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We also introduce a Markov chain Monte Carlo resampling method to address the degeneracy problem of the adaptive space points. Numerical experiments are carried out against the auxiliary particle filter method in the rugged double well potential problem as well as the multitarget tracking problem to demonstrate the superior performance of our algorithm.<\/jats:p>","DOI":"10.1137\/16m1100277","type":"journal-article","created":{"date-parts":[[2017,11,28]],"date-time":"2017-11-28T13:15:30Z","timestamp":1511874930000},"page":"A2664-A2683","source":"Crossref","is-referenced-by-count":24,"title":["Adaptive Meshfree Backward SDE Filter"],"prefix":"10.1137","volume":"39","author":[{"given":"Feng","family":"Bao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vasileios","family":"Maroulas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,11,28]]},"reference":[{"key":"atypb1","volume-title":"Optimal Filtering","author":"Anderson B.","year":"2005"},{"key":"atypb2","volume-title":"Forward Backward Doubly Stochastic Differential Equations and Optimal Filtering of Diffusion Processes, arXiv:1509.06352","author":"Bao F.","year":"2015"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/140952910"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2015.20.1297"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/14095546X"},{"key":"atypb6","volume-title":"Math. 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