{"id":"https://openalex.org/W2167292702","doi":"https://doi.org/10.4304/jcp.7.4.971-976","title":"Numerical Results of Nonlinear Filtering Problem from Yau-Yau Method","display_name":"Numerical Results of Nonlinear Filtering Problem from Yau-Yau Method","publication_year":2012,"publication_date":"2012-04-01","ids":{"openalex":"https://openalex.org/W2167292702","doi":"https://doi.org/10.4304/jcp.7.4.971-976","mag":"2167292702"},"language":"en","primary_location":{"id":"doi:10.4304/jcp.7.4.971-976","is_oa":false,"landing_page_url":"https://doi.org/10.4304/jcp.7.4.971-976","pdf_url":null,"source":{"id":"https://openalex.org/S77894049","display_name":"Journal of Computers","issn_l":"1796-203X","issn":["1796-203X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318660","host_organization_name":"Academy Publisher","host_organization_lineage":["https://openalex.org/P4310318660"],"host_organization_lineage_names":["Academy Publisher"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computers","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/A5100412083","display_name":"Zhen Liu","orcid":"https://orcid.org/0000-0003-0917-5475"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhen Liu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063930171","display_name":"Fangfang Dong","orcid":"https://orcid.org/0000-0003-2914-3227"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fangfang Dong","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5018937403","display_name":"Luwei Ding","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luwei Ding","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100412083"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6911,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.73870091,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"7","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9843999743461609,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9553999900817871,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.8683366775512695},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7254486083984375},{"id":"https://openalex.org/keywords/kolmogorov-equations","display_name":"Kolmogorov equations (Markov jump process)","score":0.6536791324615479},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5772861838340759},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5112776756286621},{"id":"https://openalex.org/keywords/filtering-problem","display_name":"Filtering problem","score":0.46406444907188416},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.43319568037986755},{"id":"https://openalex.org/keywords/kolmogorov-structure-function","display_name":"Kolmogorov structure function","score":0.4159635305404663},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3499391973018646},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19192183017730713},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.17061352729797363},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07421353459358215},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06588101387023926}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.8683366775512695},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7254486083984375},{"id":"https://openalex.org/C59465623","wikidata":"https://www.wikidata.org/wiki/Q6427428","display_name":"Kolmogorov equations (Markov jump process)","level":5,"score":0.6536791324615479},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5772861838340759},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5112776756286621},{"id":"https://openalex.org/C41614226","wikidata":"https://www.wikidata.org/wiki/Q5449244","display_name":"Filtering problem","level":4,"score":0.46406444907188416},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.43319568037986755},{"id":"https://openalex.org/C15995199","wikidata":"https://www.wikidata.org/wiki/Q5805968","display_name":"Kolmogorov structure function","level":3,"score":0.4159635305404663},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3499391973018646},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19192183017730713},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.17061352729797363},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07421353459358215},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06588101387023926},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2779341405","wikidata":"https://www.wikidata.org/wiki/Q1456811","display_name":"Kolmogorov complexity","level":2,"score":0.0},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.0},{"id":"https://openalex.org/C206833254","wikidata":"https://www.wikidata.org/wiki/Q5421817","display_name":"Extended Kalman filter","level":3,"score":0.0},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.4304/jcp.7.4.971-976","is_oa":false,"landing_page_url":"https://doi.org/10.4304/jcp.7.4.971-976","pdf_url":null,"source":{"id":"https://openalex.org/S77894049","display_name":"Journal of Computers","issn_l":"1796-203X","issn":["1796-203X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318660","host_organization_name":"Academy Publisher","host_organization_lineage":["https://openalex.org/P4310318660"],"host_organization_lineage_names":["Academy Publisher"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computers","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.845.1588","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.845.1588","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ojs.academypublisher.com/index.php/jcp/article/download/jcp0704971976/4670/","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1479099019","https://openalex.org/W1840194220","https://openalex.org/W1968152720","https://openalex.org/W1968199753","https://openalex.org/W1969855058","https://openalex.org/W1972585329","https://openalex.org/W1973928397","https://openalex.org/W1974139409","https://openalex.org/W1979105746","https://openalex.org/W1987388741","https://openalex.org/W1988745485","https://openalex.org/W1995041236","https://openalex.org/W1996374249","https://openalex.org/W2009987092","https://openalex.org/W2010905284","https://openalex.org/W2018295752","https://openalex.org/W2027837379","https://openalex.org/W2037500161","https://openalex.org/W2038775671","https://openalex.org/W2042602209","https://openalex.org/W2047912374","https://openalex.org/W2073880616","https://openalex.org/W2076365212","https://openalex.org/W2080273507","https://openalex.org/W2081051679","https://openalex.org/W2083402998","https://openalex.org/W2093688995","https://openalex.org/W2095440665","https://openalex.org/W2109557300","https://openalex.org/W2111103100","https://openalex.org/W2113328155","https://openalex.org/W2132012225","https://openalex.org/W2138277708","https://openalex.org/W2140426996","https://openalex.org/W2316272470","https://openalex.org/W2317540099","https://openalex.org/W2609181632","https://openalex.org/W2741850185","https://openalex.org/W2951273062","https://openalex.org/W2952267552","https://openalex.org/W4230217767"],"related_works":["https://openalex.org/W4360890123","https://openalex.org/W1546391260","https://openalex.org/W4298056523","https://openalex.org/W756244707","https://openalex.org/W4252389405","https://openalex.org/W636594073","https://openalex.org/W2548376734","https://openalex.org/W4246258635","https://openalex.org/W226726922","https://openalex.org/W59321076"],"abstract_inverted_index":{"Abstract":[0],"\u2014":[1],"In":[2],"the":[3,13,20,25,37,43,53,56,62,65,69,74,79,84],"paper,":[4],"we":[5,18,35],"introduce":[6],"a":[7],"kind":[8],"of":[9,55,64,68],"method":[10,40,81],"to":[11,31,41,50,61],"solve":[12,42],"nonlinear":[14],"filtering":[15,22,89],"problem.":[16],"Firstly,":[17],"review":[19],"basic":[21],"problem":[23,67],"and":[24],"reduction":[26],"from":[27],"robust":[28],"Duncan-Mortensen-Zakai":[29],"equation":[30,94],"Kolmogorov":[32,44,70,93],"equation.":[33,45,71],"Then":[34],"use":[36],"difference":[38,57],"discrete":[39],"The":[46],"result":[47],"is":[48],"given":[49],"prove":[51],"that":[52,78],"solution":[54,63],"scheme":[58],"convergences":[59],"pointwise":[60],"initial-value":[66],"At":[72],"last,":[73],"numerical":[75,80],"results":[76],"show":[77],"can":[82],"give":[83],"exact":[85],"result.":[86],"Index":[87],"Terms\u2014Nonlinear":[88],"equation,":[90,92],"DMZ":[91],"I.":[95]},"counts_by_year":[{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
