{"id":"https://openalex.org/W7135173376","doi":"https://doi.org/10.1109/lsp.2026.3674044","title":"CNPE-KalmanNet: Learning-Aided Kalman Filter With Complex Number Position Encoding","display_name":"CNPE-KalmanNet: Learning-Aided Kalman Filter With Complex Number Position Encoding","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7135173376","doi":"https://doi.org/10.1109/lsp.2026.3674044"},"language":null,"primary_location":{"id":"doi:10.1109/lsp.2026.3674044","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2026.3674044","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","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/A5128939909","display_name":"Yucheng Long","orcid":null},"institutions":[{"id":"https://openalex.org/I4210163363","display_name":"PLA Army Engineering University","ror":"https://ror.org/05mgp8x93","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210163363"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yucheng Long","raw_affiliation_strings":["Shijiazhuang Campus, Army Engineering University of PLA, Shijiazhuang, China"],"raw_orcid":"https://orcid.org/0009-0000-6328-5494","affiliations":[{"raw_affiliation_string":"Shijiazhuang Campus, Army Engineering University of PLA, Shijiazhuang, China","institution_ids":["https://openalex.org/I4210163363"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072778059","display_name":"Wei Mei","orcid":"https://orcid.org/0000-0002-5736-189X"},"institutions":[{"id":"https://openalex.org/I4210163363","display_name":"PLA Army Engineering University","ror":"https://ror.org/05mgp8x93","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210163363"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Mei","raw_affiliation_strings":["Shijiazhuang Campus, Army Engineering University of PLA, Shijiazhuang, China"],"raw_orcid":"https://orcid.org/0000-0002-5736-189X","affiliations":[{"raw_affiliation_string":"Shijiazhuang Campus, Army Engineering University of PLA, Shijiazhuang, China","institution_ids":["https://openalex.org/I4210163363"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101822651","display_name":"Jian Song","orcid":"https://orcid.org/0009-0009-8891-5320"},"institutions":[{"id":"https://openalex.org/I4210163363","display_name":"PLA Army Engineering University","ror":"https://ror.org/05mgp8x93","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210163363"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Song","raw_affiliation_strings":["Shijiazhuang Campus, Army Engineering University of PLA, Shijiazhuang, China"],"raw_orcid":"https://orcid.org/0009-0009-8891-5320","affiliations":[{"raw_affiliation_string":"Shijiazhuang Campus, Army Engineering University of PLA, Shijiazhuang, China","institution_ids":["https://openalex.org/I4210163363"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128966187","display_name":"Yunfeng Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210163363","display_name":"PLA Army Engineering University","ror":"https://ror.org/05mgp8x93","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210163363"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yunfeng Xu","raw_affiliation_strings":["Shijiazhuang Campus, Army Engineering University of PLA, Shijiazhuang, China"],"raw_orcid":"https://orcid.org/0000-0002-2674-3721","affiliations":[{"raw_affiliation_string":"Shijiazhuang Campus, Army Engineering University of PLA, Shijiazhuang, China","institution_ids":["https://openalex.org/I4210163363"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129044673","display_name":"Qiang Fu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210163363","display_name":"PLA Army Engineering University","ror":"https://ror.org/05mgp8x93","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210163363"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiang Fu","raw_affiliation_strings":["Shijiazhuang Campus, Army Engineering University of PLA, Shijiazhuang, China"],"raw_orcid":"https://orcid.org/0000-0002-3831-9856","affiliations":[{"raw_affiliation_string":"Shijiazhuang Campus, Army Engineering University of PLA, Shijiazhuang, China","institution_ids":["https://openalex.org/I4210163363"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062414392","display_name":"Lina Bu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210163363","display_name":"PLA Army Engineering University","ror":"https://ror.org/05mgp8x93","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210163363"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lina Bu","raw_affiliation_strings":["Shijiazhuang Campus, Army Engineering University of PLA, Shijiazhuang, China"],"raw_orcid":"https://orcid.org/0009-0005-8391-3423","affiliations":[{"raw_affiliation_string":"Shijiazhuang Campus, Army Engineering University of PLA, Shijiazhuang, China","institution_ids":["https://openalex.org/I4210163363"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210163363"],"apc_list":null,"apc_paid":null,"fwci":8.9492,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.9657378,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"33","issue":null,"first_page":"1556","last_page":"1560"},"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":0.16369999945163727,"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":0.16369999945163727,"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":0.13169999420642853,"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":0.09390000253915787,"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/kalman-filter","display_name":"Kalman filter","score":0.5370000004768372},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.5230000019073486},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.4496000111103058},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.3312000036239624},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.3154999911785126},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.3133000135421753},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.3125},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.3000999987125397},{"id":"https://openalex.org/keywords/radar-tracker","display_name":"Radar tracker","score":0.28870001435279846}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6197999715805054},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5537999868392944},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.5370000004768372},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.5230000019073486},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.4496000111103058},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.40059998631477356},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.3312000036239624},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3197999894618988},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.3154999911785126},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.3133000135421753},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.3125},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.3000999987125397},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.2897999882698059},{"id":"https://openalex.org/C32283439","wikidata":"https://www.wikidata.org/wiki/Q1407014","display_name":"Radar tracker","level":3,"score":0.28870001435279846},{"id":"https://openalex.org/C29265498","wikidata":"https://www.wikidata.org/wiki/Q7047719","display_name":"Noise measurement","level":3,"score":0.27959999442100525},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.27709999680519104},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.27649998664855957},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2709999978542328},{"id":"https://openalex.org/C50151734","wikidata":"https://www.wikidata.org/wiki/Q1759577","display_name":"Matched filter","level":3,"score":0.2705000042915344},{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.2694000005722046},{"id":"https://openalex.org/C2988922011","wikidata":"https://www.wikidata.org/wiki/Q5449244","display_name":"Filtering theory","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C206833254","wikidata":"https://www.wikidata.org/wiki/Q5421817","display_name":"Extended Kalman filter","level":3,"score":0.26589998602867126},{"id":"https://openalex.org/C132094186","wikidata":"https://www.wikidata.org/wiki/Q641585","display_name":"Clutter","level":3,"score":0.26260000467300415},{"id":"https://openalex.org/C78548338","wikidata":"https://www.wikidata.org/wiki/Q2493","display_name":"Data compression","level":2,"score":0.26030001044273376},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.257099986076355},{"id":"https://openalex.org/C100515483","wikidata":"https://www.wikidata.org/wiki/Q3268235","display_name":"Filter bank","level":3,"score":0.2529999911785126},{"id":"https://openalex.org/C106516650","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm design","level":2,"score":0.25200000405311584},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.25049999356269836},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.25040000677108765}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lsp.2026.3674044","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2026.3674044","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"KalmanNet":[0,78],"demonstrates":[1],"potential":[2],"for":[3],"nonlinear":[4],"state":[5,106],"estimation,":[6],"but":[7],"it":[8],"directly":[9],"concatenates":[10],"heterogeneous":[11],"components":[12],"with":[13,61,75],"disparate":[14],"semantics":[15],"into":[16],"a":[17,46,71],"composite":[18],"vector.":[19],"This":[20],"approach":[21],"ignores":[22],"capturing":[23],"semantic":[24,53],"component":[25,54],"correlations,":[26],"limiting":[27],"the":[28,37,65,82,95,101],"network's":[29],"ability":[30],"to":[31,94],"utilize":[32],"this":[33],"information":[34],"when":[35],"computing":[36],"Kalman":[38,49],"gain.":[39],"To":[40],"address":[41],"this,":[42],"we":[43],"propose":[44],"CNPE-KalmanNet,":[45],"novel":[47],"learning-aided":[48],"filter":[50],"that":[51,87],"models":[52],"correlations":[55],"by":[56,103,110],"integrating":[57],"element-wise":[58],"rotary":[59],"encoding":[60],"multilayer":[62],"perceptrons":[63],"in":[64,105,112],"complex":[66],"domain.":[67],"CNPE":[68],"serves":[69],"as":[70],"plug-and-play":[72],"module":[73],"compatible":[74],"two":[76],"baseline":[77],"architectures.":[79],"Experiments":[80],"on":[81],"Michigan":[83],"NCLT":[84],"dataset":[85],"demonstrate":[86],"CNPE-KalmanNet":[88],"significantly":[89],"improves":[90],"estimation":[91,107],"accuracy.":[92],"Compared":[93],"existing":[96],"KalmanNet,":[97],"our":[98],"method":[99],"reduces":[100],"RMSE":[102],"20%-25%":[104],"tasks":[108],"and":[109],"15%-20%":[111],"sensor":[113],"fusion":[114],"tasks.":[115]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2026-03-14T00:00:00"}