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 |
| Summary: | 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. |
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