Gaussian multi-target filtering with target dynamics driven by a stochastic differential equation
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917924164337664 |
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| author | García-Fernández, Ángel F. Särkkä, Simo |
| author_facet | García-Fernández, Ángel F. Särkkä, Simo |
| contents | This paper proposes multi-target filtering algorithms in which target dynamics are given in continuous time and measurements are obtained at discrete time instants. In particular, targets appear according to a Poisson point process (PPP) in time with a given Gaussian spatial distribution, targets move according to a general time-invariant linear stochastic differential equation, and the life span of each target is modelled with an exponential distribution. For this multi-target dynamic model, we derive the distribution of the set of new born targets and calculate closed-form expressions for the best fitting mean and covariance of each target at its time of birth by minimising the Kullback-Leibler divergence via moment matching. This yields a novel Gaussian continuous-discrete Poisson multi-Bernoulli mixture (PMBM) filter, and its approximations based on Poisson multi-Bernoulli and probability hypothesis density filtering. These continuous-discrete multi-target filters are also extended to target dynamics driven by nonlinear stochastic differential equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19814 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gaussian multi-target filtering with target dynamics driven by a stochastic differential equation García-Fernández, Ángel F. Särkkä, Simo Computer Vision and Pattern Recognition Signal Processing Probability Computation This paper proposes multi-target filtering algorithms in which target dynamics are given in continuous time and measurements are obtained at discrete time instants. In particular, targets appear according to a Poisson point process (PPP) in time with a given Gaussian spatial distribution, targets move according to a general time-invariant linear stochastic differential equation, and the life span of each target is modelled with an exponential distribution. For this multi-target dynamic model, we derive the distribution of the set of new born targets and calculate closed-form expressions for the best fitting mean and covariance of each target at its time of birth by minimising the Kullback-Leibler divergence via moment matching. This yields a novel Gaussian continuous-discrete Poisson multi-Bernoulli mixture (PMBM) filter, and its approximations based on Poisson multi-Bernoulli and probability hypothesis density filtering. These continuous-discrete multi-target filters are also extended to target dynamics driven by nonlinear stochastic differential equations. |
| title | Gaussian multi-target filtering with target dynamics driven by a stochastic differential equation |
| topic | Computer Vision and Pattern Recognition Signal Processing Probability Computation |
| url | https://arxiv.org/abs/2411.19814 |