{"id":"https://openalex.org/W2793902216","doi":"https://doi.org/10.3390/rs10030377","title":"Optimal, Recursive and Sub-Optimal Linear Solutions to Attitude Determination from Vector Observations for GNSS/Accelerometer/Magnetometer Orientation Measurement","display_name":"Optimal, Recursive and Sub-Optimal Linear Solutions to Attitude Determination from Vector Observations for GNSS/Accelerometer/Magnetometer Orientation Measurement","publication_year":2018,"publication_date":"2018-03-01","ids":{"openalex":"https://openalex.org/W2793902216","doi":"https://doi.org/10.3390/rs10030377","mag":"2793902216"},"language":"en","primary_location":{"id":"doi:10.3390/rs10030377","is_oa":true,"landing_page_url":"https://doi.org/10.3390/rs10030377","pdf_url":null,"source":{"id":"https://openalex.org/S43295729","display_name":"Remote Sensing","issn_l":"2072-4292","issn":["2072-4292"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Remote Sensing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/rs10030377","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073534407","display_name":"Zebo Zhou","orcid":"https://orcid.org/0000-0002-3687-7133"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zebo Zhou","raw_affiliation_strings":["School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 610054, China"],"affiliations":[{"raw_affiliation_string":"School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 610054, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078883186","display_name":"Jin Wu","orcid":"https://orcid.org/0000-0001-5930-4170"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jin Wu","raw_affiliation_strings":["School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 610054, China","School of Automation, University of Electronic Science and Technology of China, Chengdu 610054, China"],"affiliations":[{"raw_affiliation_string":"School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 610054, China","institution_ids":["https://openalex.org/I150229711"]},{"raw_affiliation_string":"School of Automation, University of Electronic Science and Technology of China, Chengdu 610054, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100743242","display_name":"Jinling Wang","orcid":"https://orcid.org/0000-0002-6485-780X"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Jinling Wang","raw_affiliation_strings":["Surveying and Geospatial Engineering, School of Civil and Environmental Engineering, University of New South Wales, Sydney 2052, NSW, Australia"],"affiliations":[{"raw_affiliation_string":"Surveying and Geospatial Engineering, School of Civil and Environmental Engineering, University of New South Wales, Sydney 2052, NSW, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008384064","display_name":"Hassen Fourati","orcid":"https://orcid.org/0000-0002-8398-7183"},"institutions":[{"id":"https://openalex.org/I106785703","display_name":"Institut polytechnique de Grenoble","ror":"https://ror.org/05sbt2524","country_code":"FR","type":"education","lineage":["https://openalex.org/I106785703","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210124956","display_name":"Grenoble Images Parole Signal Automatique","ror":"https://ror.org/02wrme198","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]},{"id":"https://openalex.org/I4210101348","display_name":"Centre Inria de l'Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/00n8d6z93","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210101348"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Hassen Fourati","raw_affiliation_strings":["Institute of Engineering, University Grenoble Alpes, CNRS, Inria, Grenoble INP, GIPSALab, 38000 Grenoble, France"],"affiliations":[{"raw_affiliation_string":"Institute of Engineering, University Grenoble Alpes, CNRS, Inria, Grenoble INP, GIPSALab, 38000 Grenoble, France","institution_ids":["https://openalex.org/I4210101348","https://openalex.org/I1294671590","https://openalex.org/I106785703","https://openalex.org/I4210124956","https://openalex.org/I899635006"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5073534407","https://openalex.org/A5078883186"],"corresponding_institution_ids":["https://openalex.org/I150229711"],"apc_list":{"value":2500,"currency":"CHF","value_usd":2707},"apc_paid":{"value":2500,"currency":"CHF","value_usd":2707},"fwci":7.0973,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.96474252,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"10","issue":"3","first_page":"377","last_page":"377"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11325","display_name":"Inertial Sensor and Navigation","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11325","display_name":"Inertial Sensor and Navigation","score":1.0,"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/T11405","display_name":"Geophysics and Gravity Measurements","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10655","display_name":"GNSS positioning and interference","score":0.991599977016449,"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":0.7723140716552734},{"id":"https://openalex.org/keywords/accelerometer","display_name":"Accelerometer","score":0.6733095645904541},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6566150188446045},{"id":"https://openalex.org/keywords/magnetometer","display_name":"Magnetometer","score":0.5113992094993591},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5064619779586792},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4537624716758728},{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.43153107166290283},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.422420859336853},{"id":"https://openalex.org/keywords/global-positioning-system","display_name":"Global Positioning System","score":0.3934289515018463},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21758663654327393},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12664121389389038},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08529520034790039}],"concepts":[{"id":"https://openalex.org/C14279187","wikidata":"https://www.wikidata.org/wiki/Q5514012","display_name":"GNSS applications","level":3,"score":0.7723140716552734},{"id":"https://openalex.org/C89805583","wikidata":"https://www.wikidata.org/wiki/Q192940","display_name":"Accelerometer","level":2,"score":0.6733095645904541},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6566150188446045},{"id":"https://openalex.org/C153946474","wikidata":"https://www.wikidata.org/wiki/Q333921","display_name":"Magnetometer","level":3,"score":0.5113992094993591},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5064619779586792},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4537624716758728},{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.43153107166290283},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.422420859336853},{"id":"https://openalex.org/C60229501","wikidata":"https://www.wikidata.org/wiki/Q18822","display_name":"Global Positioning System","level":2,"score":0.3934289515018463},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21758663654327393},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12664121389389038},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08529520034790039},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/rs10030377","is_oa":true,"landing_page_url":"https://doi.org/10.3390/rs10030377","pdf_url":null,"source":{"id":"https://openalex.org/S43295729","display_name":"Remote Sensing","issn_l":"2072-4292","issn":["2072-4292"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Remote Sensing","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01722260v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01722260","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Remote Sensing, 2018, 10 (3), pp.1-28. ⟨10.3390/rs10030377⟩","raw_type":"Journal articles"},{"id":"pmh:oai:doaj.org/article:7c24b9a79e9441829438577992ef2d2a","is_oa":true,"landing_page_url":"https://doaj.org/article/7c24b9a79e9441829438577992ef2d2a","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":"Remote Sensing, Vol 10, Iss 3, p 377 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2072-4292/10/3/377/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/rs10030377","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Remote Sensing; Volume 10; Issue 3; Pages: 377","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/rs10030377","is_oa":true,"landing_page_url":"https://doi.org/10.3390/rs10030377","pdf_url":null,"source":{"id":"https://openalex.org/S43295729","display_name":"Remote Sensing","issn_l":"2072-4292","issn":["2072-4292"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Remote Sensing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W50340912","https://openalex.org/W192968364","https://openalex.org/W196239571","https://openalex.org/W635134541","https://openalex.org/W1489416677","https://openalex.org/W1883584114","https://openalex.org/W1985393139","https://openalex.org/W1985604452","https://openalex.org/W1988874269","https://openalex.org/W1997244800","https://openalex.org/W2001422561","https://openalex.org/W2006863675","https://openalex.org/W2016398292","https://openalex.org/W2024035513","https://openalex.org/W2048207563","https://openalex.org/W2056213672","https://openalex.org/W2057237438","https://openalex.org/W2058335135","https://openalex.org/W2058467770","https://openalex.org/W2063005413","https://openalex.org/W2071042199","https://openalex.org/W2079989234","https://openalex.org/W2085829517","https://openalex.org/W2099789189","https://openalex.org/W2105906226","https://openalex.org/W2122093596","https://openalex.org/W2125691646","https://openalex.org/W2128615445","https://openalex.org/W2153199180","https://openalex.org/W2160146756","https://openalex.org/W2165199328","https://openalex.org/W2199469138","https://openalex.org/W2296613180","https://openalex.org/W2298196161","https://openalex.org/W2333276910","https://openalex.org/W2402257423","https://openalex.org/W2466559273","https://openalex.org/W2548126792","https://openalex.org/W2607069670","https://openalex.org/W2608231861","https://openalex.org/W2693492055","https://openalex.org/W4229706427","https://openalex.org/W4237143575","https://openalex.org/W6607981818","https://openalex.org/W6629128128"],"related_works":["https://openalex.org/W3127350447","https://openalex.org/W3108700312","https://openalex.org/W4225472102","https://openalex.org/W2765080098","https://openalex.org/W2382948573","https://openalex.org/W2385749422","https://openalex.org/W2887325221","https://openalex.org/W4386936491","https://openalex.org/W2084651007","https://openalex.org/W2112493694"],"abstract_inverted_index":{"The":[0,78,95,117,196,228],"integration":[1],"of":[2,105,153,163,181,188,223],"the":[3,32,40,47,55,101,127,134,146,154,161,164,167,179,182,189,202,207],"Accelerometer":[4],"and":[5,11,21,27,80,84,93,110,126,142,157,185,216,236],"Magnetometer":[6],"(AM)":[7],"provides":[8,145],"continuous,":[9],"stable":[10],"accurate":[12],"attitude":[13,63,82,155],"information":[14],"for":[15,62,113],"land-vehicle":[16],"navigation":[17],"without":[18],"magnetic":[19,25],"distortion":[20],"external":[22],"acceleration.":[23],"However,":[24],"disturbance":[26],"linear":[28],"acceleration":[29],"strongly":[30],"degrade":[31],"overall":[33],"system":[34,61],"performance.":[35],"As":[36],"an":[37,220],"important":[38],"complement,":[39],"Global":[41],"Navigation":[42],"Satellite":[43],"System":[44],"(GNSS)":[45],"produces":[46],"heading":[48],"estimates,":[49],"thus":[50],"it":[51],"can":[52],"potentially":[53],"benefit":[54],"AM":[56],"system.":[57],"Such":[58],"a":[59,69,149,211],"GNSS/AM":[60],"estimation":[64],"is":[65,119,170],"mathematically":[66],"converted":[67],"to":[68],"multi-observation":[70],"vector":[71],"pairs":[72],"matching":[73],"problem":[74],"in":[75,225,239],"this":[76],"paper.":[77],"optimal":[79],"sub-optimal":[81],"determination":[83,156],"their":[85,233],"time-varying":[86],"recursive":[87],"variants":[88],"are":[89,98,131,140,175,198],"all":[90],"comprehensively":[91],"investigated":[92],"discussed.":[94],"developed":[96],"methods":[97],"named":[99],"as":[100],"Optimal":[102],"Linear":[103],"Estimator":[104],"Quaternion":[106],"(OLEQ),":[107],"Suboptimal-OLEQ":[108],"(SOLEQ)":[109],"Recursive-OLEQ":[111],"(ROLEQ)":[112],"different":[114],"application":[115],"scenarios.":[116,242],"theory":[118],"established":[120],"based":[121],"on":[122,206],"our":[123],"previous":[124],"contributions,":[125],"multi-vector":[128],"matrix":[129],"multiplications":[130],"decomposed":[132],"with":[133,148,193,210],"eigenvalue":[135],"factorization.":[136],"Some":[137],"analytical":[138],"results":[139],"proven":[141,232],"given,":[143],"which":[144],"reader":[147],"brand":[150],"new":[151],"viewpoint":[152],"its":[158],"evolution.":[159],"With":[160],"derivations":[162],"two-vector":[165],"case,":[166],"n-vector":[168],"case":[169],"then":[171,199],"naturally":[172],"formed.":[173],"Simulations":[174],"carried":[176],"out":[177],"showing":[178],"advantages":[180],"accuracy,":[183],"robustness":[184],"time":[186],"consumption":[187],"proposed":[190],"OLEQs,":[191],"compared":[192],"representative":[194],"methods.":[195],"algorithms":[197],"implemented":[200],"using":[201],"C++":[203],"programming":[204],"language":[205],"designed":[208,229],"hardware":[209],"GNSS":[212],"module,":[213],"three-axis":[214,217],"accelerometer":[215],"magnetometer,":[218],"giving":[219],"effective":[221],"validation":[222],"them":[224],"real-world":[226],"applications.":[227],"schemes":[230],"have":[231],"fast":[234],"speed":[235],"good":[237],"accuracy":[238],"these":[240],"verification":[241]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}