Gaussian multi-target filtering with target dynamics driven by a stochastic differential equation

• URL: http://arxiv.org/abs/2411.19814v2
• Date: Sun, 16 Feb 2025 12:12:28 GMT
• Title: Gaussian multi-target filtering with target dynamics driven by a stochastic differential equation
• Authors: Ángel F. García-Fernández, Simo Särkkä,
• Abstract summary: This paper proposes multi-target filtering algorithms in which target dynamics are given in continuous time and measurements are obtained at discrete time instants. 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. These continuous-discrete multi-target filters are also extended to target dynamics driven by nonlinear differential equations.
• Score: 10.318269780721444
• License:
• Abstract: 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.

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