{"id":"https://openalex.org/W3026047236","doi":"https://doi.org/10.1155/2020/6726139","title":"A Method for Solving LiDAR Waveform Decomposition Parameters Based on a Variable Projection Algorithm","display_name":"A Method for Solving LiDAR Waveform Decomposition Parameters Based on a Variable Projection Algorithm","publication_year":2020,"publication_date":"2020-05-20","ids":{"openalex":"https://openalex.org/W3026047236","doi":"https://doi.org/10.1155/2020/6726139","mag":"3026047236"},"language":"en","primary_location":{"id":"doi:10.1155/2020/6726139","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/6726139","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/6726139.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2020/6726139.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100360076","display_name":"Ke Wang","orcid":"https://orcid.org/0000-0001-5110-6591"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ke Wang","raw_affiliation_strings":["College of Geomatics, Shandong University of Science and Technology, Qingdao, Shandong 266590, China"],"affiliations":[{"raw_affiliation_string":"College of Geomatics, Shandong University of Science and Technology, Qingdao, Shandong 266590, China","institution_ids":["https://openalex.org/I80143920"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090095535","display_name":"Guolin Liu","orcid":"https://orcid.org/0000-0001-5044-1750"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Guolin Liu","raw_affiliation_strings":["College of Geomatics, Shandong University of Science and Technology, Qingdao, Shandong 266590, China"],"affiliations":[{"raw_affiliation_string":"College of Geomatics, Shandong University of Science and Technology, Qingdao, Shandong 266590, China","institution_ids":["https://openalex.org/I80143920"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100549049","display_name":"Qiuxiang Tao","orcid":null},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiuxiang Tao","raw_affiliation_strings":["College of Geomatics, Shandong University of Science and Technology, Qingdao, Shandong 266590, China"],"affiliations":[{"raw_affiliation_string":"College of Geomatics, Shandong University of Science and Technology, Qingdao, Shandong 266590, China","institution_ids":["https://openalex.org/I80143920"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100385116","display_name":"Luyao Wang","orcid":"https://orcid.org/0000-0003-2173-6933"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Luyao Wang","raw_affiliation_strings":["College of Geomatics, Shandong University of Science and Technology, Qingdao, Shandong 266590, China"],"affiliations":[{"raw_affiliation_string":"College of Geomatics, Shandong University of Science and Technology, Qingdao, Shandong 266590, China","institution_ids":["https://openalex.org/I80143920"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100350434","display_name":"Yang Chen","orcid":"https://orcid.org/0000-0002-5175-6997"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang Chen","raw_affiliation_strings":["College of Geomatics, Shandong University of Science and Technology, Qingdao, Shandong 266590, China"],"affiliations":[{"raw_affiliation_string":"College of Geomatics, Shandong University of Science and Technology, Qingdao, Shandong 266590, China","institution_ids":["https://openalex.org/I80143920"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5090095535","https://openalex.org/A5100360076"],"corresponding_institution_ids":["https://openalex.org/I80143920"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.2918,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.54613166,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":97},"biblio":{"volume":"2020","issue":null,"first_page":"1","last_page":"13"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11164","display_name":"Remote Sensing and LiDAR Applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11164","display_name":"Remote Sensing and LiDAR Applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10111","display_name":"Remote Sensing in Agriculture","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2303","display_name":"Ecology"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11211","display_name":"3D Surveying and Cultural Heritage","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1907","display_name":"Geology"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/non-linear-least-squares","display_name":"Non-linear least squares","score":0.6862322092056274},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6354495286941528},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.5844106078147888},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.579910933971405},{"id":"https://openalex.org/keywords/waveform","display_name":"Waveform","score":0.5687573552131653},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5417938232421875},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.508309543132782},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.47646570205688477},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.43900245428085327},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.4167526066303253},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40844565629959106},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3057301342487335},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12340173125267029},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.09378418326377869},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0768674910068512}],"concepts":[{"id":"https://openalex.org/C45923927","wikidata":"https://www.wikidata.org/wiki/Q3319230","display_name":"Non-linear least squares","level":3,"score":0.6862322092056274},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6354495286941528},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.5844106078147888},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.579910933971405},{"id":"https://openalex.org/C197424946","wikidata":"https://www.wikidata.org/wiki/Q1165717","display_name":"Waveform","level":3,"score":0.5687573552131653},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5417938232421875},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.508309543132782},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.47646570205688477},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.43900245428085327},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.4167526066303253},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40844565629959106},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3057301342487335},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12340173125267029},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.09378418326377869},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0768674910068512},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2020/6726139","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/6726139","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/6726139.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:6726139","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2020/6726139.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:29b7cf664a5146f68c75ce4c40f9e39e","is_oa":true,"landing_page_url":"https://doaj.org/article/29b7cf664a5146f68c75ce4c40f9e39e","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2020 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2020/6726139","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/6726139","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/6726139.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1121271761","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G16161867","display_name":null,"funder_award_id":"TSXZ201509","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2558877468","display_name":null,"funder_award_id":"SDKDYC190207","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3067753672","display_name":null,"funder_award_id":"41774002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3026047236.pdf","grobid_xml":"https://content.openalex.org/works/W3026047236.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1580205926","https://openalex.org/W1981263865","https://openalex.org/W2018089423","https://openalex.org/W2033908379","https://openalex.org/W2041857005","https://openalex.org/W2065288681","https://openalex.org/W2080108722","https://openalex.org/W2086480514","https://openalex.org/W2089902676","https://openalex.org/W2092604384","https://openalex.org/W2094605604","https://openalex.org/W2131256165","https://openalex.org/W2158757182","https://openalex.org/W2169457105","https://openalex.org/W2169951244","https://openalex.org/W2557573689","https://openalex.org/W2573178435","https://openalex.org/W2739833408","https://openalex.org/W2756336488","https://openalex.org/W2762021334","https://openalex.org/W2763015773","https://openalex.org/W2791255579","https://openalex.org/W2804206910","https://openalex.org/W2905923365","https://openalex.org/W2949735065","https://openalex.org/W2963284765","https://openalex.org/W2989884385","https://openalex.org/W3004690961","https://openalex.org/W4255128219"],"related_works":["https://openalex.org/W2026673180","https://openalex.org/W2063973645","https://openalex.org/W1959514624","https://openalex.org/W200101083","https://openalex.org/W2939592218","https://openalex.org/W2359835307","https://openalex.org/W327962130","https://openalex.org/W4380487384","https://openalex.org/W1997338499","https://openalex.org/W4378552425"],"abstract_inverted_index":{"Light":[0],"detection":[1],"and":[2,15,41,70,74,137,155,184,250],"ranging":[3],"(LiDAR)":[4],"is":[5],"commonly":[6],"used":[7,121,162],"to":[8,53,122,208,221,233],"create":[9],"high-resolution":[10],"maps;":[11],"however,":[12],"the":[13,28,43,48,54,67,78,82,91,94,98,102,117,128,138,142,164,169,172,175,189,196,204,209,223,227,237,240,247,254,269],"efficiency":[14,249],"convergence":[16,251],"of":[17,31,47,56,97,101,150,192,199,214,239,253],"parameter":[18,165,255,266],"estimation":[19,96,139,166,267],"are":[20,85],"difficult.":[21],"To":[22],"address":[23],"this":[24],"issue,":[25],"we":[26,65],"evaluated":[27],"structural":[29],"characteristics":[30],"received":[32],"LiDAR":[33,158,273],"signals":[34],"by":[35,90],"decomposing":[36],"them":[37],"into":[38,108],"Gaussian":[39,79,103,270],"functions":[40],"applied":[42],"variable":[44,62],"projection":[45,63],"algorithm":[46,119],"separable":[49,176,241],"nonlinear":[50,71,88,114,125,143,177,242],"least-squares":[51,110,178,243],"problem":[52,111,244],"process":[55],"waveform":[57,151,159,274],"fitting.":[58],"First,":[59],"using":[60],"a":[61,109,262],"algorithm,":[64],"separated":[66],"linear":[68,83,129],"(amplitude)":[69],"(center":[72],"position":[73],"width)":[75],"parameters":[76,84,89,100,130],"in":[77,134,268],"function":[80,104],"model;":[81],"expressed":[86],"with":[87],"function.":[92],"Thereafter,":[93],"optimal":[95,210,224],"characteristic":[99],"components":[105],"was":[106,120,201],"transformed":[107],"only":[112,217],"comprising":[113],"parameters.":[115],"Finally,":[116],"Levenberg\u2013Marquardt":[118],"solve":[123],"these":[124],"parameters,":[126],"whereas":[127],"were":[131,146,161],"calculated":[132],"simultaneously":[133],"each":[135],"iteration,":[136],"results":[140],"satisfying":[141],"least-square":[144],"criterion":[145],"obtained.":[147],"Five":[148],"groups":[149],"decomposition":[152],"simulation":[153],"data":[154,160],"ICESat/GLAS":[156],"satellite":[157],"for":[163,171,265,272],"experiments.":[167],"During":[168],"experiments,":[170],"same":[173],"accuracy,":[174],"optimization":[179],"method":[180,191,206,213,264],"required":[181,218],"fewer":[182],"iterations":[183,200,220],"lesser":[185],"calculation":[186,248],"time":[187,229],"than":[188],"traditional":[190,205],"not":[193],"separating":[194,215],"parameters;":[195],"maximum":[197],"number":[198],"reached":[202],"before":[203],"converged":[207],"estimate.":[211],"The":[212],"variables":[216],"14":[219],"obtain":[222],"estimate,":[225],"reducing":[226],"computational":[228],"from":[230],"1128":[231],"s":[232],"130":[234],"s.":[235],"Therefore,":[236],"application":[238],"can":[245,259],"improve":[246],"speed":[252],"solution":[256],"process.":[257],"It":[258],"also":[260],"provide":[261],"new":[263],"model":[271],"decomposition.":[275]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2021,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}