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...

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Main Authors: Singh, S., Vo, Ba-Ngu, Baddeley, A., Zuyev, S.
Format: Journal Article
Published: Society for Industrial and Applied Mathematics 2009
Subjects:
Online Access:http://ba-ngu.vo-au.com/vo/SVBZ_SIAM.pdf
http://hdl.handle.net/20.500.11937/36974
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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.
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institution Curtin University Malaysia
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publishDate 2009
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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