{"id":"https://openalex.org/W7222830451","doi":"https://doi.org/10.1038/s41598-026-74305-w","title":"An integrated bidirectional LSTM and adaptive cubature Kalman filter estimation method for accurate state-of-charge estimation of lithium-ion battery","display_name":"An integrated bidirectional LSTM and adaptive cubature Kalman filter estimation method for accurate state-of-charge estimation of lithium-ion battery","publication_year":2026,"publication_date":"2026-10-17","ids":{"openalex":"https://openalex.org/W7222830451","doi":"https://doi.org/10.1038/s41598-026-74305-w"},"language":"en","primary_location":{"id":"doi:10.1038/s41598-026-74305-w","doi":"https://doi.org/10.1038/s41598-026-74305-w","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-026-74305-w","pdf_url":"https://www.nature.com/articles/s41598-026-74305-w_reference.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.nature.com/articles/s41598-026-74305-w_reference.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5107512530","display_name":"Jayakara Babu Kondru","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I876193797","display_name":"Vellore Institute of Technology University","ror":"https://ror.org/00qzypv28","country_code":"IN","type":"education","lineage":["https://openalex.org/I876193797"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Jayakara Babu Kondru","raw_affiliation_strings":["School of Electrical Engineering, Vellore Institute of Technology, Vellore, 632014, Tamil Nadu, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Vellore Institute of Technology, Vellore, 632014, Tamil Nadu, India","institution_ids":["https://openalex.org/I876193797"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090661505","display_name":"Y. P. Obulesu","orcid":"https://orcid.org/0000-0003-0272-8399","observed_orcids":["https://orcid.org/0000-0003-0272-8399","https://orcid.org/0009-0003-9404-6500"]},"institutions":[{"id":"https://openalex.org/I876193797","display_name":"Vellore Institute of Technology University","ror":"https://ror.org/00qzypv28","country_code":"IN","type":"education","lineage":["https://openalex.org/I876193797"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Yeddula Pedda Obulesu","raw_affiliation_strings":["School of Electrical Engineering, Vellore Institute of Technology, Vellore, 632014, Tamil Nadu, India"],"raw_orcid":"https://orcid.org/0009-0003-9404-6500","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Vellore Institute of Technology, Vellore, 632014, Tamil Nadu, India","institution_ids":["https://openalex.org/I876193797"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5090661505"],"corresponding_institution_ids":["https://openalex.org/I876193797"],"apc_list":{"value":2690,"currency":"USD","value_usd":2690},"apc_paid":{"value":2690,"currency":"USD","value_usd":2690},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.69269112,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T10663","display_name":"Battery Modeling and Management","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive 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/T10663","display_name":"Battery Modeling and Management","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive 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":0.00019999999494757503,"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/T10018","display_name":"Advancements in Battery Materials","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/lithium-ion-batteries","display_name":"lithium-ion batteries","score":0.859000027179718},{"id":"https://openalex.org/keywords/state-of-charge-estimation","display_name":"state of charge estimation","score":0.9990000128746033},{"id":"https://openalex.org/keywords/bidirectional-lstm","display_name":"bidirectional LSTM","score":0.9919999837875366},{"id":"https://openalex.org/keywords/adaptive-cubature-kalman-filter","display_name":"adaptive cubature Kalman filter","score":0.9940000176429749},{"id":"https://openalex.org/keywords/thevenin-equivalent-circuit-model","display_name":"Thevenin equivalent circuit model","score":0.8600000143051147},{"id":"https://openalex.org/keywords/open-circuit-voltage","display_name":"open-circuit voltage","score":0.6129999756813049},{"id":"https://openalex.org/keywords/driving-cycles","display_name":"driving cycles","score":0.7039999961853027},{"id":"https://openalex.org/keywords/temperature-effects","display_name":"temperature effects","score":0.7889999747276306},{"id":"https://openalex.org/keywords/sensor-noise-robustness","display_name":"sensor noise robustness","score":0.7379999756813049}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6938999891281128},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5943999886512756},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5871999859809875},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5368000268936157},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.5232999920845032},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.48500001430511475},{"id":"https://openalex.org/C206833254","wikidata":"https://www.wikidata.org/wiki/Q5421817","display_name":"Extended Kalman filter","level":3,"score":0.4756999909877777},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.475600004196167},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46369999647140503},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.46320000290870667},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.4007999897003174},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.3695000112056732},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.3513000011444092},{"id":"https://openalex.org/C79334102","wikidata":"https://www.wikidata.org/wiki/Q3072268","display_name":"Ensemble Kalman filter","level":4,"score":0.3407999873161316},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.3312999904155731},{"id":"https://openalex.org/C83042196","wikidata":"https://www.wikidata.org/wiki/Q5178898","display_name":"Covariance intersection","level":4,"score":0.3190000057220459},{"id":"https://openalex.org/C540940223","wikidata":"https://www.wikidata.org/wiki/Q241868","display_name":"Th\u00e9venin's theorem","level":4,"score":0.3151000142097473},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3138999938964844},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.30730000138282776},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.29840001463890076},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.28780001401901245},{"id":"https://openalex.org/C8639503","wikidata":"https://www.wikidata.org/wiki/Q6059511","display_name":"Invariant extended Kalman filter","level":4,"score":0.2768000066280365},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.2759000062942505},{"id":"https://openalex.org/C102392041","wikidata":"https://www.wikidata.org/wiki/Q592860","display_name":"Sliding window protocol","level":3,"score":0.27160000801086426},{"id":"https://openalex.org/C29265498","wikidata":"https://www.wikidata.org/wiki/Q7047719","display_name":"Noise measurement","level":3,"score":0.266400009393692},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.26109999418258667},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.25270000100135803}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1038/s41598-026-74305-w","doi":"https://doi.org/10.1038/s41598-026-74305-w","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-026-74305-w","pdf_url":"https://www.nature.com/articles/s41598-026-74305-w_reference.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1038/s41598-026-74305-w","doi":"https://doi.org/10.1038/s41598-026-74305-w","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-026-74305-w","pdf_url":"https://www.nature.com/articles/s41598-026-74305-w_reference.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.8980000019073486,"display_name":"Affordable and clean energy"}],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322838","display_name":"VIT University","ror":"https://ror.org/00qzypv28"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7222830451.pdf","grobid_xml":"https://content.openalex.org/works/W7222830451.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3009664539","https://openalex.org/W2164985362","https://openalex.org/W2784324669","https://openalex.org/W2969296408","https://openalex.org/W7129504448","https://openalex.org/W2966463151","https://openalex.org/W4417310154","https://openalex.org/W4389251431","https://openalex.org/W4411408529","https://openalex.org/W4407466295"],"abstract_inverted_index":{"Abstract":[0],"Model-based":[1],"observers":[2],"for":[3],"lithium-ion":[4],"battery":[5],"state-of-charge":[6],"(SOC)":[7],"estimation":[8],"lose":[9],"accuracy":[10],"under":[11,67,176],"strong":[12],"nonlinearities":[13],"and":[14,24,60,120,148,186,206,215,218,241,264,281],"sensor":[15],"noise,":[16],"while":[17],"purely":[18],"data-driven":[19,158],"estimators":[20],"lack":[21],"physical":[22],"consistency":[23],"generalise":[25],"poorly":[26],"outside":[27],"their":[28],"training":[29],"distribution.":[30],"Existing":[31],"hybrid":[32],"designs":[33],"address":[34],"this":[35],"gap":[36],"only":[37],"partially:":[38],"neural-network":[39],"outputs":[40],"are":[41],"typically":[42],"fused":[43],"with":[44,198],"an":[45,128],"Extended":[46],"Kalman":[47,82],"Filter":[48,83],"(EKF)":[49],"as":[50,100],"a":[51,74,101,108,167,255,267,295],"loosely":[52],"coupled":[53,76],"correction":[54],"term,":[55],"so":[56,111],"first-order":[57,173],"linearisation":[58,165],"error":[59,290],"static":[61],"noise":[62,137,225],"statistics":[63],"still":[64],"limit":[65],"performance":[66],"aggressive":[68],"drive":[69],"cycles.":[70],"This":[71],"paper":[72],"proposes":[73],"tightly":[75],"Bidirectional":[77],"Long":[78],"Short-Term":[79],"Memory-Adaptive":[80],"Cubature":[81],"(BiLSTM-ACKF)":[84],"framework":[85],"that":[86,246],"resolves":[87],"these":[88],"limitations":[89],"through":[90],"three":[91,209],"distinct":[92],"mechanisms.":[93],"First,":[94],"the":[95,112,124,135,141,145,149,153,157,193,237,251],"BiLSTM":[96,146,253],"output":[97,147],"is":[98,114,121],"reformulated":[99],"scalar":[102],"pseudo-measurement":[103],"of":[104,123,184,221,257,269,285,299],"SOC,":[105,151],"rather":[106],"than":[107,262,274,301],"terminal-voltage":[109],"correction,":[110],"innovation":[113],"expressed":[115],"directly":[116],"in":[117,156,166],"SOC":[118],"units":[119],"independent":[122],"open-circuit-voltage-SOC":[125],"slope.":[126],"Second,":[127],"innovation-driven":[129],"adaptive":[130],"covariance":[131,138],"law":[132],"continuously":[133],"re-weights":[134],"measurement":[136],"according":[139],"to":[140,191,289],"real-time":[142],"agreement":[143],"between":[144],"model-predicted":[150],"self-regulating":[152],"filter\u2019s":[154],"trust":[155],"channel.":[159],"Third,":[160],"cubature-point":[161],"propagation":[162],"replaces":[163],"Jacobian":[164],"single-RC":[168],"Thevenin":[169],"equivalent-circuit":[170],"model,":[171],"eliminating":[172],"truncation":[174],"bias":[175],"strongly":[177],"nonlinear":[178],"transients.":[179],"A":[180],"sliding":[181],"window":[182],"sequence":[183],"voltage":[185,224],"current":[187],"measurements":[188],"were":[189],"used":[190],"train":[192],"BiLSTM.":[194],"Validation":[195],"was":[196],"conducted":[197],"four":[199,278],"different":[200],"driving":[201,279],"cycles":[202,280],"(DST,":[203],"FUDS,":[204],"UDDS":[205],"US06),":[207],"at":[208],"temperatures":[210],"(5\u00b0":[211],"C,":[212],"25\u00b0":[213],"C":[214],"45\u00b0":[216],"C),":[217],"six":[219,283],"levels":[220,284],"Gaussian":[222],"white":[223],"(0":[226],"mV,":[227,229],"30":[228],"80":[230],"mV)":[231],"using":[232],"two":[233],"datasets":[234],"provided":[235],"by":[236],"TU-Berlin":[238],"repository":[239],"(LA92":[240],"US06).":[242],"Comparison":[243],"results":[244],"show":[245],"BiLSTM-ACKF":[247,292],"significantly":[248],"outperformed":[249],"both":[250],"stand-alone":[252],"(with":[254,266],"range":[256,268],"40\u201360%":[258],"lower":[259,271],"RMSE":[260,272],"values":[261,273],"BiLSTM)":[263],"BiLSTM-AEKF":[265],"30\u201352%":[270],"BiLSTM-AEKF)":[275],"across":[276],"all":[277,282,304],"noise.":[286],"With":[287],"respect":[288],"magnitude,":[291],"also":[293],"demonstrated":[294],"consistent":[296],"upper":[297],"bound":[298],"less":[300],"1.5%":[302],"over":[303],"test":[305],"cases.":[306]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-18T00:00:00"}