{"id":"https://openalex.org/W7225235645","doi":"https://doi.org/10.5281/zenodo.23935674","title":"Observable systems with divergent isolated Kalman covariances: a counterexample to the isolated Kalman filtering convergence conjecture","display_name":"Observable systems with divergent isolated Kalman covariances: a counterexample to the isolated Kalman filtering convergence conjecture","publication_year":2026,"publication_date":"2026-11-04","ids":{"openalex":"https://openalex.org/W7225235645","doi":"https://doi.org/10.5281/zenodo.23935674"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23935674","doi":"https://doi.org/10.5281/zenodo.23935674","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23935674","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23935674","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Anonymous","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Anonymous","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.9765999913215637,"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":0.9765999913215637,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.010400000028312206,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11236","display_name":"Control Systems and Identification","score":0.004600000102072954,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/counterexample","display_name":"counterexample","score":0.7960000038146973},{"id":"https://openalex.org/keywords/distributed-estimation","display_name":"distributed estimation","score":0.4819999933242798},{"id":"https://openalex.org/keywords/sensor-networks","display_name":"sensor networks","score":0.5490000247955322},{"id":"https://openalex.org/keywords/perron-root","display_name":"Perron root","score":0.6539999842643738},{"id":"https://openalex.org/keywords/schur-stability","display_name":"Schur stability","score":0.7960000038146973},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"interval arithmetic","score":0.6660000085830688},{"id":"https://openalex.org/keywords/computer-assisted-proof","display_name":"computer-assisted proof","score":0.8050000071525574},{"id":"https://openalex.org/keywords/positive-definite-covariance","display_name":"positive definite covariance","score":0.49300000071525574}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7128000259399414},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7037000060081482},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.6449999809265137},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.5733000040054321},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.5436000227928162},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5016999840736389},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4799000024795532},{"id":"https://openalex.org/C206833254","wikidata":"https://www.wikidata.org/wiki/Q5421817","display_name":"Extended Kalman filter","level":3,"score":0.4577000141143799},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.43790000677108765},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.428600013256073},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38960000872612},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.37470000982284546},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.3734999895095825},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.3677000105381012},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.361299991607666},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.3515999913215637},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.3472999930381775},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3359000086784363},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3138999938964844},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29280000925064087},{"id":"https://openalex.org/C205167067","wikidata":"https://www.wikidata.org/wiki/Q3300636","display_name":"Interval estimation","level":3,"score":0.29190000891685486},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.2799000144004822},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2630999982357025},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.25940001010894775}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.5281/zenodo.23935674","doi":"https://doi.org/10.5281/zenodo.23935674","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23935674","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23935675","doi":"https://doi.org/10.5281/zenodo.23935675","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23935675","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23941896","doi":"https://doi.org/10.5281/zenodo.23941896","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23941896","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23935674","doi":"https://doi.org/10.5281/zenodo.23935674","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23935674","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1983389310","https://openalex.org/W2035326564","https://openalex.org/W2138890480","https://openalex.org/W2148234182","https://openalex.org/W2158122241","https://openalex.org/W2213796655","https://openalex.org/W2272130679","https://openalex.org/W2410440994","https://openalex.org/W2766543336","https://openalex.org/W2793866255","https://openalex.org/W4405662150","https://openalex.org/W4407424457","https://openalex.org/W4411019572","https://openalex.org/W7133337728"],"related_works":["https://openalex.org/W6903976720","https://openalex.org/W4407424457","https://openalex.org/W2219110552","https://openalex.org/W2064939225","https://openalex.org/W1578528950","https://openalex.org/W7123363366","https://openalex.org/W2105086909","https://openalex.org/W2324617856","https://openalex.org/W1734702393","https://openalex.org/W22935407"],"abstract_inverted_index":{"Unrefereed":[0],"research":[1],"candidate.":[2],"The":[3,267,289,381],"isolated":[4],"Kalman":[5,122],"filter":[6,103,123],"(IsoKF)":[7],"of":[8,19,150,219,258,264,373],"Jung,":[9],"Luft":[10,331],"and":[11,38,58,87,97,195,234,314,341,347,362,376,404,418,422,427],"Weiss":[12],"(Autonomous":[13],"Robots,":[14],"2025)":[15],"lets":[16],"the":[17,31,61,74,102,109,120,201,247,253,259,265,328,335,374],"nodes":[18,32],"a":[20,35,47,67,235,342],"robot":[21],"or":[22,148,371,397,441],"sensor":[23],"network":[24],"share":[25],"an":[26],"estimation":[27,249],"task":[28],"cheaply:":[29],"only":[30,434],"involved":[33],"in":[34,171,243,280,389],"measurement":[36],"update,":[37],"their":[39,419],"correlations":[40],"with":[41,81,310,327,407],"everyone":[42],"else":[43],"are":[44,385,445],"rescaled":[45],"by":[46],"correction":[48,336],"factor.":[49],"Its":[50],"authors":[51],"conjectured":[52],"that":[53,168,196,227,349],"for":[54,169,238,278,284],"any":[55],"completely":[56],"observable":[57,93],"controllable":[59],"system":[60,80],"covariance":[62,375],"it":[63,326],"reports":[64],"converges":[65,204],"to":[66,135,189],"finite,":[68],"unique,":[69],"stable":[70,285],"steady":[71,214],"state.":[72],"Result:":[73],"conjecture":[75],"is":[76,92,143,210,255,276,300],"false.":[77],"A":[78,89,130],"three-node":[79],"pair-sum":[82,139,270],"observations":[83],"x1+x2,":[84],"x2+x3,":[85],"x3+x1":[86],"dynamics":[88,156,286],"=":[90,191,199],"3I":[91],"from":[94,182],"one":[95],"epoch":[96],"controllable,":[98],"every":[99,125,136,229],"local":[100,230],"block":[101,231],"uses":[104,269],"stays":[105,251],"positive":[106,232,353],"definite,":[107,233],"yet":[108],"reported":[110,260],"marginal":[111],"variances":[112],"satisfy":[113],"m_k":[114],"\u2265":[115],"(5/4)(9/5)^k":[116],"\u2212":[117],"1/4,":[118],"while":[119,205],"centralised":[121],"keeps":[124],"variance":[126],"at":[127,177,185,197,319,359],"most":[128],"3/4.":[129],"Perron-root":[131],"comparison":[132],"extends":[133],"divergence":[134,263,379],"connected":[137],"non-bipartite":[138],"graph":[140],"when":[141],"a^2":[142,170,190,198,279],"large":[144,174],"enough;":[145],"extra":[146],"attenuation":[147],"deletion":[149],"cross-covariances":[151],"does":[152],"not":[153,262,272,295,447],"help.":[154],"Schur-stable":[155],"always":[157],"give":[158,377],"bounded":[159,236],"marginals":[160],"(proved).":[161],"Computer-assisted":[162],"proofs":[163],"(outward-rounded":[164],"interval":[165,413],"arithmetic)":[166],"show":[167],"(1,":[172],"1.38]":[173],"priors":[175],"diverge":[176],"rate":[178],"a^(2k),":[179],"entry":[180],"certified":[181],"10^12":[183,206],"I":[184,203,207],"eight":[186],"values":[187],"down":[188],"1":[192],"+":[193],"10^-8,":[194],"21/20":[200],"prior":[202],"diverges:":[208],"there":[209],"no":[211,297,367,378],"globally":[212],"attracting":[213],"covariance.":[215],"Also:":[216],"exact":[217,410],"classification":[218],"participant":[220],"overlaps":[221],"(|U":[222],"\u2229":[223],"V|":[224],"\u2264":[225],"1)":[226],"keep":[228],"regime":[237],"anchored":[239],"relative":[240],"measurements.":[241],"Scope:":[242],"high-precision":[244],"numerical":[245,398,416],"tests":[246],"actual":[248],"error":[250],"bounded;":[252],"failure":[254,299],"gross":[256],"pessimism":[257],"covariance,":[261],"estimate.":[266],"counterexample":[268],"measurements,":[271],"plain":[273],"differences.":[274],"Nothing":[275],"proved":[277],"(1.38,":[281],"2+\u221a5);":[282],"uniqueness":[283],"remains":[287],"open.":[288],"ikf_lib":[290],"software":[291,298],"was":[292],"inspected":[293],"but":[294],"run;":[296],"claimed.":[301],"Version":[302,305],"0.2.0":[303],"(correction).":[304],"0.1.0":[306],"compared":[307,388],"this":[308],"work":[309],"Luft,":[311],"Schubert,":[312],"Roumeliotis":[313],"Burgard":[315],"(2018,":[316],"IJRR,":[317],"doi:10.1177/0278364918760698)":[318],"abstract":[320],"level":[321],"only.":[322],"This":[323],"version":[324],"compares":[325],"full":[329,390],"text:":[330],"et":[332],"al.":[333],"introduce":[334],"factor":[337],"(their":[338],"eq.":[339],"26)":[340],"scaled":[343],"variant":[344],"(eq.":[345],"28),":[346],"prove":[348],"two-robot":[350],"blocks":[351],"stay":[352],"definite":[354],"(Proposition":[355],"1,":[356],"now":[357,386],"credited":[358],"Theorem":[360],"8.1":[361],"Corollary":[363],"5.3);":[364],"they":[365],"make":[366],"claim":[368],"about":[369],"boundedness":[370],"convergence":[372],"example.":[380],"two":[382],"citing":[383],"works":[384],"also":[387],"text.":[391],"No":[392],"theorem,":[393],"proof,":[394],"certificate,":[395],"computation":[396],"finding":[399],"changed.":[400],"Archive:":[401],"LaTeX":[402],"manuscript":[403],"PDF,":[405],"bibliography":[406],"registry":[408],"records,":[409],"rational":[411],"verifiers,":[412],"certificates":[414,444],"C1\u2013C3,":[415],"scripts":[417],"outputs":[420],"(normal":[421],"python":[423],"-O),":[424],"figures,":[425],"CI":[426],"SHA-256":[428],"manifest.":[429],"Assurance:":[430],"internal":[431],"AI-assisted":[432],"review":[433],"(not":[435],"human":[436],"peer":[437],"review,":[438],"independent":[439],"reproduction":[440],"formal":[442,448],"verification);":[443],"computer-assisted,":[446],"proofs.":[449],"Creator:":[450],"Anonymous.":[451],"Text":[452],"CC0-1.0;":[453],"code":[454],"MIT.":[455]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-11-05T00:00:00"}
