{"id":"https://openalex.org/W7212692425","doi":"https://doi.org/10.48550/arxiv.2609.12328","title":"The Iterative Equivariant Filter","display_name":"The Iterative Equivariant Filter","publication_year":2026,"publication_date":"2026-09-11","ids":{"openalex":"https://openalex.org/W7212692425","doi":"https://doi.org/10.48550/arxiv.2609.12328"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2609.12328","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12328","pdf_url":"https://arxiv.org/pdf/2609.12328","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.12328","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022864763","display_name":"Pieter van Goor","orcid":"https://orcid.org/0000-0003-4391-7014","observed_orcids":["https://orcid.org/0000-0003-4391-7014"]},"institutions":[{"id":"https://openalex.org/I114017466","display_name":"University of Technology Sydney","ror":"https://ror.org/03f0f6041","country_code":"AU","type":"education","lineage":["https://openalex.org/I114017466"]},{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"van Goor, Pieter","raw_affiliation_strings":["School of Aerospace, Mechanical, and Mechatronic Engineering The University of Sydney NSW 2006 , Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Aerospace, Mechanical, and Mechatronic Engineering The University of Sydney NSW 2006 , Australia","institution_ids":["https://openalex.org/I114017466","https://openalex.org/I129604602"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023450612","display_name":"James Richard Forbes","orcid":"https://orcid.org/0000-0002-1987-9268","observed_orcids":["https://orcid.org/0000-0002-1987-9268"]},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Forbes, James Richard","raw_affiliation_strings":["Dept. of Mechanical Engineering McGill University Montreal , QC , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Mechanical Engineering McGill University Montreal , QC , Canada","institution_ids":["https://openalex.org/I5023651"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9282000064849854,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9282000064849854,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11325","display_name":"Inertial Sensor and Navigation","score":0.04749999940395355,"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/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.023099999874830246,"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/iterative-extended-kalman-filter","display_name":"iterative extended Kalman filter","score":0.9049999713897705},{"id":"https://openalex.org/keywords/gauss-newton-iteration","display_name":"Gauss-Newton iteration","score":0.7710000276565552},{"id":"https://openalex.org/keywords/weighted-nonlinear-least-squares","display_name":"weighted nonlinear least squares","score":0.925000011920929},{"id":"https://openalex.org/keywords/state-estimation","display_name":"state estimation","score":0.5740000009536743},{"id":"https://openalex.org/keywords/homogeneous-spaces","display_name":"homogeneous spaces","score":0.8199999928474426},{"id":"https://openalex.org/keywords/lie-groups","display_name":"Lie groups","score":0.9950000047683716},{"id":"https://openalex.org/keywords/symmetry-exploitation","display_name":"symmetry exploitation","score":0.6880000233650208},{"id":"https://openalex.org/keywords/mobile-robot-localization","display_name":"mobile robot localization","score":0.8600000143051147},{"id":"https://openalex.org/keywords/navigation","display_name":"navigation","score":0.859000027179718}],"concepts":[{"id":"https://openalex.org/C206833254","wikidata":"https://www.wikidata.org/wiki/Q5421817","display_name":"Extended Kalman filter","level":3,"score":0.7620000243186951},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.6869999766349792},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6067000031471252},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5899999737739563},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5289000272750854},{"id":"https://openalex.org/C8639503","wikidata":"https://www.wikidata.org/wiki/Q6059511","display_name":"Invariant extended Kalman filter","level":4,"score":0.5041999816894531},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.4796999990940094},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4747999906539917},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4092000126838684},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.4000999927520752},{"id":"https://openalex.org/C83042196","wikidata":"https://www.wikidata.org/wiki/Q5178898","display_name":"Covariance intersection","level":4,"score":0.39800000190734863},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3905999958515167},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.38100001215934753},{"id":"https://openalex.org/C22597639","wikidata":"https://www.wikidata.org/wiki/Q5449227","display_name":"Filter design","level":3,"score":0.3686999976634979},{"id":"https://openalex.org/C11588082","wikidata":"https://www.wikidata.org/wiki/Q4735154","display_name":"Alpha beta filter","level":5,"score":0.35530000925064087},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3343999981880188},{"id":"https://openalex.org/C117619785","wikidata":"https://www.wikidata.org/wiki/Q6094414","display_name":"Iterative learning control","level":3,"score":0.3264999985694885},{"id":"https://openalex.org/C13107197","wikidata":"https://www.wikidata.org/wiki/Q6394192","display_name":"Kernel adaptive filter","level":4,"score":0.30660000443458557},{"id":"https://openalex.org/C2779982483","wikidata":"https://www.wikidata.org/wiki/Q6094420","display_name":"Iterative refinement","level":2,"score":0.29789999127388},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.29319998621940613},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.28999999165534973},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2897000014781952},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.2791999876499176},{"id":"https://openalex.org/C102248274","wikidata":"https://www.wikidata.org/wiki/Q168388","display_name":"Adaptive filter","level":2,"score":0.275299996137619},{"id":"https://openalex.org/C145249878","wikidata":"https://www.wikidata.org/wiki/Q2835868","display_name":"Recursive least squares filter","level":3,"score":0.2720000147819519},{"id":"https://openalex.org/C2780799671","wikidata":"https://www.wikidata.org/wiki/Q17087362","display_name":"Transient (computer programming)","level":2,"score":0.2651999890804291},{"id":"https://openalex.org/C137685913","wikidata":"https://www.wikidata.org/wiki/Q4316763","display_name":"Nonlinear filter","level":4,"score":0.26489999890327454},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C126090379","wikidata":"https://www.wikidata.org/wiki/Q6094424","display_name":"Iteratively reweighted least squares","level":4,"score":0.25780001282691956}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.12328","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12328","pdf_url":"https://arxiv.org/pdf/2609.12328","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"doi:10.48550/arxiv.2609.12328","doi":"https://doi.org/10.48550/arxiv.2609.12328","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.12328","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.12328","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12328","pdf_url":"https://arxiv.org/pdf/2609.12328","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212692425.pdf","grobid_xml":"https://content.openalex.org/works/W7212692425.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0,91],"paper":[1,92],"presents":[2],"the":[3,15,27,45,62,67,71,74,94,98,105,109,117,133,144],"iterative":[4,9,22],"equivariant":[5,39],"filter":[6,12,40],"(IterEqF).":[7],"The":[8,37,59],"extended":[10],"Kalman":[11],"(IterEKF)":[13],"replaces":[14],"standard":[16,38,140],"EKF":[17],"correction":[18,23],"step":[19,24,101],"with":[20],"an":[21],"that":[25,84],"is":[26,64,85],"Gauss-Newton":[28],"solution":[29,83],"to":[30,65,78,88,138],"a":[31,79,114,129,139],"nonlinear":[32],"weighted":[33],"least":[34],"squares":[35],"problem.":[36],"(EqF)":[41],"exploits":[42],"and":[43,56,73,102],"respects":[44],"underlying":[46],"symmetry":[47],"of":[48,69,108,116,125],"state":[49,81],"estimation":[50,82],"problems":[51],"posed":[52],"on":[53],"homogeneous":[54],"spaces":[55],"Lie":[57],"groups.":[58],"motivation":[60],"behind":[61],"IterEqF":[63,99],"combine":[66],"features":[68],"both":[70],"IterEKF":[72],"EqF,":[75,141],"thus":[76],"leading":[77],"high-performance":[80],"well":[86],"suited":[87],"navigation":[89],"problems.":[90],"derives":[93],"iteration":[95],"procedure":[96],"for":[97,128],"update":[100],"shows":[103],"how":[104],"intrinsic":[106],"nonlinearity":[107],"approach":[110],"naturally":[111],"results":[112],"in":[113,135],"`reset'":[115],"filter's":[118],"covariance":[119],"into":[120],"new":[121],"coordinates.":[122],"Monte-Carlo":[123],"simulations":[124],"range-based":[126],"localisation":[127],"mobile":[130],"robot":[131],"demonstrate":[132],"improvement":[134],"performance":[136],"relative":[137],"especially":[142],"during":[143],"transient":[145],"convergence.":[146]},"counts_by_year":[],"updated_date":"2026-09-30T09:27:27.532063","created_date":"2026-09-15T00:00:00"}