{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T19:30:58Z","timestamp":1777663858120,"version":"3.51.4"},"reference-count":40,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2022,10,2]],"date-time":"2022-10-02T00:00:00Z","timestamp":1664668800000},"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":["NSFC-61873087"],"award-info":[{"award-number":["NSFC-61873087"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["ZD2021F003"],"award-info":[{"award-number":["ZD2021F003"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2021-KYYWF-0027"],"award-info":[{"award-number":["2021-KYYWF-0027"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key Project of the Natural Science Foundation of Heilongjiang Province, China","award":["NSFC-61873087"],"award-info":[{"award-number":["NSFC-61873087"]}]},{"name":"Key Project of the Natural Science Foundation of Heilongjiang Province, China","award":["ZD2021F003"],"award-info":[{"award-number":["ZD2021F003"]}]},{"name":"Key Project of the Natural Science Foundation of Heilongjiang Province, China","award":["2021-KYYWF-0027"],"award-info":[{"award-number":["2021-KYYWF-0027"]}]},{"name":"University Basic Research Foundation of Heilongjiang Province","award":["NSFC-61873087"],"award-info":[{"award-number":["NSFC-61873087"]}]},{"name":"University Basic Research Foundation of Heilongjiang Province","award":["ZD2021F003"],"award-info":[{"award-number":["ZD2021F003"]}]},{"name":"University Basic Research Foundation of Heilongjiang Province","award":["2021-KYYWF-0027"],"award-info":[{"award-number":["2021-KYYWF-0027"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper concerns the distributed fusion filtering problem for descriptor systems with time-correlated measurement noises. The original descriptor is transformed into two reduced-order subsystems (ROSs) based on singular value decomposition. For the first ROS, a new measurement is obtained using measurement difference technology. Each sensor produces a local filter based on the fusion predictor from the fusion center and its own new measurement and then sends it to the fusion center. In the fusion center, based on local filters, a distributed fusion filter with feedback (DFFWF) in the linear minimum variance (LMV) sense is proposed by applying an innovative approach. The DFFWF for the second ROS is also obtained based on the DFFWF for the first ROS. Then, the DFFWF for the original descriptor is obtained. The proposed DFFWF can achieve the same estimation accuracy as the centralized fusion filter (CFF) under the condition that all local filter gain matrices are of full column rank. Its optimality is strictly proved. Moreover, it has robustness and reliability due to the parallel processing of local filters. Two simulation examples demonstrate the effectiveness of the developed fusion algorithm.<\/jats:p>","DOI":"10.3390\/s22197469","type":"journal-article","created":{"date-parts":[[2022,10,10]],"date-time":"2022-10-10T03:07:28Z","timestamp":1665371248000},"page":"7469","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Globally Optimal Distributed Fusion Filter for Descriptor Systems with Time-Correlated Measurement Noises"],"prefix":"10.3390","volume":"22","author":[{"given":"Jing","family":"Ma","sequence":"first","affiliation":[{"name":"School of Mathematics Science, Heilongjiang University, Harbin 150080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liling","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Mathematics Science, Heilongjiang University, Harbin 150080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Duan, G. (2010). Analysis and Design of Descriptor Linear Systems, Springer Science & Business Media.","DOI":"10.1007\/978-1-4419-6397-0"},{"key":"ref_2","unstructured":"Stevens, B., and Lewis, F. (1991). Aircraft Modeling, Dynamics and Control, Wiley."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1686","DOI":"10.1177\/0142331218787605","article-title":"Adaptive Kalman filtering for sensor fault estimation and isolation of satellite attitude control based on descriptor systems","volume":"41","author":"Wang","year":"2019","journal-title":"Trans. Inst. Meas. Control"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/j.sigpro.2006.05.007","article-title":"Optimal filtering and smoothing for discrete-time stochastic singular systems","volume":"87","author":"Sun","year":"2007","journal-title":"Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1080\/00207721003611649","article-title":"Distributed full-order optimal fusion filters and smoothers for discrete-time stochastic singular systems","volume":"42","author":"Sun","year":"2011","journal-title":"Int. J. Syst. Sci."},{"key":"ref_6","first-page":"3607","article-title":"An optimal filter for singular systems with stochastic multiplicative disturbance","volume":"67","author":"Yu","year":"2020","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"ref_7","first-page":"286","article-title":"Distributed reduced-order optimal fusion Kalman filters for stochastic singular system","volume":"32","author":"Sun","year":"2006","journal-title":"Acta Autom. Sin."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1016\/j.inffus.2006.10.010","article-title":"Reduced-order steady-state descriptor Kalman fuser weighted by block-diagonal matrices","volume":"9","author":"Deng","year":"2008","journal-title":"Inf. Fusion"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2543","DOI":"10.3934\/math.2022143","article-title":"Optimized distributed fusion filtering for singular systems with fading measurements and stochastic nonlinearity","volume":"7","author":"Wang","year":"2021","journal-title":"AIMS Math."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2232","DOI":"10.1049\/iet-cta.2018.5498","article-title":"WMF reduced-order robust estimators for multisensor descriptor systems","volume":"12","author":"Ran","year":"2018","journal-title":"IET Control Theory Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1873","DOI":"10.1080\/00207721.2019.1645234","article-title":"WMF self-tuning Kalman estimators for multisensor singular system","volume":"50","author":"Dou","year":"2019","journal-title":"Int. J. Syst. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"584","DOI":"10.1080\/00207179.2011.563321","article-title":"Descriptor recursive estimation for multiple sensors with different delay rates","volume":"84","author":"Feng","year":"2011","journal-title":"Int. J. Control"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"592","DOI":"10.1109\/TAES.1987.310893","article-title":"Alpha-beta filter with correlated measurement noise","volume":"23","author":"Rogers","year":"1987","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/s00190-008-0231-z","article-title":"Consideration of time-correlated errors in a Kalman filter applicable to GNSS","volume":"83","author":"Petovello","year":"2009","journal-title":"J. Geod."},{"key":"ref_15","first-page":"636","article-title":"A resilient approach to recursive distributed filtering for multirate systems over sensor networks with time-correlated fading channels","volume":"7","author":"Li","year":"2021","journal-title":"IEEE Trans. Signal Inf. Process. Netw."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3102","DOI":"10.1109\/TSMC.2021.3062848","article-title":"Robust recursive filtering for stochastic systems with time-correlated fading channels","volume":"52","author":"Tan","year":"2022","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1669","DOI":"10.1109\/TAES.2012.6178086","article-title":"Practical approaches to Kalman filtering with time-correlated measurement errors","volume":"48","author":"Wang","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4583","DOI":"10.1109\/TSP.2015.2447491","article-title":"Optimal estimation for discrete-time linear systems in the presence of multiplicative and time-correlated additive measurement noises","volume":"63","author":"Liu","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"662","DOI":"10.2514\/3.29327","article-title":"Estimation using sampled data containing sequentially correlated noise","volume":"5","author":"Bryson","year":"1968","journal-title":"J. Spacecr. Rocket."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1049\/iet-cta.2014.0545","article-title":"Optimal filtering for discrete-time linear systems with multiplicative and time-correlated additive measurement noises","volume":"9","author":"Liu","year":"2015","journal-title":"IET Control Theory Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.sigpro.2018.08.005","article-title":"State estimation under non-Gaussian L\u00e9vy and time-correlated additive sensor noises: A modified Tobit Kalman filtering approach","volume":"154","author":"Geng","year":"2019","journal-title":"Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.dsp.2016.10.003","article-title":"Distributed filtering for discrete-time linear systems with fading measurements and time-correlated noise","volume":"60","author":"Li","year":"2017","journal-title":"Digit. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.inffus.2019.07.008","article-title":"Networked fusion estimation with multiple uncertainties and time-correlated channel noise","volume":"54","year":"2020","journal-title":"Inf. Fusion"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Xu, L., Liu, S., and Ma, J. (2021, January 26\u201328). Linear optimal filter for descriptor systems with time-correlated measurement noise. Proceedings of the 40th Chinese Control Conference, Shanghai, China.","DOI":"10.23919\/CCC52363.2021.9549878"},{"key":"ref_25","unstructured":"Han, C., Zhu, H., and Duan, Z. (2006). Multi-Source Information Fusion, Tsinghua University Press."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"6117","DOI":"10.1109\/TSP.2020.3031388","article-title":"Optimal sequential estimation for asynchronous sampling discrete-time systems","volume":"68","author":"Lin","year":"2020","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_27","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_28","doi-asserted-by":"crossref","first-page":"1450","DOI":"10.1016\/j.automatica.2007.01.010","article-title":"Optimal Kalman filtering fusion with cross-correlated sensor noises","volume":"43","author":"Song","year":"2007","journal-title":"Automatica"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.inffus.2020.05.006","article-title":"Distributed optimal linear fusion estimators","volume":"63","author":"Sun","year":"2020","journal-title":"Inf. Fusion"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1064","DOI":"10.1109\/TSP.2020.2967180","article-title":"Distributed optimal linear fusion predictors and filters for systems with random parameter matrices and correlated noise","volume":"68","author":"Sun","year":"2020","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/j.automatica.2018.11.043","article-title":"Globally optimal sequential and distributed fusion state estimation for multi-sensor systems with cross-correlated noises","volume":"101","author":"Lin","year":"2019","journal-title":"Automatica"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"106447","DOI":"10.1016\/j.ast.2020.106447","article-title":"Cubature rule-based distributed optimal fusion with identification and prediction of kinematic model error for integrated UAV navigation","volume":"109","author":"Gao","year":"2021","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1049\/sil2.12120","article-title":"Reduced-order multisensory fusion estimation with application to object tracking","volume":"16","author":"Shin","year":"2022","journal-title":"IET Signal Process."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Fern\u00e1ndez-Alcal\u00e1, R., Jim\u00e9nez-L\u00f3pez, J., Navarro-Moreno, J., and Ruiz-Molina, J. (2022). Multisensor fusion estimation for systems with uncertain measurements, based on reduced dimension hypercomplex techniques. Mathematics, 10.","DOI":"10.3390\/math10142495"},{"key":"ref_35","unstructured":"Gelb, A. (1974). Applied Optimal Estimation, MIT Press."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"5672","DOI":"10.1109\/TSP.2016.2576420","article-title":"Optimal linear estimators for systems with finite-step correlated noises and packet dropout compensations","volume":"64","author":"Sun","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_37","unstructured":"Anderson, B.D.O., and Moore, J.B. (1979). Optimal Filtering, Prentice-Hall."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Caballero-\u00c1guila, R., Hermoso-Carazo, A., and Linares-P\u00e9rez, J. (2016). Networked fusion filtering from outputs with stochastic uncertainties and correlated random transmission delays. Sensors, 16.","DOI":"10.3390\/s16060847"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Wang, M., and Sun, S. (2019). Self-tuning distributed fusion filter for multi-sensor networked systems with unknown packet receiving rates, noise variances, and model parameters. Sensors, 19.","DOI":"10.3390\/s19204436"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Caballero-\u00c1guila, R., Hermoso-Carazo, A., and Linares-P\u00e9rez, J. (2020). A two-phase distributed filtering algorithm for networked uncertain systems with fading measurements under deception attacks. Sensors, 20.","DOI":"10.3390\/s20226445"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/19\/7469\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:45:24Z","timestamp":1760143524000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/19\/7469"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,2]]},"references-count":40,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["s22197469"],"URL":"https:\/\/doi.org\/10.3390\/s22197469","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,2]]}}}