{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T11:53:05Z","timestamp":1777636385841,"version":"3.51.4"},"reference-count":37,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2018,12,17]],"date-time":"2018-12-17T00:00:00Z","timestamp":1545004800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/L015463\/1"],"award-info":[{"award-number":["EP\/L015463\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Global Positioning System (GPS) has been used in many aerial and terrestrial high precision positioning applications. Multipath affects positioning and navigation performance. This paper proposes a convolutional neural network based carrier-phase multipath detection method. The method is based on the fact that the features of multipath characteristics in multipath contaminated data can be learned and identified by a convolutional neural network. The proposed method is validated with simulated and real GPS data and compared with existing multipath mitigation methods in position domain. The results show the proposed method can detect about 80% multipath errors (i.e., recall) in both simulated and real data. The impact of the proposed method on positioning accuracy improvement is demonstrated with two datasets, 18\u201330% improvement is obtained by down-weighting the detected multipath measurements. The focus of this paper is on the development and test of the proposed convolutional neural network based multipath detection algorithm.<\/jats:p>","DOI":"10.3390\/rs10122052","type":"journal-article","created":{"date-parts":[[2018,12,18]],"date-time":"2018-12-18T02:15:59Z","timestamp":1545099359000},"page":"2052","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":84,"title":["Convolutional Neural Network Based Multipath Detection Method for Static and Kinematic GPS High Precision Positioning"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5291-2712","authenticated-orcid":false,"given":"Yiming","family":"Quan","sequence":"first","affiliation":[{"name":"International Doctoral Innovation Centre, The University of Nottingham Ningbo China, Ningbo 315100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8783-9666","authenticated-orcid":false,"given":"Lawrence","family":"Lau","sequence":"additional","affiliation":[{"name":"Artificial Intelligence and Optimisation Research Group\/Department of Civil Engineering, The University of Nottingham Ningbo China, Ningbo 315100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3703-981X","authenticated-orcid":false,"given":"Gethin Wyn","family":"Roberts","sequence":"additional","affiliation":[{"name":"Department of Science and Technology, The University of The Faroe Islands, 100 T\u00f3rshavn, Faroe Islands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2440-8054","authenticated-orcid":false,"given":"Xiaolin","family":"Meng","sequence":"additional","affiliation":[{"name":"Nottingham Geospatial Engineering\/Department of Civil Engineering, The University of Nottingham, Nottingham NG7 2TU, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9218-9028","authenticated-orcid":false,"given":"Chao","family":"Zhang","sequence":"additional","affiliation":[{"name":"International Doctoral Innovation Centre, The University of Nottingham Ningbo China, Ningbo 315100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1109\/TAES.2012.6129643","article-title":"Flight Tests of Error-Bounded Heading and Pitch Determination with Two GPS Receivers","volume":"48","author":"Lau","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2166","DOI":"10.1016\/j.eswa.2013.09.015","article-title":"A novel hybrid fusion algorithm to bridge the period of GPS outages using low-cost INS","volume":"41","author":"Bhatt","year":"2014","journal-title":"Expert Syst. Appl."},{"key":"ref_3","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. Geodesy"},{"key":"ref_4","first-page":"371","article-title":"GPS multipath mitigation: A nonlinear regression approach","volume":"17","author":"Phan","year":"2013","journal-title":"GPS Solut."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Phan, Q.H., Tan, S.L., McLoughlin, I., and Vu, D.L. (2013). A unified framework for GPS code and carrier-phase multipath mitigation using support vector regression. Adv. Artif. Neural Syst.","DOI":"10.1155\/2013\/240564"},{"key":"ref_6","unstructured":"Axelrad, P., Larson, K., and Jones, B. (2005, January 13\u201316). Use of the correct satellite repeat period to characterize and reduce site-specific multipath errors. Proceedings of the ION GNSS 2005, Long Beach, CA, USA."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Larson, K.M., Bilich, A., and Axelrad, P. (2007). Improving the precision of high-rate GPS. J. Geophys. Res., 112.","DOI":"10.1029\/2006JB004367"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Reuveni, Y., Kedar, S., Owen, S.E., Moore, A.W., and Webb, F.H. (2012). Improving sub-daily strain estimates using GPS measurements. Geophys. Res. Lett., 39.","DOI":"10.1029\/2012GL051927"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1179\/1752270611Y.0000000003","article-title":"Comparison of measurement and position domain multipath filtering techniques with the repeatable GPS orbits for static antennas","volume":"44","author":"Lau","year":"2012","journal-title":"Surv. Rev."},{"key":"ref_10","unstructured":"Zhang, Y., and Bartone, C. (2004, January 21\u201324). Real-time multipath mitigation with WaveSmooth\u2122 technique using wavelets. Proceedings of the ION GNSS 2004, Long Beach, CA, USA."},{"key":"ref_11","unstructured":"Elhabiby, M., El-Ghazouly, A., and El-Sheimy, N. (2008, January 16\u201319). A new waveletbased multipath mitigation technique. Proceedings of the ION GNSS 2008, Savannah, GA, USA."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1007\/s10291-016-0533-1","article-title":"Wavelet packets based denoising method for measurement domain repeat-time multipath filtering in GPS static high-precision positioning applications","volume":"21","author":"Lau","year":"2017","journal-title":"GPS Solut."},{"key":"ref_13","unstructured":"Lau, L., and Cross, P. (2006, January 26\u201329). A new signal-to-noise-ratio based stochastic model for GNSS high-precision carrier phase data processing algorithms in the presence of multipath errors. Proceedings of the ION GNSS 2006, Fort Worth, TX, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1109\/7.640284","article-title":"Adaptive SNR-based carrier phase multipath mitigation technique","volume":"34","author":"Comp","year":"1998","journal-title":"Aerosp. Electron. Syst. IEEE Trans."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/PL00012765","article-title":"Variances of GPS phase observations: The SIGMA-e model","volume":"2","author":"Hartinger","year":"1999","journal-title":"GPS Solut."},{"key":"ref_16","unstructured":"Fenton, P.C., and Jones, J. (2005, January 13\u201316). The theory and performance of NovAtel Inc.\u2019s vision correlator. Proceedings of the ION GNSS 2005, Long Beach, CA, USA."},{"key":"ref_17","first-page":"503","article-title":"Performance evaluation of the multipath estimating delay lock loop","volume":"42","author":"Townsend","year":"1995","journal-title":"Navig. J. Inst. Navig."},{"key":"ref_18","unstructured":"Lau, L., and Cross, P. (2006, January 8\u201310). Prospects for phase multipath mitigation using antenna arrays for very high precision real-time kinematic applications in the presence of new GNSS signals. Proceedings of the European Navigation Conference GNSS 2006, Manchester, UK."},{"key":"ref_19","unstructured":"Arbib, M.A. (1995). Convolutional Networks for Images, Speech, and Time-Series. The Handbook of Brain Theory and Neural Networks, MIT Press."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1533","DOI":"10.1109\/TASLP.2014.2339736","article-title":"Convolutional neural networks for speech recognition","volume":"22","author":"Mohamed","year":"2014","journal-title":"IEEE\/ACM Trans. Audio Speech Lang. Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1126\/science.1127647","article-title":"Reducing the dimensionality of data with neural networks","volume":"313","author":"Hinton","year":"2006","journal-title":"Science"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1527","DOI":"10.1162\/neco.2006.18.7.1527","article-title":"A fast learning algorithm for deep belief nets","volume":"18","author":"Hinton","year":"2006","journal-title":"Neural Comput."},{"key":"ref_23","unstructured":"Lemme, A., Reinhart, F., and Steil, J.J. (2010, January 28\u201330). Efficient online learning of a non-negative sparse autoencoder. Proceedings of the European Symposium on Artificial Neural Networks, Bruges, Belgium."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1038\/nature14539","article-title":"Deep learning","volume":"521","author":"LeCun","year":"2015","journal-title":"Nature"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1010933404324","article-title":"Random forests","volume":"45","author":"Breiman","year":"2001","journal-title":"Mach. Learn."},{"key":"ref_26","first-page":"3133","article-title":"Do we need hundreds of classifiers to solve real world classification problems?","volume":"15","author":"Cernadas","year":"2014","journal-title":"J. Mach. Learn. Res."},{"key":"ref_27","unstructured":"Gunduz, N., and Fokoue, E. (arXiv, 2015). Robust classification of high dimension low sample size data, arXiv."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Huang, D.S., Li, K., and Irwin, G.W. Robust real-time face detection using hybrid neural networks. Computational Intelligence and Bioinformatics, Proceedings of the International Conference on Intelligent Computing, ICIC 2006, Kunming, China, 16\u201319 August 2006, Springer.","DOI":"10.1007\/11816102"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1007\/PL00012778","article-title":"TEQC: The multi-purpose toolkit for GPS\/GLONASS data","volume":"3","author":"Estey","year":"1999","journal-title":"GPS Solut."},{"key":"ref_30","unstructured":"Schmidt, M. (2014, June 28). minFunc: Unconstrained Differentiable Multivariate Optimization in Matlab. Available online: http:\/\/www.cs.ubc.ca\/~schmidtm\/Software\/minFunc.html."},{"key":"ref_31","first-page":"18","article-title":"Classification and regression by randomForest","volume":"2","author":"Liaw","year":"2002","journal-title":"R News"},{"key":"ref_32","first-page":"1","article-title":"A comparative analysis of measurement noise and multipath for four constellations: GPS, BeiDou, GLONASS and Galileo","volume":"48","author":"Cai","year":"2015","journal-title":"Surv. Rev."},{"key":"ref_33","unstructured":"Boulton, P., Read, A., MacGougan, G., Klukas, R., Cannon, E., and Lachapelle, G. (2002, January 24\u201327). Proposed models and methodologies for Verification Testing of AGPS-equipped cellular mobile phones in the laboratory. Proceedings of the 15th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2002), Portland, OR, USA."},{"key":"ref_34","unstructured":"Spirent Communications (2012). SimGEM Software User Manual, Issue:4-02SR02, Spirent Communications."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/BF00863419","article-title":"The least-squares ambiguity decorrelation adjustment: A method for fast GPS integer ambiguity estimation","volume":"70","author":"Teunissen","year":"1995","journal-title":"J. Geod."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1017\/S0373463315000624","article-title":"Measurement signal quality assessment on all available and new signals of multi-GNSS (GPS, GLONASS, Galileo, BDS, and QZSS) with real data","volume":"69","author":"Quan","year":"2015","journal-title":"J. Navig."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1017\/S0373463307004341","article-title":"Phase Multipath Mitigation Techniques for High Precision Positioning in All Conditions and Environments","volume":"60","author":"Lau","year":"2007","journal-title":"J. Navig."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/12\/2052\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:34:33Z","timestamp":1760196873000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/12\/2052"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,17]]},"references-count":37,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2018,12]]}},"alternative-id":["rs10122052"],"URL":"https:\/\/doi.org\/10.3390\/rs10122052","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,17]]}}}