International Conference on Information Fusion, Annapolis, MD, USA."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.inffus.2019.02.009","article-title":"Second-order statistics analysis and comparison between arithmetic and geometric average fusion: Application to multi-sensor target tracking","volume":"51","author":"Li","year":"2019","journal-title":"Inf. Fusion"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"868","DOI":"10.1080\/00207170802350662","article-title":"Distributed linear estimation over sensor networks","volume":"82","author":"Calafiore","year":"2009","journal-title":"Int. J. Control"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1109\/TAC.2005.846556","article-title":"Consensus seeking in multiagent systems under dynamically changing interaction topologies","volume":"50","author":"Ren","year":"2005","journal-title":"IEEE Trans. Autom. 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