{"id":"https://openalex.org/W4417473651","doi":"https://doi.org/10.48550/arxiv.2512.14520","title":"The Innovation Null Space of the Kalman Predictor: A Stochastic Perspective for DeePC","display_name":"The Innovation Null Space of the Kalman Predictor: A Stochastic Perspective for DeePC","publication_year":2025,"publication_date":"2025-12-16","ids":{"openalex":"https://openalex.org/W4417473651","doi":"https://doi.org/10.48550/arxiv.2512.14520"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2512.14520","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.14520","pdf_url":"https://arxiv.org/pdf/2512.14520","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2512.14520","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046261892","display_name":"Aihui Liu","orcid":"https://orcid.org/0000-0002-0039-1713"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Aihui","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5078077956","display_name":"Magnus Jansson","orcid":"https://orcid.org/0000-0002-7746-8838"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jansson, Magnus","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"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/T11236","display_name":"Control Systems and Identification","score":0.7063999772071838,"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"}},"topics":[{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.7063999772071838,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.21580000221729279,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.015699999406933784,"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/lemma","display_name":"Lemma (botany)","score":0.680899977684021},{"id":"https://openalex.org/keywords/kalman-filter","display_name":"Kalman filter","score":0.677299976348877},{"id":"https://openalex.org/keywords/null","display_name":"Null (SQL)","score":0.6229000091552734},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.5260000228881836},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.4860999882221222},{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.41609999537467957},{"id":"https://openalex.org/keywords/null-hypothesis","display_name":"Null hypothesis","score":0.4147000014781952},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.3630000054836273}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.680899977684021},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.677299976348877},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6266000270843506},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.6229000091552734},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5260000228881836},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.4860999882221222},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.41609999537467957},{"id":"https://openalex.org/C191988596","wikidata":"https://www.wikidata.org/wiki/Q628374","display_name":"Null hypothesis","level":2,"score":0.4147000014781952},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3630000054836273},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.33649998903274536},{"id":"https://openalex.org/C206833254","wikidata":"https://www.wikidata.org/wiki/Q5421817","display_name":"Extended Kalman filter","level":3,"score":0.33160001039505005},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3188999891281128},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3174999952316284},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.3156999945640564},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.31459999084472656},{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.29350000619888306},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2865999937057495},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2833000123500824},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2809999883174896},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2705000042915344},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.257999986410141}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2512.14520","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.14520","pdf_url":"https://arxiv.org/pdf/2512.14520","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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.2512.14520","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.14520","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2512.14520","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.14520","pdf_url":"https://arxiv.org/pdf/2512.14520","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4417473651.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Willems'":[0,111],"fundamental":[1],"lemma":[2,112],"uses":[3],"a":[4,18,29,44,96],"key":[5],"decision":[6,60,75],"variable":[7,61],"$g$":[8,35],"to":[9,87,101,113],"combine":[10],"measured":[11],"input-output":[12],"data":[13],"and":[14,145],"describe":[15],"trajectories":[16],"of":[17,68,134],"linear":[19,45],"time-invariant":[20],"system.":[21],"In":[22],"this":[23,33,59,79,150],"paper,":[24],"we":[25,50,94,99],"ask:":[26],"what":[27],"is":[28,39,64],"good":[30],"choice":[31],"for":[32,58],"vector":[34,76],"when":[36],"the":[37,65,69,74,82,88,103,114,135],"system":[38,46],"affected":[40],"by":[41,143],"noise?":[42],"For":[43],"with":[47],"Gaussian":[48],"noise,":[49],"show":[51,92],"that":[52,98],"there":[53],"exists":[54],"an":[55],"optimal":[56],"subspace":[57],"$g$,":[62],"which":[63,109],"null":[66,80,152],"space":[67],"innovation":[70,136,151],"Hankel":[71],"matrix.":[72],"If":[73],"lies":[77],"in":[78],"space,":[81],"resulting":[83],"predictor":[84],"gets":[85],"closer":[86],"Kalman":[89,104,115],"predictor.":[90,116],"To":[91],"this,":[93],"use":[95],"result":[97],"refer":[100],"as":[102,131],"Filter":[105],"Fundamental":[106],"Lemma":[107],"(KFFL),":[108],"applies":[110],"This":[117],"viewpoint":[118],"also":[119],"explains":[120],"several":[121],"existing":[122],"data-driven":[123],"predictive":[124],"control":[125],"methods:":[126],"regularized":[127],"DeePC":[128],"schemes":[129],"act":[130],"soft":[132],"versions":[133],"null-space":[137],"constraint,":[138],"instrumental-variable":[139],"methods":[140],"enforce":[141],"it":[142],"construction,":[144],"ARX-based":[146],"approaches":[147],"explicitly":[148],"estimate":[149],"space.":[153]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-12-18T00:00:00"}