{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T17:42:06Z","timestamp":1770140526580,"version":"3.49.0"},"reference-count":32,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,3,7]],"date-time":"2024-03-07T00:00:00Z","timestamp":1709769600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62176214"],"award-info":[{"award-number":["62176214"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61973253"],"award-info":[{"award-number":["61973253"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The problem of state estimation based on bearing-only sensors is increasingly important while existing research on distributed filtering solutions is rather limited. Therefore, this paper proposed the novel distributed cubature information filtering (DCIF) method for addressing the state estimation challenge in bearing-only sensor networks. Firstly, the system model of the bearing-only sensor network was constructed, and the observability of the system was analyzed. The sensor nodes are paired to measure relative angle information. Subsequently, the coordinated consistency theory is employed to achieve a unified state estimation of the maneuvering target. The DCIF method enhances the observability of the system, addressing the issues of large accuracy errors and divergence in traditional nonlinear filtering algorithms. Building upon the theoretical proof of consistency convergence in DCIF, four simulation experiments were conducted for comparison. These experiments validate the effectiveness and superiority of the DCIF method in bearing-only sensor networks.<\/jats:p>","DOI":"10.3390\/e26030236","type":"journal-article","created":{"date-parts":[[2024,3,7]],"date-time":"2024-03-07T08:59:37Z","timestamp":1709801977000},"page":"236","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Distributed Cubature Information Filtering Method for State Estimation in Bearing-Only Sensor Network"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1505-5541","authenticated-orcid":false,"given":"Zhan","family":"Chen","sequence":"first","affiliation":[{"name":"Unmanned System Research Institute, Northwestern Polytechnical University, Xi\u2019an 710072, China"}]},{"given":"Wenxing","family":"Fu","sequence":"additional","affiliation":[{"name":"Unmanned System Research Institute, Northwestern Polytechnical University, Xi\u2019an 710072, China"}]},{"given":"Ruitao","family":"Zhang","sequence":"additional","affiliation":[{"name":"Unmanned System Research Institute, Northwestern Polytechnical University, Xi\u2019an 710072, China"}]},{"given":"Yangwang","family":"Fang","sequence":"additional","affiliation":[{"name":"Unmanned System Research Institute, Northwestern Polytechnical University, Xi\u2019an 710072, China"}]},{"given":"Zhun","family":"Xiao","sequence":"additional","affiliation":[{"name":"Unmanned System Research Institute, Northwestern Polytechnical University, Xi\u2019an 710072, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1109\/LSP.2021.3074034","article-title":"Moving source localization in passive sensor network with location uncertainty","volume":"28","author":"Mao","year":"2021","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"17078","DOI":"10.1109\/JSEN.2023.3283998","article-title":"A Novel Range Selective Generalized Weighted Centroid Method for Source Localization in Bearing-Only Sensor Networks","volume":"23","author":"Luo","year":"2023","journal-title":"IEEE Sens. J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"108150","DOI":"10.1016\/j.sigpro.2021.108150","article-title":"A review of robust distributed estimation strategies over wireless sensor networks","volume":"188","author":"Modalavalasa","year":"2021","journal-title":"Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Huang, Z., Chen, S., Hao, C., and Orlando, D. (2021). Bearings-Only Target Tracking with an Unbiased Pseudo-Linear Kalman Filter. Remote. Sens., 13.","DOI":"10.3390\/rs13152915"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"23645","DOI":"10.1109\/JSEN.2021.3105541","article-title":"Distributed cooperative localization based on bearing-only sensors","volume":"21","author":"Yang","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"6029","DOI":"10.3233\/JIFS-189442","article-title":"Radar signal processing algorithm and simulation of detection system","volume":"40","author":"Song","year":"2021","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Zhu, H., Wang, C., and Wang, L. (2023). A Target Detection Method of Distributed Passive Radar without Direct-Path Signal. Electronics, 12.","DOI":"10.3390\/electronics12020433"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1109\/TMC.2011.59","article-title":"Target tracking in wireless sensor networks based on the combination of KF and MLE using distance measurements","volume":"11","author":"Wang","year":"2011","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/j.robot.2015.07.016","article-title":"A new method of target tracking by EKF using bearing and elevation measurements for underwater environment","volume":"74","author":"Modalavalasa","year":"2015","journal-title":"Robot. Auton. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1007\/s10846-021-01513-z","article-title":"Multiple Model Distributed EKF for Teams of Target Tracking UAVs using T Test Selection","volume":"104","author":"Wolfe","year":"2022","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3804","DOI":"10.1007\/s12555-022-0441-9","article-title":"A Fuzzy-based Adaptive Unscented Kalman Filter for State Estimation of Three-dimensional Target Tracking","volume":"21","author":"Kumar","year":"2023","journal-title":"Int. J. Control Autom. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Huang, P., Li, H., and Wen, G. (2022). Application of Adaptive Weighted Strong Tracking Unscented Kalman Filter in Non-Cooperative Maneuvering Target Tracking. Aerospace, 9.","DOI":"10.3390\/aerospace9080468"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1795","DOI":"10.1049\/iet-rsn.2020.0165","article-title":"Noise-aware manoeuvring target tracking algorithm in wireless sensor networks by a novel adaptive cubature Kalman filter","volume":"14","author":"Fang","year":"2020","journal-title":"IET Radar Sonar Navig."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2489","DOI":"10.1016\/j.cja.2019.07.025","article-title":"A novel strong tracking cubature Kalman filter and its application in maneuvering target tracking","volume":"32","author":"Zhang","year":"2019","journal-title":"Chin. J. Aeronaut."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"750","DOI":"10.1109\/JSEN.2012.2226441","article-title":"Square root cubature information filter","volume":"13","author":"Chandra","year":"2012","journal-title":"IEEE Sens. J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1016\/j.sigpro.2013.06.015","article-title":"Cubature information filters with correlated noises and their applications in decentralized fusion","volume":"94","author":"Ge","year":"2014","journal-title":"Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1049\/iet-cta.2017.0575","article-title":"Distributed event-triggered cubature information filtering based on weighted average consensus","volume":"12","author":"Tan","year":"2018","journal-title":"IET Control Theory Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"107445","DOI":"10.1016\/j.ast.2022.107445","article-title":"Simplified augmented cubature information filtering and multi-sensor fusion for additive noise systems","volume":"123","author":"Li","year":"2022","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.isatra.2022.10.027","article-title":"Privacy-preserving push-sum distributed cubature information filter for nonlinear target tracking with switching directed topologies","volume":"136","author":"Zha","year":"2023","journal-title":"ISA Trans."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"9925","DOI":"10.1109\/JSEN.2023.3261180","article-title":"Distributed Maximum Correntropy Cubature Information Filtering for Tracking Unmanned Aerial Vehicle","volume":"9","author":"Zhou","year":"2023","journal-title":"IEEE Sens. J."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2975","DOI":"10.1109\/TSP.2017.2679685","article-title":"Improved cubature Kalman filter for GNSS\/INS based on transformation of posterior sigma-points error","volume":"65","author":"Cui","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3052","DOI":"10.1177\/0142331220940228","article-title":"A consensus-based square-root cubature Kalman filter for manoeuvring target tracking in sensor networks","volume":"42","author":"Zhong","year":"2020","journal-title":"Trans. Inst. Meas. Control"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"107873","DOI":"10.1016\/j.ast.2022.107873","article-title":"An improved adaptive robust information filter for spacecraft relative navigation","volume":"130","author":"Chu","year":"2022","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.neucom.2017.03.004","article-title":"Distributed cubature information filtering based on weighted average consensus","volume":"243","author":"Chen","year":"2017","journal-title":"Neurocomputing"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"10526","DOI":"10.3390\/s150510526","article-title":"A Novel Square-Root Cubature Information Weighted Consensus Filter Algorithm for Multi-Target Tracking in Distributed Camera Networks","volume":"15","author":"Chen","year":"2015","journal-title":"Sensors"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhou, R., Chen, J., Tan, W., Yan, Q., and Cai, C. (2021). Optimal 3D Angle of Arrival Sensor Placement with Gaussian Priors. Entropy, 23.","DOI":"10.3390\/e23111379"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.inffus.2019.08.010","article-title":"Collaborative detection and power allocation framework for target tracking in multiple radar system","volume":"55","author":"Yan","year":"2020","journal-title":"Inf. Fusion"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1109\/TAC.2012.2206693","article-title":"Analysis of Noisy Bearing-Only Network Localization","volume":"58","author":"Shames","year":"2013","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Li, X., Zhao, C., Yu, J., and Wei, W. (2019). Underwater Bearing-Only and Bearing-Doppler Target Tracking Based on Square Root Unscented Kalman Filter. Entropy, 21.","DOI":"10.3390\/e21080740"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"107661","DOI":"10.1016\/j.epsr.2021.107661","article-title":"Parameters estimation of horizontal multilayer soils using a heuristic algorithm","volume":"203","author":"Dan","year":"2022","journal-title":"Electr. Power Syst. Res."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"508","DOI":"10.1109\/JSEN.2013.2284201","article-title":"Optimization Design and Research Character of the Passive Electric Field Sensor","volume":"14","author":"Zhang","year":"2014","journal-title":"IEEE Sens. J."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Ali, W., Li, Y., Raja, M.A.Z., Khan, W.U., and He, Y. (2021). State Estimation of an Underwater Markov Chain Maneuvering Target Using Intelligent Computing. Entropy, 23.","DOI":"10.3390\/e23091124"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/3\/236\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:10:23Z","timestamp":1760105423000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/3\/236"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,7]]},"references-count":32,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["e26030236"],"URL":"https:\/\/doi.org\/10.3390\/e26030236","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,3,7]]}}}