{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,25]],"date-time":"2025-12-25T07:24:13Z","timestamp":1766647453072,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2019,8,21]],"date-time":"2019-08-21T00:00:00Z","timestamp":1566345600000},"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":["61803077"],"award-info":[{"award-number":["61803077"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"publisher","award":["F2016501080"],"award-info":[{"award-number":["F2016501080"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["N172304024"],"award-info":[{"award-number":["N172304024"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>As one of the most essential technologies, wireless sensor networks (WSNs) integrate sensor technology, embedded computing technology, and modern network and communication technology, which have become research hotspots in recent years. The localization technique, one of the key techniques for WSN research, determines the application prospects of WSNs to a great extent. The positioning errors of wireless sensor networks are mainly caused by the non-line of sight (NLOS) propagation, occurring in complicated channel environments such as the indoor conditions. Traditional techniques such as the extended Kalman filter (EKF) perform unsatisfactorily in the case of NLOS. In contrast, the robust extended Kalman filter (REKF) acquires accurate position estimates by applying the robust techniques to the EKF in NLOS environments while losing efficiency in LOS. Therefore it is very hard to achieve high performance with a single filter in both LOS and NLOS environments. In this paper, a localization method using a robust extended Kalman filter and track-quality-based (REKF-TQ) fusion algorithm is proposed to mitigate the effect of NLOS errors. Firstly, the EKF and REKF are used in parallel to obtain the location estimates of mobile nodes. After that, we regard the position estimates as observation vectors, which can be implemented to calculate the residuals in the Kalman filter (KF) process. Then two KFs with a new observation vector and equation are used to further filter the estimates, respectively. At last, the acquired position estimates are combined by the fusion algorithm based on the track quality to get the final position vector of mobile node, which will serve as the state vector of both KFs at the next time step. Simulation results illustrate that the TQ-REKF algorithm yields better positioning accuracy than the EKF and REKF in the NLOS environment. Moreover, the proposed algorithm achieves higher accuracy than interacting multiple model algorithm (IMM) with EKF and REKF.<\/jats:p>","DOI":"10.3390\/s19173638","type":"journal-article","created":{"date-parts":[[2019,8,21]],"date-time":"2019-08-21T11:19:06Z","timestamp":1566386346000},"page":"3638","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["A Fusion Localization Method based on a Robust Extended Kalman Filter and Track-Quality for Wireless Sensor Networks"],"prefix":"10.3390","volume":"19","author":[{"given":"Yan","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Computer and Communication Engineering, Northeastern University, Qinhuangdao 066004, Hebei Province, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huihui","family":"Jie","sequence":"additional","affiliation":[{"name":"Department of Computer and Communication Engineering, Northeastern University, Qinhuangdao 066004, Hebei Province, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Long","family":"Cheng","sequence":"additional","affiliation":[{"name":"Department of Computer and Communication Engineering, Northeastern University, Qinhuangdao 066004, Hebei Province, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,21]]},"reference":[{"key":"ref_1","unstructured":"Wann, C.-D., Yeh, Y.-J., and Hsueh, C.-S. (2006, January 7\u201310). Hybrid TDOA\/AOA Indoor Positioning and Tracking Using Extended Kalman Filters. Proceedings of the 2006 IEEE 63rd Vehicular Technology Conference, Melbourne, Australia."},{"key":"ref_2","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_3","doi-asserted-by":"crossref","unstructured":"Ou, X.H., Wu, X.Q., He, X.X., Chen, Z.T., and Yu, Q.-A. (2015, January 15\u201317). An Improved Node Localization Based on Adaptive Iterated Unscented Kalman Filter for WSN. Proceedings of the 2015 10th IEEE Conference on Industrial Electronics and Applications, Auckland, New Zealand.","DOI":"10.1109\/ICIEA.2015.7334145"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1109\/78.978396","article-title":"Particle filters for positioning, navigation, and tracking","volume":"50","author":"Gustafsson","year":"2002","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_5","unstructured":"Delemontex, T., and Lucotte, A. (2013). Monte Carlo methods. SOS 2012\u2014IN2P3 School of Statistics, EDP Sciences."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1007\/s11222-011-9271-y","article-title":"An adaptive sequential Monte Carlo method for approximate Bayesian computation","volume":"22","author":"Doucet","year":"2012","journal-title":"Stat. Comput."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.dsp.2013.11.006","article-title":"Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking","volume":"25","author":"Mihaylova","year":"2014","journal-title":"Digit. Signal Prog."},{"key":"ref_8","unstructured":"Chen, P.-C. (1999, January 21\u201324). A non-line-of-sight error mitigation algorithm in location estimation. Proceedings of the WCNC. 1999 IEEE Wireless Communications and Networking Conference (Cat. No.99TH8466), New Orleans, LA, USA."},{"key":"ref_9","unstructured":"Chen, P.C. (1999, January 16\u201320). A cellular based mobile location tracking system. Proceedings of the 1999 IEEE 49th Vehicular Technology Conference (Cat. No.99CH36363), Houston, TX, USA."},{"key":"ref_10","unstructured":"Grosicki, E., and Abed-Meraim, K. (2005, January 23). A new trilateration method to mitigate the impact of some non-line-of-sight errors in TOA measurements for mobile localization. Proceedings of the 2005 IEEE International Conference on Acoustics, Speech, and Signal Processing, Philadelphia, PA, USA."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5872","DOI":"10.1109\/TSP.2010.2063425","article-title":"Robust Mobile Terminal Tracking in NLOS Environments Based on Data Association","volume":"58","author":"Hammes","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1016\/j.sigpro.2017.09.019","article-title":"A bisection-based approach for exact target localization in NLOS environments","volume":"143","author":"Tomic","year":"2018","journal-title":"Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1430","DOI":"10.1109\/LCOMM.2017.2787739","article-title":"Semidefinite Programming for NLOS Error Mitigation in TDOA Localization","volume":"22","author":"Su","year":"2018","journal-title":"IEEE Commun. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4311","DOI":"10.1109\/JSEN.2018.2818158","article-title":"NLOS Mitigation for UWB Localization Based on Sparse Pseudo-Input Gaussian Process","volume":"18","author":"Yang","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"31772","DOI":"10.1109\/ACCESS.2018.2838590","article-title":"An Indoor Localization Method Based on AOA and PDOA Using Virtual Stations in Multipath and NLOS Environments for Passive UHF RFID","volume":"6","author":"Ma","year":"2018","journal-title":"IEEE Access"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2775","DOI":"10.1109\/TSP.2009.2016891","article-title":"Efficient Convex Relaxation Methods for Robust Target Localization by a Sensor Network Using Time Differences of Arrivals","volume":"57","author":"Yang","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3281","DOI":"10.1109\/TSP.2016.2539139","article-title":"Robust Convex Approximation Methods for TDOA-Based Localization Under NLOS Conditions","volume":"64","author":"Wang","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Lee, K., Oh, J., and You, K. (2016). TDOA\/AOA Based Geolocation Using Newton Method under NLOS Environment, IEEE.","DOI":"10.1109\/ICIIBMS.2017.8279746"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3002","DOI":"10.1109\/TWC.2006.04747","article-title":"Robust mobile location estimator with NLOS mitigation using interacting multiple model algorithm","volume":"5","author":"Liao","year":"2006","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1109\/TITS.2011.2171033","article-title":"Interacting Multiple Model Filter-Based Sensor Fusion of GPS with In-Vehicle Sensors for Real-Time Vehicle Positioning","volume":"13","author":"Jo","year":"2012","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1157","DOI":"10.1109\/TVT.2008.928649","article-title":"Mobile Location Estimator in a Rough Wireless Environment Using Extended Kalman-Based IMM and Data Fusion","volume":"58","author":"Chen","year":"2009","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2909","DOI":"10.1109\/78.969500","article-title":"An improvement to the interacting multiple model (IMM) algorithm","volume":"49","author":"Johnston","year":"2001","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1307","DOI":"10.1088\/0957-0233\/17\/6\/003","article-title":"An interacting multiple model particle filter for manoeuvring target location","volume":"17","author":"Yang","year":"2006","journal-title":"Meas. Sci. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1049\/ip-rsn:20030741","article-title":"Interacting multiple model particle filter","volume":"150","author":"Boers","year":"2003","journal-title":"IEE Proc. Radar Sonar Navig."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1109\/MSP.2005.1458284","article-title":"Mobile positioning using wireless networks","volume":"22","author":"Gustafsson","year":"2005","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1109\/TSMCA.2009.2034836","article-title":"Robust Extended Kalman Filtering for Nonlinear Systems with Stochastic Uncertainties","volume":"40","author":"Kai","year":"2010","journal-title":"IEEE Trans. Syst. Man Cybern. Part A Syst. Hum."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2596","DOI":"10.1109\/78.782219","article-title":"Robust extended Kalman filtering","volume":"47","author":"Einicke","year":"1999","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1016\/j.cma.2014.06.001","article-title":"Robust and optimal multi-iterative techniques for IgA Galerkin linear systems","volume":"284","author":"Donatelli","year":"2015","journal-title":"Comput. Meth. Appl. Mech. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1002\/widm.2","article-title":"Robust statistics for outlier detection","volume":"1","author":"Rousseeuw","year":"2011","journal-title":"Wiley Interdiscip. Rev. Data Min. Knowl. Discov."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/s10291-012-0260-1","article-title":"Estimation and exclusion of multipath range error for robust positioning","volume":"17","author":"Iwase","year":"2013","journal-title":"GPS Solut."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1109\/JSTSP.2009.2028383","article-title":"Robust Tracking and Geolocation for Wireless Networks in NLOS Environments","volume":"3","author":"Hammes","year":"2009","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1431","DOI":"10.1007\/s11071-015-1953-0","article-title":"M-estimator-based robust Kalman filter for systems with process modeling errors and rank deficient measurement models","volume":"80","author":"Chang","year":"2015","journal-title":"Nonlinear Dyn."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Huber, P., and Ronchetti, E.M. (2009). Robust Statistics, Wiley. [2nd ed.].","DOI":"10.1002\/9780470434697"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1214\/aos\/1176343348","article-title":"Robust Estimation of a Location Parameter in the Presence of Asymmetry","volume":"4","author":"Collins","year":"1976","journal-title":"Ann. Stat."},{"key":"ref_35","first-page":"281","article-title":"Robust Statistics: The Approach Based on Influence Functions","volume":"150","author":"Jennison","year":"1987","journal-title":"Wiley Online Libr."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/17\/3638\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:12:44Z","timestamp":1760188364000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/17\/3638"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,21]]},"references-count":35,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2019,9]]}},"alternative-id":["s19173638"],"URL":"https:\/\/doi.org\/10.3390\/s19173638","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,8,21]]}}}