{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:42:02Z","timestamp":1787319722875,"version":"build-2736575974"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2009,1]]},"abstract":"We study the general problem of estimating a \u201chidden\u201d point process $\\mathbf{X}$, given the realization of an \u201cobserved\u201d point process $\\mathbf{Y}$ (possibly defined in different spaces) with known joint distribution. We characterize the posterior distribution of $\\mathbf{X}$ under marginal Poisson and Gauss\u2013Poisson priors and when the transformation from $\\mathbf{X}$ to $\\mathbf{Y}$ includes thinning, displacement, and augmentation with extra points. These results are then applied in a filtering context when the hidden process evolves in discrete time in a Markovian fashion. The dynamics of $\\mathbf{X}$ considered are general enough for many target tracking applications.<\/jats:p>","DOI":"10.1137\/070710457","type":"journal-article","created":{"date-parts":[[2009,6,25]],"date-time":"2009-06-25T18:04:45Z","timestamp":1245953085000},"page":"2275-2295","source":"Crossref","is-referenced-by-count":43,"title":["Filters for Spatial Point Processes"],"prefix":"10.1137","volume":"48","author":[{"given":"Sumeetpal S.","family":"Singh","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ba-Ngu","family":"Vo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Adrian","family":"Baddeley","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sergei","family":"Zuyev","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,6,25]]},"reference":[{"key":"R1","unstructured":"B. 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