This paper uses multi-object tracking methods known from the radar tracking community to address the problem of pedestrian tracking using 2D bounding box detections. The standard point-object (SPO) model is adopted, and the posterior density is computed using the Poisson multi-Bernoulli mixture (PMBM) filter. The selection of the model parameters rooted in continuous time is discussed, including the birth and survival probabilities. Some parameters are selected from the first principles, while others are identified from the data, which is, in this case, the publicly available MOT-17 dataset. Although the resulting PMBM algorithm yields promising results, a mismatch between the SPO model and the data is revealed. The model-based approach assumes that modifying the problematic components causing the SPO model-data mismatch will lead to better modelbased algorithms in future developments.

This paper presents an efficient implementation of the trajectory Poisson multi-Bernoulli (PMB) filter for multiple extended object tracking (EOT), which directly estimates a set of object trajectories. The trajectory PMB filter propagates a PMB density on the posterior of sets of trajectories through the filtering recursions over time, where the multi-Bernoulli (MB) mixture in the PMB mixture (PMBM) posterior after each update step is approximated as a single MB. The efficient MB approximation is achieved by first running a blocked Gibbs sampler on the joint posterior of the set of trajectories and the measurement association variables. The single-object measurement model is assumed to be a Poisson point process which enables us to parallelize the sampling across all objects and association variables, respectively. Then, samples of object states are utilized to form the approximate MB density via Kullback-Leibler divergence minimization. Simulation results on EOT with known and constant elliptical shapes show that the TPMB implementation using blocked Gibbs sampling outperforms the state-of-the-art TPMB implementation using loopy belief propagation with significantly reduced runtime.

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.

This paper presents the probability hypothesis density (PHD) filter for sets of trajectories: the trajectory probability density (TPHD) filter. The TPHD filter is capable of estimating trajectories in a principled way without requiring to evaluate all measurement-to-target association hypotheses. The TPHD filter is based on recursively obtaining the best Poisson approximation to the multitrajectory filtering density in the sense of minimising the Kullback-Leibler divergence. We also propose a Gaussian mixture implementation of the TPHD recursion. Finally, we include simulation results to show the performance of the proposed algorithm.

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.

This paper proposes an efficient implementation of the Poisson multi-Bernoulli mixture (PMBM) trajectory filter. The proposed implementation performs track-oriented N-scan pruning to limit complexity, and uses dual decomposition to solve the involved multi-frame assignment problem. In contrast to the existing PMBM filter for sets of targets, the PMBM trajectory filter is based on sets of trajectories which ensures that track continuity is formally maintained. The resulting filter is an efficient and scalable approximation to a Bayes optimal multi-target tracking algorithm, and its performance is compared, in a simulation study, to the PMBM target filter, and the delta generalized labelled multi-Bernoulli filter, in terms of state/trajectory estimation error and computational time.

This paper presents the generalized optimal sub-pattern assignment (GOSPA) metric on the space of finite sets of targets. Compared to the well-established optimal sub-pattern assignment (OSPA) metric, GOSPA is not normalised by the cardinality of the largest set and it penalizes cardinality errors differently, which enables us to express it as an optimisation over assignments instead of permutations. An important consequence of this is that GOSPA allows us to penalize localization errors for detected targets and the errors due to missed and false targets, as indicated by traditional multiple target tracking (MTT) performance measures, in a sound manner. In addition, we extend the GOSPA metric to the space of random finite sets, which is important to evaluate MTT algorithms via simulations in a rigorous way.

In this paper, we evaluate the performance of labelled and unlabelled multi-Bernoulli conjugate priors for multi-target filtering. Filters are compared in two different scenarios with performance assessed using the generalised optimal sub-pattern assignment (GOSPA) metric. The first scenario under consideration is tracking of well-spaced targets. The second scenario is more challenging and considers targets in close proximity, for which filters may suffer from coalescence. We analyse various aspects of the filters in these two scenarios. Though all filters have pros and cons, the Poisson multi-Bernoulli filters arguably provide the best overall performance concerning GOSPA and computational time.

The interacting multiple model filter has long been the preferred method to handle multiple models in target tracking. The filter finds a suboptimal solution to a problem, which implicitly assumes that immediate model shifts have the highest probability. We argue that this model-shift property does not capture the typical nature of maneuvering targets, namely that changes in target dynamics persist for some time. In this paper, we propose an adjusted switch time assumption that forces the dynamic models to remain fixed for a specified time. The modified filtering problem has lower complexity, and we derive a state estimation algorithm that is close to optimal in many scenarios. From Monte Carlo simulations, the new filter is found to yield a 20% decrease in root mean square position error, compared to the interacting multiple model filter in situations where the switch-time conditions are fulfilled.