{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T18:35:14Z","timestamp":1761676514562,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2017,6,29]],"date-time":"2017-06-29T00:00:00Z","timestamp":1498694400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>As the largest ellipsoid (LE) data fusion algorithm can only be applied to two-sensor system, in this contribution, parallel fusion structure is proposed to introduce the LE algorithm into a multisensor system with unknown cross-covariances, and three parallel fusion structures based on different estimate pairing methods are presented and analyzed. In order to assess the influence of fusion structure on fusion performance, two fusion performance assessment parameters are defined as Fusion Distance and Fusion Index. Moreover, the formula for calculating the upper bounds of actual fused error covariances of the presented multisensor LE fusers is also provided. Demonstrated with simulation examples, the Fusion Index indicates fuser\u2019s actual fused accuracy and its sensitivity to the sensor orders, as well as its robustness to the accuracy of newly added sensors. Compared to the LE fuser with sequential structure, the LE fusers with proposed parallel structures not only significantly improve their properties in these aspects, but also embrace better performances in consistency and computation efficiency. The presented multisensor LE fusers generally have better accuracies than that of covariance intersection (CI) fusion algorithm and are consistent when the local estimates are weakly correlated.<\/jats:p>","DOI":"10.3390\/s17071526","type":"journal-article","created":{"date-parts":[[2017,6,29]],"date-time":"2017-06-29T10:40:04Z","timestamp":1498732804000},"page":"1526","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Multisensor Parallel Largest Ellipsoid Distributed Data Fusion with Unknown Cross-Covariances"],"prefix":"10.3390","volume":"17","author":[{"given":"Baoyu","family":"Liu","sequence":"first","affiliation":[{"name":"School of Aeronautics and Astronautics, Shanghai Jiao Tong University, 800 Dongchuan Road, Minhang District, Shanghai 200240, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xingqun","family":"Zhan","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, Shanghai Jiao Tong University, 800 Dongchuan Road, Minhang District, Shanghai 200240, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zheng","family":"Zhu","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,6,29]]},"reference":[{"key":"ref_1","first-page":"803","article-title":"The effect of the common process noise on the two-sensor fused-track covariance","volume":"22","author":"Campo","year":"1986","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_2","unstructured":"Kim, K.H. (July, January 29). Development of Track to Track Fusion Algorithms. Proceedings of the American Control Conference, Baltimore, MD, USA."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1016\/j.automatica.2004.01.014","article-title":"Multi-sensor optimal information fusion kalman filter","volume":"40","author":"Sun","year":"2004","journal-title":"Automatica"},{"key":"ref_4","unstructured":"Lewis, F.L. (1986). Optimal Estimation: With an Introduction to Stochastic Control Theory, John Wiley & Sons."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1874","DOI":"10.1016\/j.automatica.2012.05.077","article-title":"State fusion with unknown correlation: Ellipsoidal intersection","volume":"48","author":"Sijs","year":"2012","journal-title":"Automatica"},{"key":"ref_6","unstructured":"Benaskeur, A.R. (2002, January 5\u20138). Consistent Fusion of Correlated Data Sources. Proceedings of the Annual Conference of the Industrial Electronics Society, Sevilla, Spain."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Julier, S.J., and Uhlmann, J.K. (1997, January 4\u20136). A Non-Divergent Estimation Algorithm in the Presence of Unknown Correlations. Proceedings of the American Control Conference, Alberqueque, NM, USA.","DOI":"10.1109\/ACC.1997.609105"},{"key":"ref_8","unstructured":"Zhou, Y., and Li, J. (2008, January 6\u201311). Data Fusion of Unknown Correlations Using Internal Ellipsoidal Approximation. Proceedings of the International Federation of Automatic Control, Seoul, Korea."},{"key":"ref_9","unstructured":"Niehsen, W. (2002, January 8\u201311). Information Fusion Based on Fast Covariance Intersection Filtering. Proceedings of the International Conference on Information Fusion, Annapolis, MD, USA."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.inffus.2011.08.001","article-title":"Multisensor data fusion: A review of the state-of-the-art","volume":"14","author":"Khaleghi","year":"2013","journal-title":"Inf. Fusion"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.inffus.2013.09.003","article-title":"Estimation fusion algorithms in the presence of partially known cross-correlation of local estimation errors","volume":"18","author":"Zhu","year":"2014","journal-title":"Inf. Fusion"},{"key":"ref_12","unstructured":"Llinas, J., and David, L.H. (2001). General Decentralized Data Fusion with Covariance Intersection (CI). Handbook of Multisensor Data Fusion, CRC Press."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1109\/TAES.2012.6129634","article-title":"Distributed estimation fusion with unavailable cross-correlation","volume":"48","author":"Wang","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Franken, D., and Hupper, A. (2005, January 25\u201328). Improved Fast Covariance Intersection for Distributed Data Fusion. Proceedings of the International Conference on Information Fusion, Philadelphia, PA, USA.","DOI":"10.1109\/ICIF.2005.1591849"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/S1566-2535(03)00036-8","article-title":"Covariance consistency methods for fault-tolerant distributed data fusion","volume":"4","author":"Uhlmann","year":"2003","journal-title":"Inf. Fusion"},{"key":"ref_16","unstructured":"Wang, Y., and Li, X.R. (2010, January 26\u201329). Distributed estimation fusion under unknown cross-correlation: An analytic center approach. Proceedings of the International Conference on Information Fusion, Edinburgh, UK."},{"key":"ref_17","unstructured":"Farrell, W.J., and Ganesh, C. (2009, January 6\u20139). Generalized Chernoff Fusion Approximation for Practical Distributed Data Fusion. Proceedings of the International Conference on Information Fusion, Seattle, WA, USA."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/j.ins.2011.11.038","article-title":"Sequential covariance intersection fusion kalman filter","volume":"189","author":"Deng","year":"2012","journal-title":"Inf. Sci."},{"key":"ref_19","unstructured":"Wang, J., Gao, Y., Ran, C., and Huo, Y. (2015, January 10\u201311). State Estimation with Two-Level Fusion Structure. Proceedings of the International Conference on Estimation, Detection and Information Fusion, Harbin, China."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1016\/j.isatra.2013.10.002","article-title":"Cascaded kalman and particle filters for photogrammetry based gyroscope drift and robot attitude estimation","volume":"53","author":"Nargess","year":"2014","journal-title":"ISA Trans."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Bernstein, D.S. (2009). Matrix Mathematics: Theory, Facts, and Formulas, Princeton University Press. [2nd ed.].","DOI":"10.1515\/9781400833344"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.inffus.2012.05.005","article-title":"The accuracy comparison of multisensor covariance intersection fuser and three weighting fusers","volume":"14","author":"Deng","year":"2013","journal-title":"Inf. Fusion"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1879","DOI":"10.1109\/TAC.2002.804475","article-title":"Estimation under unknown correlation: Covariance intersection revisited","volume":"47","author":"Chen","year":"2002","journal-title":"IEEE Trans. Autom. Control."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1109\/7.106130","article-title":"Federated square root filter for decentralized parallel processors","volume":"26","author":"Carlson","year":"1990","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_25","unstructured":"Lennart, L. (1999). System Identification, Theory for the User, Prentice Hall. [2nd ed.]."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/7\/1526\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:40:49Z","timestamp":1760208049000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/7\/1526"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,29]]},"references-count":25,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2017,7]]}},"alternative-id":["s17071526"],"URL":"https:\/\/doi.org\/10.3390\/s17071526","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2017,6,29]]}}}