{"id":"https://openalex.org/W2035411603","doi":"https://doi.org/10.1109/acc.2013.6580197","title":"Efficient deterministic dirac mixture approximation of Gaussian distributions","display_name":"Efficient deterministic dirac mixture approximation of Gaussian distributions","publication_year":2013,"publication_date":"2013-06-01","ids":{"openalex":"https://openalex.org/W2035411603","doi":"https://doi.org/10.1109/acc.2013.6580197","mag":"2035411603"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2013.6580197","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2013.6580197","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 American Control Conference","raw_type":"proceedings-article"},"type":"conference-paper","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/A5078356081","display_name":"Igor Gilitschenski","orcid":"https://orcid.org/0000-0001-6426-365X"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Igor Gilitschenski","raw_affiliation_strings":["Intelligent Sensor-Actuator-Systems Laboratory (ISAS), Institute for Anthropomatics, Karlsruhe Institute of Technology, Germany","Intell. Sensor-Actuator-Syst. Lab. (ISAS), Karlsruhe Inst. of Technol. (KIT), Karlsruhe, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Intelligent Sensor-Actuator-Systems Laboratory (ISAS), Institute for Anthropomatics, Karlsruhe Institute of Technology, Germany","institution_ids":["https://openalex.org/I102335020"]},{"raw_affiliation_string":"Intell. Sensor-Actuator-Syst. Lab. (ISAS), Karlsruhe Inst. of Technol. (KIT), Karlsruhe, Germany","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055331421","display_name":"Uwe D. Hanebeck","orcid":"https://orcid.org/0000-0001-9870-2331"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Uwe D. Hanebeck","raw_affiliation_strings":["Intelligent Sensor-Actuator-Systems Laboratory (ISAS), Institute for Anthropomatics, Karlsruhe Institute of Technology, Germany","Intell. Sensor-Actuator-Syst. Lab. (ISAS), Karlsruhe Inst. of Technol. (KIT), Karlsruhe, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Intelligent Sensor-Actuator-Systems Laboratory (ISAS), Institute for Anthropomatics, Karlsruhe Institute of Technology, Germany","institution_ids":["https://openalex.org/I102335020"]},{"raw_affiliation_string":"Intell. Sensor-Actuator-Syst. Lab. (ISAS), Karlsruhe Inst. of Technol. (KIT), Karlsruhe, Germany","institution_ids":["https://openalex.org/I102335020"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I102335020"],"apc_list":null,"apc_paid":null,"fwci":2.0593,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.88192535,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"2422","last_page":"2427"},"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":0.9984999895095825,"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":0.9984999895095825,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9983000159263611,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.992900013923645,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.6902798414230347},{"id":"https://openalex.org/keywords/cumulative-distribution-function","display_name":"Cumulative distribution function","score":0.6846320629119873},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.6457628607749939},{"id":"https://openalex.org/keywords/dirac","display_name":"Dirac (video compression format)","score":0.5828871130943298},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5803427696228027},{"id":"https://openalex.org/keywords/von-mises-distribution","display_name":"von Mises distribution","score":0.5422784090042114},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5217893123626709},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.503102719783783},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4823690950870514},{"id":"https://openalex.org/keywords/multivariate-normal-distribution","display_name":"Multivariate normal distribution","score":0.4784548282623291},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.45762547850608826},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.45176154375076294},{"id":"https://openalex.org/keywords/dirac-measure","display_name":"Dirac measure","score":0.4172181487083435},{"id":"https://openalex.org/keywords/von-mises-yield-criterion","display_name":"von Mises yield criterion","score":0.34785550832748413},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.30404675006866455},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2071843445301056},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19012564420700073},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17215311527252197},{"id":"https://openalex.org/keywords/dirac-equation","display_name":"Dirac equation","score":0.1571328043937683},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.12294894456863403},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.07687973976135254}],"concepts":[{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.6902798414230347},{"id":"https://openalex.org/C103784038","wikidata":"https://www.wikidata.org/wiki/Q386228","display_name":"Cumulative distribution function","level":3,"score":0.6846320629119873},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6457628607749939},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.5828871130943298},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5803427696228027},{"id":"https://openalex.org/C198138136","wikidata":"https://www.wikidata.org/wiki/Q7941490","display_name":"von Mises distribution","level":4,"score":0.5422784090042114},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5217893123626709},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.503102719783783},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4823690950870514},{"id":"https://openalex.org/C177384507","wikidata":"https://www.wikidata.org/wiki/Q1149000","display_name":"Multivariate normal distribution","level":3,"score":0.4784548282623291},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.45762547850608826},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.45176154375076294},{"id":"https://openalex.org/C111118313","wikidata":"https://www.wikidata.org/wiki/Q1227387","display_name":"Dirac measure","level":5,"score":0.4172181487083435},{"id":"https://openalex.org/C155165730","wikidata":"https://www.wikidata.org/wiki/Q1319519","display_name":"von Mises yield criterion","level":3,"score":0.34785550832748413},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.30404675006866455},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2071843445301056},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19012564420700073},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17215311527252197},{"id":"https://openalex.org/C82601208","wikidata":"https://www.wikidata.org/wiki/Q272621","display_name":"Dirac equation","level":2,"score":0.1571328043937683},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12294894456863403},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.07687973976135254},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C149545384","wikidata":"https://www.wikidata.org/wiki/Q5280160","display_name":"Dirac algebra","level":3,"score":0.0},{"id":"https://openalex.org/C156785651","wikidata":"https://www.wikidata.org/wiki/Q688945","display_name":"Dirac spinor","level":4,"score":0.0},{"id":"https://openalex.org/C186453547","wikidata":"https://www.wikidata.org/wiki/Q2126","display_name":"Neutrino","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2013.6580197","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2013.6580197","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W2008149271","https://openalex.org/W2009104157","https://openalex.org/W2012940290","https://openalex.org/W2042138306","https://openalex.org/W2099502403","https://openalex.org/W2105934661","https://openalex.org/W2121360982","https://openalex.org/W2123487311","https://openalex.org/W2124665963","https://openalex.org/W2136661846","https://openalex.org/W2145938889","https://openalex.org/W2160337655","https://openalex.org/W4300223101"],"related_works":["https://openalex.org/W1849160524","https://openalex.org/W3100559232","https://openalex.org/W2090246884","https://openalex.org/W2148833582","https://openalex.org/W2169980973","https://openalex.org/W2004510682","https://openalex.org/W2051615645","https://openalex.org/W2968610876","https://openalex.org/W2035411603","https://openalex.org/W3203308283"],"abstract_inverted_index":{"We":[0],"propose":[1],"an":[2],"efficient":[3],"method":[4],"for":[5,45,74,95],"approximating":[6],"arbitrary":[7],"Gaussian":[8],"densities":[9],"by":[10,36],"a":[11,43,57,61,96],"mixture":[12],"of":[13,23,56,66,91],"Dirac":[14,93],"components.":[15],"This":[16],"approach":[17],"is":[18,30,83],"based":[19],"on":[20],"the":[21,24,33,46,52,67,89,92],"modification":[22,65],"classical":[25],"Cram\u00e9r-von":[26,68],"Mises":[27,69],"distance,":[28],"which":[29],"adapted":[31],"to":[32,87],"multivariate":[34],"scenario":[35],"using":[37],"Localized":[38],"Cumulative":[39],"Distributions":[40],"(LCDs)":[41],"as":[42],"replacement":[44],"cumulative":[47],"distribution":[48],"function.":[49],"LCDs":[50],"consider":[51],"local":[53],"probabilistic":[54],"influence":[55],"probability":[58],"density":[59],"around":[60],"given":[62],"point.":[63],"Our":[64],"distance":[70],"can":[71],"be":[72],"approximated":[73],"certain":[75],"special":[76],"cases":[77],"in":[78,85],"closed-form.":[79],"The":[80],"created":[81],"measure":[82],"minimized":[84],"order":[86],"compute":[88],"positions":[90],"components":[94],"standard":[97],"normal":[98],"distribution.":[99]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}