{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T00:41:25Z","timestamp":1781052085386,"version":"3.54.1"},"reference-count":45,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2018,2,11]],"date-time":"2018-02-11T00:00:00Z","timestamp":1518307200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41504004"],"award-info":[{"award-number":["41504004"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["91546106"],"award-info":[{"award-number":["91546106"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the State Key Laboratory of Earthquake Dynamics","award":["LED2016B03"],"award-info":[{"award-number":["LED2016B03"]}]},{"name":"the Shenzhen Future Industry Development Funding program","award":["201507211219247860"],"award-info":[{"award-number":["201507211219247860"]}]},{"name":"the Shenzhen Scientific Research and Development Funding Program","award":["JCYJ20170302144002028"],"award-info":[{"award-number":["JCYJ20170302144002028"]}]},{"name":"the Shenzhen Scientific Research and Development Funding Program","award":["JCYJ20150324141711606"],"award-info":[{"award-number":["JCYJ20150324141711606"]}]},{"name":"the Graduate Innovation and Development Funding program of Shenzhen University","award":["00003327"],"award-info":[{"award-number":["00003327"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, an improved method based on a mixture of Gaussian and quadrilateral functions is presented to process airborne bathymetric LiDAR waveforms. In the presented method, the LiDAR waveform is fitted to a combination of three functions: one Gaussian function for the water surface contribution, another Gaussian function for the water bottom contribution, and a new quadrilateral function to fit the water column contribution. The proposed method was tested on a simulated dataset and a real dataset, with the focus being mainly on the performance of retrieving bottom response and water depths. We also investigated the influence of the parameter settings on the accuracy of the bathymetry estimates. The results demonstrate that the improved quadrilateral fitting algorithm shows a superior performance in terms of low RMSE and a high detection rate in the water depth and magnitude retrieval. What\u2019s more, compared with the use of a triangular function or the existing quadrilateral function to fit the water column contribution, the presented method retrieved the least noise and the least number of unidentified waveforms, showed the best performance in fitting the return waveforms, and had consistent fitting goodness for all different water depths.<\/jats:p>","DOI":"10.3390\/s18020552","type":"journal-article","created":{"date-parts":[[2018,2,12]],"date-time":"2018-02-12T10:50:38Z","timestamp":1518432638000},"page":"552","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["An Improved Quadrilateral Fitting Algorithm for the Water Column Contribution in Airborne Bathymetric Lidar Waveforms"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4214-1923","authenticated-orcid":false,"given":"Kai","family":"Ding","sequence":"first","affiliation":[{"name":"Key Laboratory for Geo-Environment Monitoring of Coastal Zone of the National Administration of Surveying, Mapping and GeoInformation, Shenzhen University, Shenzhen 518060, China"},{"name":"Shenzhen Key Laboratory of Spatial Smart Sensing and Services, Shenzhen University, Shenzhen 518060, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qingquan","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory for Geo-Environment Monitoring of Coastal Zone of the National Administration of Surveying, Mapping and GeoInformation, Shenzhen University, Shenzhen 518060, China"},{"name":"Shenzhen Key Laboratory of Spatial Smart Sensing and Services, Shenzhen University, Shenzhen 518060, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiasong","family":"Zhu","sequence":"additional","affiliation":[{"name":"Key Laboratory for Geo-Environment Monitoring of Coastal Zone of the National Administration of Surveying, Mapping and GeoInformation, Shenzhen University, Shenzhen 518060, China"},{"name":"Shenzhen Key Laboratory of Spatial Smart Sensing and Services, Shenzhen University, Shenzhen 518060, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chisheng","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory for Geo-Environment Monitoring of Coastal Zone of the National Administration of Surveying, Mapping and GeoInformation, Shenzhen University, Shenzhen 518060, China"},{"name":"Shenzhen Key Laboratory of Spatial Smart Sensing and Services, Shenzhen University, Shenzhen 518060, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Minglei","family":"Guan","sequence":"additional","affiliation":[{"name":"Key Laboratory for Geo-Environment Monitoring of Coastal Zone of the National Administration of Surveying, Mapping and GeoInformation, Shenzhen University, Shenzhen 518060, China"},{"name":"Shenzhen Key Laboratory of Spatial Smart Sensing and Services, Shenzhen University, Shenzhen 518060, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhipeng","family":"Chen","sequence":"additional","affiliation":[{"name":"Key Laboratory for Geo-Environment Monitoring of Coastal Zone of the National Administration of Surveying, Mapping and GeoInformation, Shenzhen University, Shenzhen 518060, China"},{"name":"Shenzhen Key Laboratory of Spatial Smart Sensing and Services, Shenzhen University, Shenzhen 518060, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7724-0385","authenticated-orcid":false,"given":"Chao","family":"Yang","sequence":"additional","affiliation":[{"name":"Key Laboratory for Geo-Environment Monitoring of Coastal Zone of the National Administration of Surveying, Mapping and GeoInformation, Shenzhen University, Shenzhen 518060, China"},{"name":"Shenzhen Key Laboratory of Spatial Smart Sensing and Services, Shenzhen University, Shenzhen 518060, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yang","family":"Cui","sequence":"additional","affiliation":[{"name":"Key Laboratory for Geo-Environment Monitoring of Coastal Zone of the National Administration of Surveying, Mapping and GeoInformation, Shenzhen University, Shenzhen 518060, China"},{"name":"Shenzhen Key Laboratory of Spatial Smart Sensing and Services, Shenzhen University, Shenzhen 518060, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianghai","family":"Liao","sequence":"additional","affiliation":[{"name":"Key Laboratory for Geo-Environment Monitoring of Coastal Zone of the National Administration of Surveying, Mapping and GeoInformation, Shenzhen University, Shenzhen 518060, China"},{"name":"Shenzhen Key Laboratory of Spatial Smart Sensing and Services, Shenzhen University, Shenzhen 518060, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,2,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1080\/15210608009379375","article-title":"Multibeam bathymetric sonar: Sea beam and hydro chart","volume":"4","author":"Farr","year":"1980","journal-title":"Mar. Geodesy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1177\/0309133308096030","article-title":"Very-high-resolution mapping of river-immersed topography by remote sensing","volume":"32","author":"Feurer","year":"2008","journal-title":"Prog. Phys. Geogr."},{"key":"ref_3","first-page":"1271","article-title":"Remote sensing of clear-water, shallow, gravel-bed rivers using digital photogrammetry","volume":"67","author":"Westaway","year":"2001","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s11001-007-9023-8","article-title":"Strategies for waveform processing in sparker data","volume":"28","author":"Duchesne","year":"2007","journal-title":"Mar. Geophys. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2973","DOI":"10.1080\/01431160116928","article-title":"The bathymetry assessment system: Efficient depth mapping in shallow seas using radar images","volume":"22","author":"Calkoen","year":"2001","journal-title":"Int. J. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3831","DOI":"10.1364\/AO.38.003831","article-title":"Hyperspectral remote sensing for shallow waters. 2. Deriving bottom depths and water properties by optimization","volume":"38","author":"Lee","year":"1999","journal-title":"Appl. Opt."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2080","DOI":"10.1364\/AO.25.002080","article-title":"Airborne estimation of sea turbidity parameters from the WRELADS laser airborne depth sounder","volume":"25","author":"Billard","year":"1986","journal-title":"Appl. Opt."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Smart, J.H., and Kang, H.K.K. (1996). Comparisons between in-situ and remote sensing estimates of diffuse attenuation profiles. Proc. SPIE, 2964.","DOI":"10.1117\/12.258356"},{"key":"ref_9","unstructured":"Maune, D. (2007). Airborne lidar bathymetry. Digital Elevation Model Technologies and Applications: The Dem Users Manual, ASPRS."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Yang, B., Huang, R., Li, J., Tian, M., Dai, W., and Zhong, R. (2016). Automated reconstruction of building lods from airborne lidar point clouds using an improved morphological scale space. Remote Sensing, 9.","DOI":"10.3390\/rs9010014"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/S0034-4257(69)90088-1","article-title":"Application of an airborne pulsed laser for near shore bathymetric measurements","volume":"1","author":"Hickman","year":"1969","journal-title":"Remote Sens. Environ."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Banic, J., Sizgoric, S., and O\u2019Neil, R. (1986, January 3\u20135). Scanning lidar bathymeter for water depth measurement. Proceedings of the SPIE Laser Radar Technology and Applications, Quebec, Canada.","DOI":"10.1117\/12.938673"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"769511","DOI":"10.1117\/12.851978","article-title":"Predicted bathymetric lidar performance of coastal zone mapping and imaging lidar (CZMIL)","volume":"7695","author":"Feygels","year":"2010","journal-title":"Proc. SPIE"},{"key":"ref_14","first-page":"191","article-title":"Assessment of depth and turbidity with airborne Lidar bathymetry and multiband satellite imagery in shallow water bodies of the Alaskan North Slope","volume":"58","author":"Saylam","year":"2017","journal-title":"Int. J. Appl. Earth Obs. Geoinf."},{"key":"ref_15","first-page":"201","article-title":"From single-pulse to full-waveform airborne laser scanners: Potential and practical challenges","volume":"35","author":"Wagner","year":"2004","journal-title":"Int. Arch. Photogramm. Remote Sens."},{"key":"ref_16","unstructured":"Bretar, F., Chauve, A., Mallet, C., and Jutzi, B. (2008, January 3\u201311). Managing full waveform lidar data: A challenging task for the forthcoming years. Proceedings of the 21st International Society for Photogrammetry and Remote Sensing (ISPRS) Congress, Beijing, China."},{"key":"ref_17","first-page":"413","article-title":"Waveform analysis techniques in airborne laser scanning","volume":"36","author":"Wagner","year":"2007","journal-title":"Int. Arch. Photogramm. Remote Sens."},{"key":"ref_18","unstructured":"Chauve, A., Mallet, C., Bretar, F., Durrieu, S., Deseilligny, M.P., and Puech, W. (2007, January 12\u201314). Processing full-waveform lidar data: Modelling raw signals. Proceedings of the International Society for Photogrammetry and Remote Sensing (ISPRS) Workshop on Laser Scanning 2007 and SilviLaser 2007, Espoo, Finland."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1109\/JSTARS.2012.2209864","article-title":"Potential of space-borne lidar sensors for global bathymetry in coastal and inland waters","volume":"6","author":"Abdallah","year":"2013","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1109\/LGRS.2013.2279271","article-title":"Assessment of quadrilateral fitting of the water column contribution in lidar waveforms on bathymetry estimates","volume":"11","author":"Abady","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/j.isprsjprs.2017.03.006","article-title":"Decomposition of lidar waveforms by b-spline-based modeling","volume":"128","author":"Shen","year":"2017","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1111\/j.1467-9868.2004.02056.x","article-title":"Wavelet deconvolution in a periodic setting","volume":"66","author":"Johnstone","year":"2004","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.isprsjprs.2006.09.001","article-title":"Range determination with waveform recording laser systems using a wiener filter","volume":"61","author":"Jutzi","year":"2006","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2402","DOI":"10.1109\/TGRS.2010.2103080","article-title":"A comparison of signal deconvolution algorithms based on small-footprint lidar waveform simulation","volume":"49","author":"Wu","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"824","DOI":"10.14358\/PERS.77.8.825","article-title":"Empirical comparison of full-waveform lidar algorithms: Range extraction and discrimination performance","volume":"77","author":"Parrish","year":"2011","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.isprsjprs.2014.11.005","article-title":"A comparison of waveform processing algorithms for single-wavelength lidar bathymetry","volume":"101","author":"Wang","year":"2015","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"5133","DOI":"10.3390\/rs70505133","article-title":"Performance assessment of high resolution airborne full waveform lidar for shallow river bathymetry","volume":"7","author":"Pan","year":"2015","journal-title":"Remote Sens."},{"key":"ref_28","first-page":"207","article-title":"Airborne lidar feature selection for urban classification using random forests","volume":"39","author":"Chehata","year":"2009","journal-title":"Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1101","DOI":"10.1080\/01431169408954143","article-title":"An airborne sensor for primary productivity and related parameters of coastal waters and large water bodies","volume":"15","author":"Seshamani","year":"1994","journal-title":"Int. J. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Park, J.Y., Ramnath, V., and Tuell, G. (2014, January 7\u201310). Using lidar waveforms to detect environmental hazards through visualization of the water column. Proceedings of the OCEANS 2014, Taipei, Taiwan.","DOI":"10.1109\/OCEANS-TAIPEI.2014.6964506"},{"key":"ref_31","first-page":"31","article-title":"An approach to determining turbidity and correcting for signal attenuation in airborne lidar bathymetry","volume":"85","author":"Richter","year":"2017","journal-title":"J. Photogramm. Remote Sens. Geoinf. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Long, B., Cottin, A., and Collin, A. (2007, January 23\u201328). What Optech\u2019s bathymetric LIDAR sees underwater. Proceedings of the IEEE International Geoscience and Remote Sensing Symposium, Barcelona, Spain.","DOI":"10.1109\/IGARSS.2007.4423518"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1137\/0111030","article-title":"An algorithm for least square estimation of non-linear parameters","volume":"11","author":"Marquardt","year":"1963","journal-title":"J. Soc. Ind. Appl. Math."},{"key":"ref_34","unstructured":"Guenther, G.C. (1985). Airborne Laser Hydrography: System Design and Performance Factors, National Ocean Service 1."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"McLean, J.W. (1990, January 16\u201320). Modeling of ocean wave effects for lidar remote sensing. Proceedings of the Technical Symposium on Optics, Electro-Optics, and Sensors, Orlando, FL, USA.","DOI":"10.1117\/12.21467"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1117\/12.140676","article-title":"Lidars for oceanological research: Criteria for comparison, main limitations, perspectives","volume":"1750","author":"Feigels","year":"1992","journal-title":"Proc. SPIE"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"744","DOI":"10.1109\/LGRS.2011.2180506","article-title":"Wa-lid: A new lidar simulator for waters","volume":"9","author":"Abdallah","year":"2012","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1145\/357290.357293","article-title":"A reflectance model for computer graphics","volume":"1","author":"Cook","year":"1982","journal-title":"ACM Trans. Graphics (TOG)"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Guenther, G.C., and Mesick, H.C. (1988, January 4\u20138). Analysis of airborne laser hydrography waveforms. Proceedings of the Technical Symposium on Optics, Electro-Optics, and Sensors, Orlando, FL, USA.","DOI":"10.1117\/12.945729"},{"key":"ref_40","unstructured":"Feygels, V.I., Park, J.Y., Wozencraft, J., Aitken, J., Macon, C., Mathur, A., Payment, A., and Ramnath, V. (May, January 29). Czmil (coastal zone mapping and imaging lidar): From first flights to first mission through system validation. Proceedings of the SPIE Defense, Security, and Sensing, Baltimore, MD, USA."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1989","DOI":"10.1109\/36.851780","article-title":"Decomposition of laser altimeter waveforms","volume":"38","author":"Hofton","year":"2000","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/j.isprsjprs.2005.12.001","article-title":"Gaussian decomposition and calibration of a novel small-footprint full-waveform digitising airborne laser scanner","volume":"60","author":"Wagner","year":"2006","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"640","DOI":"10.1002\/esp.1959","article-title":"Comparison of lidar waveform processing methods for very shallow water bathymetry using Raman, near-infrared and green signals","volume":"35","author":"Allouis","year":"2010","journal-title":"Earth Surf. Process. Landf."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1285","DOI":"10.1109\/LGRS.2013.2292814","article-title":"Modeling the water bottom geometry effect on peak time shifting in lidar bathymetric waveforms","volume":"11","author":"Bouhdaoui","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"906","DOI":"10.1109\/TIP.2003.814255","article-title":"An EM algorithm for wavelet-based image restoration","volume":"12","author":"Figueiredo","year":"2003","journal-title":"IEEE Trans. Image Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/2\/552\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:54:41Z","timestamp":1760194481000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/2\/552"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,11]]},"references-count":45,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,2]]}},"alternative-id":["s18020552"],"URL":"https:\/\/doi.org\/10.3390\/s18020552","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,2,11]]}}}