# Continuous-discrete multiple target tracking with out-of-sequence measurements

arXiv: https://arxiv.org/abs/2106.04898 · HTML: https://mlsanity.com/paper/2106.04898/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 43 references that are in the map.
- First posted on arXiv 9 Jun 2021.

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

- [Poisson multi-Bernoulli mixture filter: direct derivation and implementation](https://mlsanity.com/paper/1703.04264/) (2017)
- [A metric on the space of finite sets of trajectories for evaluation of multi-target tracking algorithms](https://mlsanity.com/paper/1605.01177/) (2016)
- [Multiple target tracking based on sets of trajectories](https://mlsanity.com/paper/1605.08163/) (2016)
- [Trajectory Poisson multi-Bernoulli filters](https://mlsanity.com/paper/2003.12767/) (2020)
- [Poisson multi-Bernoulli mixture trackers: continuity through random finite sets of trajectories](https://mlsanity.com/paper/1812.05131/) (2018)
- [Trajectory PHD and CPHD filters](https://mlsanity.com/paper/1811.08820/) (2018)
- [Multi-Scan Implementation of the Trajectory Poisson Multi-Bernoulli Mixture Filter](https://mlsanity.com/paper/1912.01748/) (2019)
- [Decentralized Poisson Multi-Bernoulli Filtering for Vehicle Tracking](https://mlsanity.com/paper/1901.04518/) (2019)
- [Spatiotemporal Constraints for Sets of Trajectories with Applications to PMBM Densities](https://mlsanity.com/paper/2002.12696/) (2020)

## Built on by (most cited first, 1 of 1)

- [Gaussian multi-target filtering with target dynamics driven by a stochastic differential equation](https://mlsanity.com/paper/2411.19814/) (2024)

## Abstract (arXiv)

This paper derives the optimal Bayesian processing of an out-of-sequence (OOS) set of measurements in continuous-time for multiple target tracking. We consider a multi-target system modelled in continuous time that is discretised at the time steps when we receive the measurements, which are distributed according to the standard point target model. All information about this system at the sampled time steps is provided by the posterior density on the set of all trajectories. This density can be computed via the continuous-discrete trajectory Poisson multi-Bernoulli mixture (TPMBM) filter. When we receive an OOS measurement, the optimal Bayesian processing performs a retrodiction step that adds trajectory information at the OOS measurement time stamp followed by an update step. After the OOS measurement update, the posterior remains in TPMBM form. We also provide a computationally lighter alternative based on a trajectory Poisson multi-Bernoulli filter. The effectiveness of the two approaches to handle OOS measurements is evaluated via simulations.