In many multiobject tracking applications, including radar and sonar tracking, after prefiltering the received signal, measurement data is typically structured in cells. The cells, e.g., represent different range and bearing values. However, conventional multiobject tracking methods use so-called point measurements. Point measurements are provided by a preprocessing stage that applies a threshold or detector and breaks up the cell’s structure by converting cell indexes into, e.g., range and bearing measurements. We here propose a Bayesian multiobject tracking method that processes measurements that have been thresholded but are still cell-structured. We first derive a likelihood function that systematically incorporates an adjustable detection threshold which makes it possible to control the number of cell measurements. We then propose a Poisson Multi-Bernoulli (PMB) filter based on the likelihood function for cell measurements. Furthermore, we establish a link to the conventional point measurement model by deriving the likelihood function for point measurements with amplitude information (AM) and discuss the PMB filter that uses point measurements with AM. Our numerical results demonstrate the advantages of the proposed PMB filter for thresholded cell measurements compared to the conventional PMB filter for point measurements with and without AM.

This paper presents two multi-Bernoulli filters on sets of trajectories for multiple target tracking. The first filter provides a multi-Bernoulli approximation of the posterior density over the set of alive trajectories at the current time step. The second filter provides a multi-Bernoulli approximation of the posterior density over the set of all trajectories (alive and dead) up to the current time. We also explain the Gaussian implementation of the filters and compare them with other multiple target tracking algorithms in a simulated scenario.

In this paper we introduce spatiotemporal constraints for trajectories, i.e., restrictions that the trajectory must be in some part of the state space (spatial constraint) at some point in time (temporal constraint). Spatiotemporal contraints on trajectories can be used to answer a range of important questions, including, e.g., “where did the person that were in area A at time t, go afterwards?”. We discuss how multiple constraints can be combined into sets of constraints, and we then apply sets of constraints to set of trajectories densities, specifically Poisson Multi-Bernoulli Mixture (PMBM) densities. For Poisson target birth, the exact posterior density is PMBM for both point targets and extended targets. In the paper we show that if the unconstrained set of trajectories density is PMBM, then the constrained density is also PMBM. Examples of constrained trajectory densities motivate and illustrate the key results.

This paper presents a solution for recovering full trajectory information, via the calculation of the posterior of the set of trajectories, from a sequence of multitarget (unlabelled) filtering densities and the multitarget dynamic model. Importantly, the proposed solution opens an avenue of trajectory estimation possibilities for multitarget filters that do not explicitly estimate trajectories. In this paper, we first derive a general multitrajectory forward-backward smoothing equation based on sets of trajectories and the random finite set framework. Then we show how to sample sets of trajectories using backward simulation when the multitarget filtering densities are multi-Bernoulli processes. The proposed approach is demonstrated in a simulation study.

The Poisson multi-Bernoulli mixture (PMBM) is an unlabelled multi-target distribution for which the prediction and update are closed. It has a Poisson birth process, and new Bernoulli components are generated on each new measurement as a part of the Bayesian measurement update. The PMBM filter is similar to the multiple hypothesis tracker (MHT), but seemingly does not provide explicit continuity between time steps. This paper considers a recently developed formulation of the multi-target tracking problem as a random finite set (RFS) of trajectories, and derives two trajectory RFS filters, called PMBM trackers. The PMBM trackers efficiently estimate the set of trajectories, and share hypothesis structure with the PMBM filter. By showing that the prediction and update in the PMBM filter can be viewed as an efficient method for calculating the time marginals of the RFS of trajectories, continuity in the same sense as MHT is established for the PMBM filter.