Filters for Spatial point Processes
Let X and Y be two jointly distributed spatial Point Processes on X and Y respectively (both complete separable metric spaces). We address the problem of estimating X, which is the hidden Point Process (PP), given the realisation y of the observed PP Y. We characterise the posterior distribution of...
| Main Authors: | , , , |
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| Format: | Journal Article |
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Society for Industrial and Applied Mathematics
2009
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| Subjects: | |
| Online Access: | http://ba-ngu.vo-au.com/vo/SVBZ_SIAM.pdf http://hdl.handle.net/20.500.11937/36974 |
| _version_ | 1848754919840940032 |
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| author | Singh, S. Vo, Ba-Ngu Baddeley, A. Zuyev, S. |
| author_facet | Singh, S. Vo, Ba-Ngu Baddeley, A. Zuyev, S. |
| author_sort | Singh, S. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Let X and Y be two jointly distributed spatial Point Processes on X and Y respectively (both complete separable metric spaces). We address the problem of estimating X, which is the hidden Point Process (PP), given the realisation y of the observed PP Y. We characterise the posterior distribution of X when it is marginally distributed according to a Poisson and Gauss-Poisson prior and when the transformation from X to 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 X considered are general enough for many target tracking applications. |
| first_indexed | 2025-11-14T08:48:04Z |
| format | Journal Article |
| id | curtin-20.500.11937-36974 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:48:04Z |
| publishDate | 2009 |
| publisher | Society for Industrial and Applied Mathematics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-369742017-01-30T13:58:50Z Filters for Spatial point Processes Singh, S. Vo, Ba-Ngu Baddeley, A. Zuyev, S. PHD filter target tracking online filtering hidden point process inference Poisson point process prior Gauss-Poisson point process Let X and Y be two jointly distributed spatial Point Processes on X and Y respectively (both complete separable metric spaces). We address the problem of estimating X, which is the hidden Point Process (PP), given the realisation y of the observed PP Y. We characterise the posterior distribution of X when it is marginally distributed according to a Poisson and Gauss-Poisson prior and when the transformation from X to 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 X considered are general enough for many target tracking applications. 2009 Journal Article http://hdl.handle.net/20.500.11937/36974 http://ba-ngu.vo-au.com/vo/SVBZ_SIAM.pdf Society for Industrial and Applied Mathematics fulltext |
| spellingShingle | PHD filter target tracking online filtering hidden point process inference Poisson point process prior Gauss-Poisson point process Singh, S. Vo, Ba-Ngu Baddeley, A. Zuyev, S. Filters for Spatial point Processes |
| title | Filters for Spatial point Processes |
| title_full | Filters for Spatial point Processes |
| title_fullStr | Filters for Spatial point Processes |
| title_full_unstemmed | Filters for Spatial point Processes |
| title_short | Filters for Spatial point Processes |
| title_sort | filters for spatial point processes |
| topic | PHD filter target tracking online filtering hidden point process inference Poisson point process prior Gauss-Poisson point process |
| url | http://ba-ngu.vo-au.com/vo/SVBZ_SIAM.pdf http://hdl.handle.net/20.500.11937/36974 |