{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T01:02:13Z","timestamp":1780448533555,"version":"3.54.1"},"reference-count":41,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2021,6,26]],"date-time":"2021-06-26T00:00:00Z","timestamp":1624665600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Hebei Natural Science Foundation Ecological Smart Mine Joint Fund","award":["No. E2020402086"],"award-info":[{"award-number":["No. E2020402086"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>At present, GNSS (Global Navigation Satellite System) positioning technology is widely used for outdoor positioning services because of its high-precision positioning characteristics. However, in indoor environments, effective position information cannot be provided, because of the signals being obscured. In order to improve the accuracy and continuity of indoor positioning systems, in this paper, we propose a PDR\/UWB (Pedestrian Dead Reckoning and Ultra Wide Band) integrated navigation algorithm based on an adaptively robust EKF (Extended Kalman Filter) to address the problem of error accumulation in the PDR algorithm and gross errors in the location results of the UWB in non-line-of-sight scenarios. First, the basic principles of UWB and PDR location algorithms are given. Then, we propose a loose combination of the PDR and UWB algorithms by using the adaptively robust EKF. By using the robust factor to adjust the weight of the observation value to resist the influence of the gross error, and by adjusting the variance of the system adaptively according to the positioning scene, the algorithm can improve the robustness and heading factor of the PDR algorithm, which is constrained by indoor maps. Finally, the effectiveness of the algorithm is verified by the measured data. The experimental results showed that the algorithm can not only reduce the accumulation of PDR errors, but can also resist the influence of gross location errors under non-line-of-sight UWB scenarios.<\/jats:p>","DOI":"10.3390\/s21134390","type":"journal-article","created":{"date-parts":[[2021,6,27]],"date-time":"2021-06-27T23:57:22Z","timestamp":1624838242000},"page":"4390","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["Robustly Adaptive EKF PDR\/UWB Integrated Navigation Based on Additional Heading Constraint"],"prefix":"10.3390","volume":"21","author":[{"given":"Debao","family":"Yuan","sequence":"first","affiliation":[{"name":"School of Geoscience and Surveying Engineering, China University of Mining and Technology-Beijing (CUMTB), Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jian","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Geoscience and Surveying Engineering, China University of Mining and Technology-Beijing (CUMTB), Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jian","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Geomatics and Urban Spatial Informatics, Beijing University of Civil Engineering and Architecture (BUCEA), Beijing 102616, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2736-9102","authenticated-orcid":false,"given":"Ximin","family":"Cui","sequence":"additional","affiliation":[{"name":"School of Geoscience and Surveying Engineering, China University of Mining and Technology-Beijing (CUMTB), Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6249-8674","authenticated-orcid":false,"given":"Fei","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Geomatics and Urban Spatial Informatics, Beijing University of Civil Engineering and Architecture (BUCEA), Beijing 102616, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yalei","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Geomatics and Urban Spatial Informatics, Beijing University of Civil Engineering and Architecture (BUCEA), Beijing 102616, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Li, Z., Liu, C., Gao, J., and Li, X. (2016). An Improved WiFi\/PDR Integrated System Using an Adaptive and Robust Filter for Indoor Localization. ISPRS Int. J. Geo-Inf., 5.","DOI":"10.3390\/ijgi5120224"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1007\/s10015-005-0358-4","article-title":"Adaptive occupancy grid mapping with clusters","volume":"10","author":"Jang","year":"2006","journal-title":"Artif. Life Robot."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Guerra, A., Guidi, F., Dall\u2019Ara, J., and Dardari, D. (2018, January 10\u201313). Occupancy Grid Mapping for Personal Radar Applications. Proceedings of the IEEE Statistical Signal Processing Workshop (SSP), Freiburg im Breisgau, Germany.","DOI":"10.1109\/SSP.2018.8450813"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1109\/MSP.2004.1359140","article-title":"Ultra-wideband communications: An idea whose time has come","volume":"21","author":"Yang","year":"2004","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1109\/JPROC.2008.2008846","article-title":"Ranging with Ultrawide Bandwidth Signals in Multipath Environments","volume":"97","author":"Dardari","year":"2009","journal-title":"Proc. IEEE"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/s11277-007-9375-z","article-title":"A Survey on Wireless Position Estimation","volume":"44","author":"Gezici","year":"2008","journal-title":"Wirel. Pers. Commun."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Guvenc, I., Chong, C., and Watanabe, F. (2007, January 11\u201315). NLOS Identification and Mitigation for UWB Localization Systems. Proceedings of the 2007 IEEE Wireless Communications and Networking Conference, Hong Kong, China.","DOI":"10.1109\/WCNC.2007.296"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1689","DOI":"10.1109\/TWC.2014.2372341","article-title":"Non-Line-of-Sight Identification and Mitigation Using Received Signal Strength","volume":"14","author":"Xiao","year":"2015","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_9","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_10","doi-asserted-by":"crossref","first-page":"3007","DOI":"10.1007\/s11276-021-02631-0","article-title":"UWB anchor nodes self-calibration in NLOS conditions: A machine learning and adaptive PHY error correction approach","volume":"27","author":"Ridolfi","year":"2001","journal-title":"Wirel. Netw."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Liu, M., Lou, X., Jin, X., Jiang, R., Ye, K., and Wang, S. (2021). NLOS Identification for Localization Based on the Application of UWB. Wirel. Pers. Commun.","DOI":"10.1007\/s11277-021-08425-z"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1109\/LCOMM.2020.3039251","article-title":"LOS\/NLOS Identification for Indoor UWB Positioning Based on Morlet Wavelet Transform and Convolutional Neural Networks","volume":"25","author":"Cui","year":"2020","journal-title":"IEEE Commun. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"9","DOI":"10.25103\/jestr.071.02","article-title":"An autonomous waist-mounted pedestrian dead reckoning system by coupling low-cost MEMS inertial sensors and GPS receiver for 3D urban navigation","volume":"7","author":"Li","year":"2014","journal-title":"J. Eng. Sci. Technol. Rev."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1017\/S0373463305003486","article-title":"MEMS Based Pedestrian Navigation System","volume":"59","author":"Cho","year":"2006","journal-title":"J. Navig."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Klingbeil, L., and Wark, T. (2008, January 22\u201324). A Wireless Sensor Network for Real-Time Indoor Localisation and Motion Monitoring. Proceedings of the 2008 International Conference on Information Processing in Sensor Networks (ipsn 2008), St. Louis, MO, USA.","DOI":"10.1109\/IPSN.2008.15"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3351","DOI":"10.1109\/JSEN.2018.2789431","article-title":"Multi-phase fingerprint map based on interpolation for indoor localization using iBeacons","volume":"18","author":"Zuo","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3733","DOI":"10.1109\/JSEN.2019.2894714","article-title":"A low-cost INS and UWB fusion pedestrian tracking system","volume":"19","author":"Tian","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"9691","DOI":"10.1109\/JSEN.2018.2873052","article-title":"A fusion algorithm of indoor positioning based on PDR and RSS fingerprint","volume":"18","author":"Shi","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Chen, P., Kuang, Y., and Chen, X. (2017). A UWB\/Improved PDR Integration Algorithm Applied to Dynamic Indoor Positioning for Pedestrians. Sensors, 17.","DOI":"10.3390\/s17092065"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"7096","DOI":"10.3390\/s150407096","article-title":"A floor-map-aided WiFi\/pseudo-odometry integration algorithm for an indoor positioning system","volume":"15","author":"Wang","year":"2015","journal-title":"Sensors"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"747","DOI":"10.3390\/mi6060747","article-title":"WiFi-aided magnetic matching for indoor navigation with consumer portable devices","volume":"6","author":"Li","year":"2015","journal-title":"Micromachines"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1016\/j.robot.2008.10.022","article-title":"Mobile robot localization based on Ultra-Wide-Band ranging: A particle filter approach","volume":"57","author":"Blanco","year":"2009","journal-title":"Robot. Auton. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/s001900000157","article-title":"Adaptively robust filtering for kinematic geodetic positioning","volume":"75","author":"Yang","year":"2001","journal-title":"J. Geod."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1007\/s00190-002-0256-7","article-title":"Robust estimator for correlated observations based on bifactor equivalent weights","volume":"76","author":"Yang","year":"2002","journal-title":"J. Geod."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1179\/003962608X325330","article-title":"Adaptively robust filter with multi adaptive factors","volume":"40","author":"Yang","year":"2008","journal-title":"Surv. Rev."},{"key":"ref_26","first-page":"22","article-title":"Integrated Navigation by Using Variance Component Estimates of Multi-sensor Measurements and Adaptive Weights of Dynamic Model Information","volume":"33","author":"Yang","year":"2004","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_27","first-page":"293","article-title":"Adaptive Robust Filtering for Kinematic CPS Positioning","volume":"30","author":"Yang","year":"2001","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1016\/j.measurement.2008.10.002","article-title":"A consistent and robust Kalman filter design for in-motion alignment of inertial navigation system","volume":"42","author":"Ali","year":"2009","journal-title":"Measurement"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2816","DOI":"10.1109\/TIM.2016.2608425","article-title":"Analysis of Non-Ideal Effects and Performance in Magnetic Positioning Systems","volume":"65","author":"Pasku","year":"2016","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.1017\/S0373463315001083","article-title":"An enhanced GPS\/INS integrated navigation system with GPS observation expansion","volume":"69","author":"Li","year":"2016","journal-title":"J. Navig."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1016\/j.ast.2010.08.007","article-title":"Robust adaptive filtering method for SINS\/SAR integrated navigation system","volume":"15","author":"Gao","year":"2011","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1007\/s10291-012-0254-z","article-title":"Real-time estimation of satellite clock offset using adaptively robust Kalman filter with classified adaptive factors","volume":"16","author":"Huang","year":"2012","journal-title":"GPS Solut."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1088\/0957-0233\/25\/10\/105011","article-title":"Adaptive robust Kalman filtering for precise point positioning","volume":"25","author":"Guo","year":"2014","journal-title":"Meas. Sci. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.ejcon.2013.12.002","article-title":"Robust Kalman filtering for small satellite attitude estimation in the presence of measurement faults","volume":"20","author":"Soken","year":"2014","journal-title":"Eur. J. Control."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"960","DOI":"10.1109\/JSEN.2009.2037013","article-title":"Predicting Millimeter Wave Radar Spectra for Autonomous Navigation","volume":"10","author":"Jose","year":"2010","journal-title":"IEEE Sens. J."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Jose, E., and Adams, M.D. (2005, January 2\u20136). An augmented state SLAM formulation for multiple line-of-sight features with millimetre wave RADAR. Proceedings of the 2005 IEEE\/RSJ International Conference on Intelligent Robots and Systems, Edmonton, AB, Canada.","DOI":"10.1109\/IROS.2005.1545232"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"084002","DOI":"10.1088\/1361-6501\/ab87ea","article-title":"WiFi\/PDR integrated navigation with robustly constrained Kalman filter","volume":"31","author":"Li","year":"2020","journal-title":"Meas. Sci. Technol."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Liu, F., Wang, J., Zhang, J., and Han, H. (2019). An Indoor Localization Method for Pedestrians Base on Combined UWB\/PDR\/Floor Map. Sensors, 19.","DOI":"10.3390\/s19112578"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"8046","DOI":"10.1109\/JSEN.2020.2981635","article-title":"An Improved PDR\/UWB Integrated System for Indoor Navigation Applications","volume":"20","author":"Guo","year":"2020","journal-title":"IEEE Sens. J."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Tong, H., Xin, N., Su, X., Chen, T., and Wu, J. (2020). A Robust PDR\/UWB Integrated Indoor Localization Approach for Pedestrians in Harsh Environments. Sensors, 20.","DOI":"10.3390\/s20010193"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.jprocont.2013.12.017","article-title":"Kalman filter with both adaptivity and robustness","volume":"24","author":"Chang","year":"2014","journal-title":"J. Process Control"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/13\/4390\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:24:56Z","timestamp":1760163896000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/13\/4390"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,26]]},"references-count":41,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["s21134390"],"URL":"https:\/\/doi.org\/10.3390\/s21134390","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,26]]}}}