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The filter is constructed in a coordinate-invariant way, and explicitly takes into account the geometry of<jats:italic>SE<\/jats:italic>(3) and<jats:italic>P<\/jats:italic>(<jats:italic>n<\/jats:italic>), the space of symmetric positive definite matrices. Some basic results for bilinear systems on<jats:italic>SE<\/jats:italic>(3) with linear and quadratic measurements are also derived. Three examples\u2014GPS attitude estimation, needle tip location, and vision-based robot end-effector pose estimation\u2014are presented to illustrate the framework.<\/jats:p>","DOI":"10.1017\/s0263574707003529","type":"journal-article","created":{"date-parts":[[2007,6,27]],"date-time":"2007-06-27T09:22:58Z","timestamp":1182936178000},"page":"725-737","source":"Crossref","is-referenced-by-count":55,"title":["Particle filtering on the Euclidean group: framework and applications"],"prefix":"10.1017","volume":"25","author":[{"given":"Junghyun","family":"Kwon","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Minseok","family":"Choi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F. C.","family":"Park","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Changmook","family":"Chun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2007,11,1]]},"reference":[{"key":"S0263574707003529_ref10","doi-asserted-by":"crossref","unstructured":"10. Fletcher P. and Joshi S. , \u201cPrincipal Geodesic Analysis on Symmetric Spaces: Statistics of Diffusion Tensors,\u201d Proceedings of the ECCV'04 Workshop Computer Vision Approaches to Medical Image Analysis (2004), pp. 87\u201398.","DOI":"10.1007\/978-3-540-27816-0_8"},{"key":"S0263574707003529_ref40","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2003.809169"},{"key":"S0263574707003529_ref14","first-page":"1203","article-title":"A self-organizing state-space model","volume":"93","author":"Kitagawa","year":"1998","journal-title":"J. Amer. Statist. 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