{"id":"https://openalex.org/W4283763043","doi":"https://doi.org/10.3390/s22134970","title":"Tracking an Underwater Object with Unknown Sensor Noise Covariance Using Orthogonal Polynomial Filters","display_name":"Tracking an Underwater Object with Unknown Sensor Noise Covariance Using Orthogonal Polynomial Filters","publication_year":2022,"publication_date":"2022-06-30","ids":{"openalex":"https://openalex.org/W4283763043","doi":"https://doi.org/10.3390/s22134970","pmid":"https://pubmed.ncbi.nlm.nih.gov/35808465"},"language":"en","primary_location":{"id":"doi:10.3390/s22134970","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s22134970","pdf_url":"https://www.mdpi.com/1424-8220/22/13/4970/pdf?version=1657003070","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1424-8220/22/13/4970/pdf?version=1657003070","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068306473","display_name":"Kundan Kumar","orcid":"https://orcid.org/0000-0002-2977-8815"},"institutions":[{"id":"https://openalex.org/I132153292","display_name":"Indian Institute of Technology Patna","ror":"https://ror.org/01ft5vz71","country_code":"IN","type":"education","lineage":["https://openalex.org/I132153292"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Kundan Kumar","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Technology Patna, Patna 801103, India"],"raw_orcid":"https://orcid.org/0000-0002-2977-8815","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Technology Patna, Patna 801103, India","institution_ids":["https://openalex.org/I132153292"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071565438","display_name":"Shovan Bhaumik","orcid":"https://orcid.org/0000-0002-7980-9923"},"institutions":[{"id":"https://openalex.org/I132153292","display_name":"Indian Institute of Technology Patna","ror":"https://ror.org/01ft5vz71","country_code":"IN","type":"education","lineage":["https://openalex.org/I132153292"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Shovan Bhaumik","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Technology Patna, Patna 801103, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Technology Patna, Patna 801103, India","institution_ids":["https://openalex.org/I132153292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028610249","display_name":"Sanjeev Arulampalam","orcid":"https://orcid.org/0000-0003-3557-3258"},"institutions":[{"id":"https://openalex.org/I1303474014","display_name":"Defence Science and Technology Group","ror":"https://ror.org/05ddrvt52","country_code":"AU","type":"government","lineage":["https://openalex.org/I1303474014","https://openalex.org/I2801453606","https://openalex.org/I3139952251"]},{"id":"https://openalex.org/I5681781","display_name":"The University of Adelaide","ror":"https://ror.org/00892tw58","country_code":"AU","type":"education","lineage":["https://openalex.org/I5681781"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Sanjeev Arulampalam","raw_affiliation_strings":["Faculty of Engineering, Computer & Mathematical Sciences, The University of Adelaide, Adelaide, SA 5005, Australia","Maritime Division, Defence Science and Technology (DST) Group, Edinburgh, SA 5111, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Computer & Mathematical Sciences, The University of Adelaide, Adelaide, SA 5005, Australia","institution_ids":["https://openalex.org/I5681781"]},{"raw_affiliation_string":"Maritime Division, Defence Science and Technology (DST) Group, Edinburgh, SA 5111, Australia","institution_ids":["https://openalex.org/I1303474014"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5028610249"],"corresponding_institution_ids":["https://openalex.org/I1303474014","https://openalex.org/I5681781"],"apc_list":{"value":2400,"currency":"CHF","value_usd":2673},"apc_paid":{"value":2400,"currency":"CHF","value_usd":2673},"fwci":1.5083,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.84435078,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"22","issue":"13","first_page":"4970","last_page":"4970"},"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":1.0,"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":1.0,"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/T11192","display_name":"Underwater Vehicles and Communication Systems","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/T11698","display_name":"Underwater Acoustics Research","score":0.9925000071525574,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6101012229919434},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.5946838855743408},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5327781438827515},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.5116475224494934},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.4991004467010498},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.497835636138916},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.49270084500312805},{"id":"https://openalex.org/keywords/kalman-filter","display_name":"Kalman filter","score":0.4919435679912567},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.44776779413223267},{"id":"https://openalex.org/keywords/minimum-mean-square-error","display_name":"Minimum mean square error","score":0.438416063785553},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.4290081262588501},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34199702739715576},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.267591655254364},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12791365385055542},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11787381768226624}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6101012229919434},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5946838855743408},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5327781438827515},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5116475224494934},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.4991004467010498},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.497835636138916},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.49270084500312805},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.4919435679912567},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.44776779413223267},{"id":"https://openalex.org/C90652560","wikidata":"https://www.wikidata.org/wiki/Q11091747","display_name":"Minimum mean square error","level":3,"score":0.438416063785553},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.4290081262588501},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34199702739715576},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.267591655254364},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12791365385055542},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11787381768226624},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/s22134970","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s22134970","pdf_url":"https://www.mdpi.com/1424-8220/22/13/4970/pdf?version=1657003070","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors","raw_type":"journal-article"},{"id":"pmid:35808465","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35808465","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:dad7d5e407674eeea43edcc37ed71e12","is_oa":true,"landing_page_url":"https://doaj.org/article/dad7d5e407674eeea43edcc37ed71e12","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Sensors, Vol 22, Iss 13, p 4970 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1424-8220/22/13/4970/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/s22134970","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Sensors; Volume 22; Issue 13; Pages: 4970","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:9269813","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9269813","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Sensors (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/s22134970","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s22134970","pdf_url":"https://www.mdpi.com/1424-8220/22/13/4970/pdf?version=1657003070","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Life below water","score":0.8199999928474426,"id":"https://metadata.un.org/sdg/14"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4283763043.pdf","grobid_xml":"https://content.openalex.org/works/W4283763043.grobid-xml"},"referenced_works_count":51,"referenced_works":["https://openalex.org/W1503726741","https://openalex.org/W1540088375","https://openalex.org/W1574175273","https://openalex.org/W1855746731","https://openalex.org/W1901822353","https://openalex.org/W1924570469","https://openalex.org/W1966184693","https://openalex.org/W1980487656","https://openalex.org/W1982322007","https://openalex.org/W1996567593","https://openalex.org/W2002193010","https://openalex.org/W2014698533","https://openalex.org/W2033529017","https://openalex.org/W2043357888","https://openalex.org/W2048312361","https://openalex.org/W2054091988","https://openalex.org/W2085558428","https://openalex.org/W2099371695","https://openalex.org/W2100180525","https://openalex.org/W2101051269","https://openalex.org/W2106040279","https://openalex.org/W2106161781","https://openalex.org/W2108696877","https://openalex.org/W2121990344","https://openalex.org/W2126423185","https://openalex.org/W2140242774","https://openalex.org/W2140928899","https://openalex.org/W2146332636","https://openalex.org/W2189183289","https://openalex.org/W2249232467","https://openalex.org/W2556886647","https://openalex.org/W2737188128","https://openalex.org/W2744953120","https://openalex.org/W2769438230","https://openalex.org/W2782436561","https://openalex.org/W2796370545","https://openalex.org/W2896923686","https://openalex.org/W2941639077","https://openalex.org/W2966205082","https://openalex.org/W3011709223","https://openalex.org/W3017237243","https://openalex.org/W3156128252","https://openalex.org/W3160081959","https://openalex.org/W3214785359","https://openalex.org/W3217692928","https://openalex.org/W4205432086","https://openalex.org/W4239782249","https://openalex.org/W6655473528","https://openalex.org/W6681633639","https://openalex.org/W6697682879","https://openalex.org/W7000791799"],"related_works":["https://openalex.org/W2102148524","https://openalex.org/W2760382975","https://openalex.org/W2314720829","https://openalex.org/W2349716249","https://openalex.org/W1583991000","https://openalex.org/W2075897667","https://openalex.org/W2907746047","https://openalex.org/W3125536267","https://openalex.org/W2073909383","https://openalex.org/W2274645452"],"abstract_inverted_index":{"In":[0],"this":[1],"manuscript,":[2],"an":[3,83],"underwater":[4,133],"target":[5,19,63,190],"tracking":[6,134,206],"problem":[7],"with":[8,46,65,209,231],"passive":[9],"sensors":[10],"is":[11,35,52,105,119,129,146,182,222],"considered.":[12],"The":[13,75,100,126,143,216],"measurements":[14],"used":[15],"to":[16,37,112,131,224],"track":[17,158],"the":[18,57,62,66,79,90,93,122,178,185,189,196,205,210,219,225,232],"trajectories":[20],"are":[21,95],"(i)":[22,149],"only":[23],"bearing":[24,31],"angles,":[25],"and":[26,30,59,89,170,198],"(ii)":[27,155],"Doppler-shifted":[28],"frequencies":[29],"angles.":[32],"Measurement":[33],"noise":[34,48,69,103,201],"assumed":[36],"follow":[38],"a":[39,138,235],"zero":[40],"mean":[41,151],"Gaussian":[42],"probability":[43],"density":[44],"function":[45],"unknown":[47,67,101,197],"covariance.":[49],"A":[50],"method":[51,128,187,221],"developed":[53,127],"which":[54,136],"can":[55],"estimate":[56],"position":[58],"velocity":[60,141],"of":[61,86,92,157,212,218,234],"along":[64],"measurement":[68,81,200],"covariance":[70,104,202],"at":[71],"each":[72],"time":[73],"step.":[74],"proposed":[76,186,220],"estimator":[77],"linearises":[78],"nonlinear":[80],"using":[82,97,148],"orthogonal":[84],"polynomial":[85,94],"first":[87],"order,":[88],"coefficients":[91],"evaluated":[96,147],"numerical":[98],"integration.":[99],"sensor":[102],"estimated":[106],"online":[107],"from":[108,121],"residual":[109],"measurements.":[110,215],"Compared":[111],"available":[113],"adaptive":[114,226],"sigma":[115],"point":[116,173,229],"filters,":[117,230],"it":[118,181],"free":[120],"Cholesky":[123],"decomposition":[124],"error.":[125],"applied":[130],"two":[132],"scenarios":[135],"consider":[137],"nearly":[139],"constant":[140],"target.":[142],"filter's":[144],"efficacy":[145],"root":[150],"square":[152],"error":[153,164],"(RMSE),":[154],"percentage":[156],"loss,":[159],"(iii)":[160],"normalised":[161],"(state)":[162],"estimation":[163],"squared":[165],"(NEES),":[166],"(iv)":[167],"bias":[168],"norm,":[169],"(v)":[171],"floating":[172],"operations":[174],"(flops)":[175],"count.":[176],"From":[177],"simulation":[179],"results,":[180],"observed":[183],"that":[184],"tracks":[188],"in":[191],"both":[192],"scenarios,":[193],"even":[194],"for":[195],"time-varying":[199],"case.":[203],"Furthermore,":[204],"accuracy":[207],"increases":[208],"incorporation":[211],"Doppler":[213],"frequency":[214],"performance":[217],"comparable":[223],"deterministic":[227],"support":[228],"advantage":[233],"considerably":[236],"reduced":[237],"flops":[238],"requirement.":[239]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}