{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:03:45Z","timestamp":1760241825998,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,9,26]],"date-time":"2018-09-26T00:00:00Z","timestamp":1537920000000},"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>The multi-sensor information fusion particle filter (PF) has been put forward for nonlinear systems with correlated noises. The proposed algorithm uses the Taylor series expansion method, which makes the nonlinear measurement functions have a linear relationship by the intermediary function. A weighted measurement fusion PF (WMF-PF) was put forward for systems with correlated noises by applying the full rank decomposition and the weighted least square theory. Compared with the augmented optimal centralized fusion particle filter (CF-PF), it could greatly reduce the amount of calculation. Moreover, it showed asymptotic optimality as the Taylor series expansion increased. The simulation examples illustrate the effectiveness and correctness of the proposed algorithm.<\/jats:p>","DOI":"10.3390\/s18103242","type":"journal-article","created":{"date-parts":[[2018,9,28]],"date-time":"2018-09-28T02:54:54Z","timestamp":1538103294000},"page":"3242","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Weighted Measurement Fusion Particle Filter for Nonlinear Systems with Correlated Noises"],"prefix":"10.3390","volume":"18","author":[{"given":"Ke Wei","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Electronic Engineering, Heilongjiang University, Harbin 150080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1252-5771","authenticated-orcid":false,"given":"Gang","family":"Hao","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Heilongjiang University, Harbin 150080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5325-3608","authenticated-orcid":false,"given":"Shu Li","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Heilongjiang University, Harbin 150080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,9,26]]},"reference":[{"key":"ref_1","unstructured":"Bar-Shalom, Y., and Li, X.R. (1995). Multitarget-Multisensor Tracking: Principles and Techniques, YBS Publishing."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4977","DOI":"10.1109\/TSP.2010.2056923","article-title":"Cubature Kalman filtering for continuous-discrete systems: Theory and simulations","volume":"58","author":"Arasaratnam","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"576","DOI":"10.1016\/j.ymssp.2015.12.002","article-title":"Accurate state estimation for a hydraulic actuator via a SDRE nonlinear filter","volume":"75","author":"Strano","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1325","DOI":"10.1007\/s00419-018-1374-x","article-title":"A time-domain system identification numerical procedure for obtaining linear dynamical models of multibody mechanical systems","volume":"88","author":"Pappalardo","year":"2018","journal-title":"Arch. Appl. Mech."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"928","DOI":"10.1115\/1.2909600","article-title":"Robust piecewise-linear state observers for flexible link mechanisms","volume":"130","author":"Caracciolo","year":"2008","journal-title":"J. Dyn. Syst. Meas. Control"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Pappalard, C.M., and Guida, D. (2018). System identification algorithm for computing the modal parameters of linear. Machines, 6.","DOI":"10.3390\/machines6020012"},{"key":"ref_7","first-page":"56","article-title":"System identification and experimental modal analysis of a frame structure","volume":"26","author":"Pappalardo","year":"2018","journal-title":"Eng. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1016\/j.aeue.2014.09.017","article-title":"Novel cubature Kalman filtering for systems involving nonlinear states and linear measurements","volume":"69","author":"Wang","year":"2015","journal-title":"Int. J. Electron. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Calabrese, A., Strano, S., Serino, G., and Terzo, M. (2014, January 17\u201318). An extended Kalman Filter procedure for damage detection of base-isolated structures. Proceedings of the 2014 IEEE Workshop on Environmental, Energy, and Structural Monitoring Systems, Naples, Italy.","DOI":"10.1109\/EESMS.2014.6923262"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1109\/87.911389","article-title":"Experimental application of extended Kalman filtering for sensor validation","volume":"9","author":"Gobbo","year":"2001","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Julier, S.J., and Uhlmann, J.K. (1997, January 28). A new extension of the Kalman filter to nonlinear systems. Proceedings of the International Symposium on Aerospace\/Defense Sensing, Simulation and Controls, Orlando, FL, USA.","DOI":"10.1117\/12.280797"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1109\/JPROC.2003.823141","article-title":"Unscented filtering and nonlinear estimation","volume":"92","author":"Julier","year":"2004","journal-title":"Proc. IEEE"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1254","DOI":"10.1109\/TAC.2009.2019800","article-title":"Cubature Kalman filters","volume":"54","author":"Arasaratnam","year":"2009","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"786","DOI":"10.1111\/j.2517-6161.1954.tb00145.x","article-title":"Poor man\u2019s Monte Carlo","volume":"16","author":"Hammersley","year":"1954","journal-title":"J. R. Stat. Soc. B"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Doucet, A., Freitas, N.D., and Gordon, N. (2001). Sequential Monte Carlo Methods in Practice, Statistics for Engineering and Information Science, Springer.","DOI":"10.1007\/978-1-4757-3437-9"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Berg, B.A. (2004). Markov Chain Monte Carlo Simulations and Their Statistical Analysis, World Scientific.","DOI":"10.1142\/5602"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"912","DOI":"10.1109\/TSMC.2016.2523911","article-title":"Multisensor nonlinear fusion methods based on adaptive ensemble fifth-degree iterated Cubature information filter for biomechatronics","volume":"46","author":"Ge","year":"2016","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"736","DOI":"10.1109\/78.984773","article-title":"A survey of convergence results on Particle filtering methods for practitioners","volume":"50","author":"Crisan","year":"2002","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_19","unstructured":"Bruno, M.G.S., and Pavlov, A. (2004, January 17\u201321). Improved particle filters for ballistic target tracking. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Montreal, QC, Canada."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1049\/ip-f-2.1993.0015","article-title":"Novel approach to nonlinear\/non-Gaussian Bayesian state estimation","volume":"140","author":"Gordon","year":"2002","journal-title":"IEEE Proc. Radar Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1415","DOI":"10.1109\/TIE.2016.2610403","article-title":"Carrier Tracking Estimation Analysis by Using the Extended Strong Tracking Filtering","volume":"64","author":"Ge","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.inffus.2017.03.006","article-title":"Multi-sensor distributed fusion estimation with applications in networked systems: A review paper","volume":"38","author":"Sun","year":"2017","journal-title":"Inf. Fusion"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.dsp.2017.05.005","article-title":"Decentralized estimation of regression coefficients in sensor networks","volume":"68","author":"Gispan","year":"2017","journal-title":"Digit. Signal Process."},{"key":"ref_24","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_25","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.ijnonlinmec.2013.01.016","article-title":"State estimation using multibody models and non-linear Kalman filters","volume":"53","author":"Pastorino","year":"2013","journal-title":"Int. J. Non-Linear Mech."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.inffus.2010.11.003","article-title":"Information fusion estimators for systems with multiple sensors of different packet dropout rates","volume":"12","author":"Ma","year":"2011","journal-title":"Inf. Fusion"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.inffus.2015.06.001","article-title":"Multi-sensor information fusion estimators for stochastic uncertain systems with correlated noises","volume":"27","author":"Tian","year":"2016","journal-title":"Inf. Fusion"},{"key":"ref_28","first-page":"2057","article-title":"Weighted measurement fusion estimation algorithm with correlated noises and its global optimality","volume":"32","author":"Wang","year":"2010","journal-title":"Syst. Eng. Electron."},{"key":"ref_29","first-page":"857","article-title":"Weighted measurement fusion white noise deconvolution Filter with correlated noise for multisensor stochastic systems","volume":"21","author":"Wang","year":"2012","journal-title":"Math. Probl. Eng."},{"key":"ref_30","first-page":"1362","article-title":"Design of unscented Kalman filter with correlative noises","volume":"27","author":"Wang","year":"2010","journal-title":"Control Theory Appl."},{"key":"ref_31","first-page":"1393","article-title":"Design of UKF with correlative noises based on minimum mean square error estimation","volume":"25","author":"Wang","year":"2010","journal-title":"Control Decis."},{"key":"ref_32","first-page":"2214","article-title":"Design of CKF with correlative noises based on Bayesian estimation, systems engineering and electronics","volume":"34","author":"Qian","year":"2012","journal-title":"Syst. Eng. Electron."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1011","DOI":"10.1016\/j.amc.2013.12.168","article-title":"Design and implementation of Gaussian filter for nonlinear system with randomly delayed measurements and correlated noises","volume":"232","author":"Wang","year":"2014","journal-title":"Appl. Math. Comput."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2290","DOI":"10.1016\/j.automatica.2012.06.035","article-title":"A Gaussian approximation recursive filter for nonlinear systems with correlated noises","volume":"48","author":"Wang","year":"2012","journal-title":"Automatica"},{"key":"ref_35","unstructured":"Xu, J.H., Dimirovski, G.M., Jing, Y.W., and Shen, C. (2007, January 2\u201314). UKF design and stability for nonlinear stochastic systems with correlated noises. Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, LA, USA."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Fu, A., Zhu, Y.M., and Song, E. (2008, January 22\u201326). The optimal Kalman type state estimator with multi-step correlated process and measurement noises. Proceedings of the 2008 International Conference on Embedded Software and Systems, Chengdu, China.","DOI":"10.1109\/ICESS.2008.54"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.automatica.2015.06.035","article-title":"Gaussian filter for nonlinear systems with correlated noises at the same epoch","volume":"60","author":"Huang","year":"2015","journal-title":"Automatica"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2131","DOI":"10.1016\/j.automatica.2005.07.011","article-title":"Sensors\u2019 optimal dimensionality compression matrix in estimation fusion","volume":"41","author":"Song","year":"2005","journal-title":"Automatica"},{"key":"ref_39","first-page":"233","article-title":"Correlated measurement fusion steady-state Kalman filtering algorithms and their optimality","volume":"34","author":"Ran","year":"2008","journal-title":"Acta Autom. Sin."},{"key":"ref_40","first-page":"1160","article-title":"Multisensor centralized fusion tracking with correlated measurement noises","volume":"27","author":"Duan","year":"2005","journal-title":"Syst. Eng. Electron."},{"key":"ref_41","first-page":"690","article-title":"Multiple correlated measurements fusion algorithm and its optimality","volume":"34","author":"Ou","year":"2005","journal-title":"Inf. Control"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1109\/7.913685","article-title":"Comparison of two measurement fusion methods for Kalman filter based multisensor data fusion","volume":"37","author":"Gan","year":"2001","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Kitagawa, G. (1987, January 9\u201311). Non-Gaussian state space modeling of time series. Proceedings of the 26th Conference on decision and Control, Los Angeles, CA, USA.","DOI":"10.1109\/CDC.1987.272759"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/10\/3242\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:22:40Z","timestamp":1760196160000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/10\/3242"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9,26]]},"references-count":43,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2018,10]]}},"alternative-id":["s18103242"],"URL":"https:\/\/doi.org\/10.3390\/s18103242","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2018,9,26]]}}}