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

arXiv: https://arxiv.org/abs/2411.19814 · HTML: https://mlsanity.com/paper/2411.19814/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 53 references that are in the map.
- First posted on arXiv 29 Nov 2024.

## Builds on (most cited first, 9 of 9)

- [Variational inference via Wasserstein gradient flows](https://mlsanity.com/paper/2205.15902/) (2022)
- [Generalized optimal sub-pattern assignment metric](https://mlsanity.com/paper/1601.05585/) (2016)
- [Poisson multi-Bernoulli mixture filter: direct derivation and implementation](https://mlsanity.com/paper/1703.04264/) (2017)
- [Trajectory Poisson multi-Bernoulli filters](https://mlsanity.com/paper/2003.12767/) (2020)
- [Poisson multi-Bernoulli conjugate prior for multiple extended object filtering](https://mlsanity.com/paper/1605.06311/) (2016)
- [Multi-Object Tracking using Poisson Multi-Bernoulli Mixture Filtering for Autonomous Vehicles](https://mlsanity.com/paper/2103.07783/) (2021)
- [An efficient, variational approximation of the best fitting multi-Bernoulli filter](https://mlsanity.com/paper/1403.5022/) (2014)
- [Iterative Statistical Linear Regression for Gaussian Smoothing in Continuous-Time Non-linear Stochastic Dynamic Systems](https://mlsanity.com/paper/1805.11258/) (2018)
- [Continuous-discrete multiple target tracking with out-of-sequence measurements](https://mlsanity.com/paper/2106.04898/) (2021)

## Abstract (arXiv)

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.