{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T13:38:53Z","timestamp":1780407533685,"version":"3.54.1"},"reference-count":40,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,6,9]],"date-time":"2021-06-09T00:00:00Z","timestamp":1623196800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Postgraduate Research\uff06Practice Innovation Program of Jiangsu Province","award":["KYCX20_0131"],"award-info":[{"award-number":["KYCX20_0131"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["3221002106D"],"award-info":[{"award-number":["3221002106D"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["6522000058"],"award-info":[{"award-number":["6522000058"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>A multipath is a major error source in bridge deformation monitoring and the key to achieving millimeter-level monitoring. Although the traditional MHM (multipath hemispherical map) algorithm can be applied to multipath mitigation in real-time scenarios, accuracy needs to be further improved due to the influence of observation noise and the multipath differences between different satellites. Aiming at the insufficiency of MHM in dealing with the adverse impact of observation noise, we proposed the MHM_V model, based on Variational Mode Decomposition (VMD) and the MHM algorithm. Utilizing the VMD algorithm to extract the multipath from single-difference (SD) residuals, and according to the principle of the closest elevation and azimuth, the original observation of carrier phase in the few days following the implementation are corrected to mitigate the influence of the multipath. The MHM_V model proposed in this paper is verified and compared with the traditional MHM algorithm by using the observed data of the Forth Road Bridge with a seven day and 10 s sampling rate. The results show that the correlation coefficient of the multipath on two adjacent days was increased by about 10% after residual denoising with the VMD algorithm; the standard deviations of residual error in the L1\/L2 frequencies were improved by 37.8% and 40.7%, respectively, which were better than the scores of 26.1% and 31.0% for the MHM algorithm. Taking a ratio equal to three as the threshold value, the fixed success rates of ambiguity were 88.0% without multipath mitigation and 99.4% after mitigating the multipath with MHM_V. The MHM_V algorithm can effectively improve the success rate, reliability, and convergence rate of ambiguity resolution in a bridge multipath environment and perform better than the MHM algorithm.<\/jats:p>","DOI":"10.3390\/rs13122259","type":"journal-article","created":{"date-parts":[[2021,6,9]],"date-time":"2021-06-09T14:16:04Z","timestamp":1623248164000},"page":"2259","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["An Improved Multipath Mitigation Method and Its Application in Real-Time Bridge Deformation Monitoring"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5566-1450","authenticated-orcid":false,"given":"Ruicheng","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Transportation, Southeast University, Nanjing 211189, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chengfa","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Transportation, Southeast University, Nanjing 211189, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4145-3941","authenticated-orcid":false,"given":"Qing","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Transportation, Southeast University, Nanjing 211189, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zihan","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Transportation, Southeast University, Nanjing 211189, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rui","family":"Shang","sequence":"additional","affiliation":[{"name":"School of Transportation, Southeast University, Nanjing 211189, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,9]]},"reference":[{"key":"ref_1","unstructured":"Xu, G. (2003). GPS Theory, Algorithms and Applications, Springer."},{"key":"ref_2","first-page":"505","article-title":"Multipath effects","volume":"11","author":"Braasch","year":"1996","journal-title":"Parkinson"},{"key":"ref_3","unstructured":"Hofmann-Wellenhof, B., Lichtenegger, H., and Wasle, E. (2007). GNSS\u2013Global Navigation Satellite Systems: GPS, GLONASS, Galileo, and More, Springer Science & Business Media."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1061\/(ASCE)0733-9453(1999)125:4(185)","article-title":"Improvement of GPS Relative Positioning Accuracy by Using SNR","volume":"125","author":"Lau","year":"1999","journal-title":"J. Surv. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1029\/2007RS003652","article-title":"Mapping the GPS multipath environment using the signal-to-noise ratio (SNR)","volume":"42","author":"Bilich","year":"2007","journal-title":"Radio Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1515\/JAG.2009.009","article-title":"Carrier phase multipath mitigation based on GNSS signal quality measurements","volume":"3","author":"Rost","year":"2009","journal-title":"J. Appl. Geodesy"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1179\/sre.2005.38.295.2","article-title":"Multipath mitigation by wavelet analysis for GPS basestation applications","volume":"38","author":"Satirapod","year":"2005","journal-title":"Surv. Rev."},{"key":"ref_8","unstructured":"Bernelli-Zazzera, F., Campana, R., Gottifredi, F., and Marradi, L. (1998). GPS Attitude Determination by Kalman Filtering: Simulation of Multipath Rejection, AAS 98-199."},{"key":"ref_9","first-page":"161","article-title":"Study of GPS multipath effects with method of CVVF","volume":"34","author":"Zhong","year":"2005","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/s00190-005-0474-x","article-title":"Filtering GPS time-series using a Vondrak filter and cross-validation","volume":"79","author":"Zheng","year":"2005","journal-title":"J. Geod."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3261","DOI":"10.1029\/91JB02997","article-title":"Rapid resolution of crustal motion at short ranges with the global positioning system","volume":"97","author":"Genrich","year":"1992","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/s10291-006-0038-4","article-title":"Finding the repeat times of the GPS constellation","volume":"11","author":"Agnew","year":"2006","journal-title":"GPS Solut."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/s10291-015-0473-1","article-title":"Effectiveness of observation-domain sidereal filtering for GPS precise point positioning","volume":"20","author":"Atkins","year":"2015","journal-title":"GPS Solut."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Choi, K., Bilich, A., Larson, K.M., and Axelrad, P. (2004). Modified sidereal filtering: Implications for high-rate GPS positioning. Geophys. Res. Lett., 31.","DOI":"10.1029\/2004GL021621"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/s00190-015-0870-9","article-title":"Mitigation of multipath efect in GNSS short baseline positioning by the multipath hemispherical map","volume":"90","author":"Dong","year":"2016","journal-title":"J. Geod."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/s00190-006-0113-1","article-title":"GPS sidereal filtering: Coordinate- and carrier-phase-level strategies","volume":"81","author":"Ragheb","year":"2007","journal-title":"J. Geod."},{"key":"ref_17","unstructured":"Cohen, C., and Parkinson, B. (1991, January 4\u20138). Mitigating multipath error in GPS-based attitude determination. Proceedings of the Advances in the Astronautical Sciences, AAS Guidance and Control Conference, San Diego, CA, USA."},{"key":"ref_18","unstructured":"W\u00fcbbena, G., Schmitz, M., and Matzke, N. (2010, January 11\u201314). On GNSS in situ-station calibration of near feld multipath. Proceedings of the International Symposium on GNSS Space Based and Ground Based Augmentation Systems and Applications, Brussels, Belgium."},{"key":"ref_19","unstructured":"Lidberg, M., Eksr\u00f6m, C., and Johansson, J.M. (2009). Site-Dependent Efects in High-Accuracy Applications of GNSS, Mitteilungen des Bundesamtes f\u00fcr Kartographie und Geod\u00e4sie. EUREF Publication No. 17, Band 42."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1127\/0941-2948\/2008\/0341","article-title":"Validation of GPS slant delays using water vapour radiometers and weather models","volume":"17","author":"Bender","year":"2008","journal-title":"Meteorol. Z."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1007\/s00190-014-0729-5","article-title":"Empirical modelling of site-specific errors in continuous GPS data","volume":"88","author":"Moore","year":"2014","journal-title":"J. Geod."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/s10291-014-0367-7","article-title":"Generating statistically robust multipath stacking maps using congruent cells","volume":"19","author":"Fuhrmann","year":"2014","journal-title":"GPS Solut."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2037","DOI":"10.1007\/s00190-019-01300-7","article-title":"Multipath extraction and mitigation for high-rate multi-GNSS precise point positioning","volume":"93","author":"Zheng","year":"2019","journal-title":"J. Geod."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Chang, G., Chen, C., Yang, Y., and Xu, T. (2018). Tikhonov Regularization Based Modeling and Sidereal Filtering Mitigation of GNSS Multipath Errors. Remote. Sens., 10.","DOI":"10.3390\/rs10111801"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2882","DOI":"10.1016\/j.asr.2017.01.007","article-title":"Multipath extraction and mitigation for bridge deformation monitoring using a single-difference model","volume":"60","author":"Wang","year":"2017","journal-title":"Adv. Space Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1007\/s00190-007-0139-z","article-title":"Development and testing of a new ray-tracing approach to GNSS carrier-phase multipath modelling","volume":"81","author":"Lau","year":"2007","journal-title":"J. Geod."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1588","DOI":"10.1049\/iet-rsn.2018.5587","article-title":"GNSS multipath estimation and mitigation based on particle filter","volume":"13","author":"Qin","year":"2019","journal-title":"IET Radar Sonar Navig."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1007\/s10291-016-0538-9","article-title":"Multipath interference mitigation in GNSS via WRELAX","volume":"21","author":"Jia","year":"2016","journal-title":"GPS Solut."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1007\/s10291-018-0708-z","article-title":"A new multipath mitigation method based on adaptive thresholding wavelet denoising and double reference shift strategy","volume":"22","author":"Su","year":"2018","journal-title":"GPS Solut."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1098\/rspa.1998.0193","article-title":"The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis","volume":"454","author":"Huang","year":"1998","journal-title":"Proc. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Baykut, S., Akg\u00fcl, T., and Ergintav, S. (2009, January 9\u201311). EMD-based analysis and denoising of GPS data. Proceedings of the 2009 IEEE 17th Signal Processing and Communications Applications Conference, Antalya, Turkey.","DOI":"10.1109\/SIU.2009.5136478"},{"key":"ref_32","unstructured":"Dodson, A.H., Meng, X., and Roberts, G.W. (2001, January 5\u20138). Adaptive method for multipath mitigation and its application for structural deflection monitoring. Proceedings of the Int Symp Kinemat Syst Geod, Geomat Navig (KIS 2001), Banff, AB, Canada."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1293","DOI":"10.1016\/j.proeps.2009.09.200","article-title":"Gps\/pseudolites technology based on emd-wavelet in the complex field conditions of mine","volume":"1","author":"Yan","year":"2009","journal-title":"Procedia Earth Planet. Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1109\/TSP.2013.2288675","article-title":"Variational Mode Decomposition","volume":"62","author":"Dragomiretskiy","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_35","first-page":"81","article-title":"Vibration based fault diagnosis of a hydraulic brake system using variational mode decomposition (vmd)","volume":"10","author":"Jegadeeshwaran","year":"2014","journal-title":"Sdhm Struct. Durab. Health Monit."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1177\/0142331215592064","article-title":"Denoising of hydropower unit vibration signal based on variational mode decomposition and approximate entropy","volume":"38","author":"An","year":"2016","journal-title":"Trans. Inst. Meas. Control."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.ymssp.2017.11.029","article-title":"A parameter-adaptive VMD method based on grasshopper optimization algorithm to analyze vibration signals from rotating machinery","volume":"108","author":"Zhang","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1109\/LGRS.2016.2644723","article-title":"Mitigation of Ionospheric Scintillation Effects on GNSS Signals Using Variational Mode Decomposition","volume":"14","author":"Sivavaraprasad","year":"2017","journal-title":"IEEE Geosci. Remote. Sens. Lett."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Zhang, R., Gao, C., Pan, S., and Shang, R. (2020). Fusion of GNSS and Speedometer Based on VMD and Its Application in Bridge Deformation Monitoring. Sensors, 20.","DOI":"10.3390\/s20030694"},{"key":"ref_40","first-page":"172","article-title":"On carrier signal multipath efects in relative GPS positioning","volume":"13","author":"Georgiadou","year":"1988","journal-title":"Manuscr Geod."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/12\/2259\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:12:32Z","timestamp":1760163152000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/12\/2259"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,9]]},"references-count":40,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["rs13122259"],"URL":"https:\/\/doi.org\/10.3390\/rs13122259","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,9]]}}}