{"id":"https://openalex.org/W2908268118","doi":"https://doi.org/10.1109/tgrs.2018.2853046","title":"Geometric Modeling of the Z-Surface and Z-Curve of GNSS Signals and Their Solution Techniques","display_name":"Geometric Modeling of the Z-Surface and Z-Curve of GNSS Signals and Their Solution Techniques","publication_year":2018,"publication_date":"2018-08-02","ids":{"openalex":"https://openalex.org/W2908268118","doi":"https://doi.org/10.1109/tgrs.2018.2853046","mag":"2908268118"},"language":"en","primary_location":{"id":"doi:10.1109/tgrs.2018.2853046","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tgrs.2018.2853046","pdf_url":null,"source":{"id":"https://openalex.org/S111326731","display_name":"IEEE Transactions on Geoscience and Remote Sensing","issn_l":"0196-2892","issn":["0196-2892","1558-0644"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Geoscience and Remote Sensing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074925174","display_name":"Guoyu Fu","orcid":"https://orcid.org/0000-0002-9186-8993"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Guoyu Fu","raw_affiliation_strings":["Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA"],"raw_orcid":"https://orcid.org/0000-0002-9186-8993","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057327763","display_name":"Colton Riedel","orcid":"https://orcid.org/0000-0001-9862-4740"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Colton Riedel","raw_affiliation_strings":["Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014915283","display_name":"Tyler Holmes","orcid":null},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tyler Holmes","raw_affiliation_strings":["Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024732465","display_name":"Jyh\u2010Charn Liu","orcid":"https://orcid.org/0000-0003-1330-5092"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jyh-Charn Liu","raw_affiliation_strings":["Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA"],"raw_orcid":"https://orcid.org/0000-0003-1330-5092","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I91045830"],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":0.2999,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.59296951,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"57","issue":"1","first_page":"212","last_page":"223"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10326","display_name":"Indoor and Outdoor Localization Technologies","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10326","display_name":"Indoor and Outdoor Localization Technologies","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11325","display_name":"Inertial Sensor and Navigation","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10655","display_name":"GNSS positioning and interference","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/gnss-applications","display_name":"GNSS applications","score":0.7531147003173828},{"id":"https://openalex.org/keywords/geodesy","display_name":"Geodesy","score":0.5349453687667847},{"id":"https://openalex.org/keywords/remote-sensing","display_name":"Remote sensing","score":0.5164594650268555},{"id":"https://openalex.org/keywords/geometric-modeling","display_name":"Geometric modeling","score":0.5129086971282959},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.46357491612434387},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3893592357635498},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.35097408294677734},{"id":"https://openalex.org/keywords/global-positioning-system","display_name":"Global Positioning System","score":0.31527361273765564},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.25633883476257324},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2373315989971161},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.12239396572113037}],"concepts":[{"id":"https://openalex.org/C14279187","wikidata":"https://www.wikidata.org/wiki/Q5514012","display_name":"GNSS applications","level":3,"score":0.7531147003173828},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.5349453687667847},{"id":"https://openalex.org/C62649853","wikidata":"https://www.wikidata.org/wiki/Q199687","display_name":"Remote sensing","level":1,"score":0.5164594650268555},{"id":"https://openalex.org/C104065381","wikidata":"https://www.wikidata.org/wiki/Q1002535","display_name":"Geometric modeling","level":2,"score":0.5129086971282959},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.46357491612434387},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3893592357635498},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.35097408294677734},{"id":"https://openalex.org/C60229501","wikidata":"https://www.wikidata.org/wiki/Q18822","display_name":"Global Positioning System","level":2,"score":0.31527361273765564},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25633883476257324},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2373315989971161},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.12239396572113037}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tgrs.2018.2853046","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tgrs.2018.2853046","pdf_url":null,"source":{"id":"https://openalex.org/S111326731","display_name":"IEEE Transactions on Geoscience and Remote Sensing","issn_l":"0196-2892","issn":["0196-2892","1558-0644"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Geoscience and Remote Sensing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306175","display_name":"Lynde and Harry Bradley Foundation","ror":"https://ror.org/05ycax488"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W29275650","https://openalex.org/W816605525","https://openalex.org/W1553285187","https://openalex.org/W1680364674","https://openalex.org/W1979154650","https://openalex.org/W1995339988","https://openalex.org/W1996242206","https://openalex.org/W2001902860","https://openalex.org/W2008354767","https://openalex.org/W2025626286","https://openalex.org/W2026082049","https://openalex.org/W2038166203","https://openalex.org/W2058160370","https://openalex.org/W2062605698","https://openalex.org/W2063085808","https://openalex.org/W2064186449","https://openalex.org/W2080830113","https://openalex.org/W2087313454","https://openalex.org/W2095869928","https://openalex.org/W2096117387","https://openalex.org/W2117062628","https://openalex.org/W2132639726","https://openalex.org/W2133161369","https://openalex.org/W2140266441","https://openalex.org/W2149123816","https://openalex.org/W2151168534","https://openalex.org/W2151975955","https://openalex.org/W2166339508","https://openalex.org/W2168298782","https://openalex.org/W2225765004","https://openalex.org/W2406282705","https://openalex.org/W2473094635","https://openalex.org/W2566510693","https://openalex.org/W2727006465","https://openalex.org/W3046229330","https://openalex.org/W3144248865","https://openalex.org/W4206360718","https://openalex.org/W4243100138","https://openalex.org/W4249989757","https://openalex.org/W6623115271","https://openalex.org/W6720450528","https://openalex.org/W6731781941","https://openalex.org/W6740393530"],"related_works":["https://openalex.org/W4386936491","https://openalex.org/W3110195467","https://openalex.org/W3033823235","https://openalex.org/W2881093137","https://openalex.org/W4386787199","https://openalex.org/W4384916587","https://openalex.org/W2765672153","https://openalex.org/W2022870883","https://openalex.org/W2153741582","https://openalex.org/W2356895184"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,20,59,155,182,191,215],"novel":[4],"geometric":[5],"model":[6,92,162],"to":[7,43,171,226],"characterize":[8],"the":[9,33,47,50,55,68,72,84,90,118,122,126,131,159,165,172,184,198,210],"zero-crossing":[10],"surface":[11,34,137],"(z-surface)":[12],"and":[13,46,104,108,112,130,177,193,207,234],"its":[14],"z-curve":[15,48,119,150],"for":[16,96,110,205],"signals":[17,141],"emitted":[18],"by":[19,83],"pair":[21,85],"of":[22,35,52,61,64,67,74,86,98,117,125,138,158,167,209,217,231],"Global":[23],"Navigation":[24],"Satellite":[25],"System":[26],"satellites":[27],"(A,":[28,44,139,202],"B).":[29,203],"The":[30,115,149,161],"z-surface":[31,53],"is":[32,49],"points":[36],"which":[37],"have":[38],"zero":[39],"difference":[40,63,200],"in":[41,174,229],"pseudorange":[42,199],"B),":[45],"intersection":[51],"with":[54,121,169],"earth's":[56,132],"surface.":[57,133],"As":[58,181],"form":[60],"time":[62],"arrival,":[65],"modeling":[66,124,206],"z-surface/z-curve":[69],"benefits":[70],"from":[71],"elimination":[73],"common":[75],"error":[76],"terms":[77,230],"(e.g.,":[78],"receiver":[79],"clock":[80],"offset)":[81],"shared":[82],"pseudoranges,":[87],"so":[88],"that":[89],"resulting":[91],"can":[93,142,151,163,186],"be":[94,143,152,187],"used":[95],"design":[97],"advanced":[99],"applications,":[100],"such":[101],"as":[102,154],"timing":[103],"positioning":[105],"integrity":[106],"monitors":[107],"tools":[109],"geodetic":[111],"atmospheric":[113],"measurements.":[114],"derivation":[116],"starts":[120],"shape":[123,147],"terrestrial":[127],"service":[128],"volume":[129],"Then,":[134],"an":[135,223],"equi-pseudorange":[136],"B)'s":[140],"placed":[144],"within":[145],"these":[146],"models.":[148],"derived":[153],"boundary":[156],"condition":[157],"z-surface.":[160],"represent":[164],"morphing":[166],"z-curves":[168],"respect":[170],"changes":[173],"satellite":[175],"positions":[176],"signal":[178],"propagation":[179],"delays.":[180],"result,":[183],"z-models":[185],"readily":[188],"generalized":[189],"into":[190],"k-surface":[192],"k-curve,":[194],"where":[195],"k":[196],"represents":[197],"between":[201],"Solutions":[204],"analysis":[208],"z(k)-surface/curve":[211],"are":[212],"based":[213],"on":[214],"system":[216],"quadratic":[218],"Cartesian":[219],"equations.":[220],"We":[221],"propose":[222],"algebraic":[224],"method":[225],"parameterize":[227],"them":[228],"geocentric":[232],"latitude":[233],"longitude.":[235]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}