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This article is concerned with sensor management for target search and track using the generalized optimal subpattern assignment (GOSPA) metric. Utilizing the GOSPA metric to predict future system performance is computationally challenging, because of the need to account for uncertainties within the scenario, notably the number of targets, the locations of targets, and the measurements generated by the targets subsequent to performing sensing actions. In this article, efficient sample-based techniques are developed to calculate the predicted mean square GOSPA metric. These techniques allow for missed detections and false alarms, and thereby enable the metric to be exploited in scenarios more complex than those previously considered. Furthermore, the GOSPA methodology is extended to perform nonmyopic (i.e., multistep) sensor management via the development of a Bellman-type recursion that optimizes a conditional GOSPA-based metric. Simulations for scenarios with missed detections, false alarms, and planning horizons of up to three time steps demonstrate the approach, in particular showing that optimal plans align with an intuitive understanding of how taking into account the opportunity to make future observations should influence the current action. It is concluded that the GOSPA-based, nonmyopic search and track algorithm offers a powerful mechanism for sensor management.

Belief propagation (BP) is a useful probabilistic inference algorithm for efficiently computing approximate marginal probability densities of random variables. However, in its standard form, BP is only applicable to the vector-type random variables with a fixed and known number of vector elements, while certain applications rely on random finite sets (RFSs) with an unknown number of vector elements. In this paper, we develop BP rules for factor graphs defined on sequences of RFSs where each RFS has an unknown number of elements, with the intention of deriving novel inference methods for RFSs. Furthermore, we show that vector-type BP is a special case of set-type BP, where each RFS follows the Bernoulli process. To demonstrate the validity of developed set-type BP, we apply it to the Poisson multi-Bernoulli (PMB) filter for simultaneous localization and mapping (SLAM), which naturally leads to a set-type BP PMB-SLAM method, which is analogous to a vector type SLAM method, subject to minor modifications.

In this paper we derive the Information Exchange track-before-detect Multi-Bernoulli (IEMB) filter for multi-target filtering with superpositional sensors. The IEMB filter propagates a multi-Bernoulli density through the filtering recursion and each Bernoulli is propagated with its own prediction and update step. At each update step, each Bernoulli filter exchanges the predicted mean and covariance matrix of its measurement contribution with the other Bernoulli filters. The exchanged information is then used by the filters to perform the update step. Additionally, we propose the Iterated Posterior Linearisation Filter (IPLF) implementation of the IEMB filter (IEMB-IPLF). We compare the IEMB-IPLF filter to a number of other non-linear filtering methods showing the benefits of the proposed filter.

This article proposes a multi-object tracking (MOT) algorithm for traffic monitoring using a drone equipped with optical and thermal cameras. Object detections on the images are obtained using a neural network for each type of camera. The cameras are modelled as direction-of-arrival (DOA) sensors. Each DOA detection follows a von-Mises Fisher distribution, whose mean direction is obtain by projecting a vehicle position on the ground to the camera. We then use the trajectory Poisson multi-Bernoulli mixture filter (TPMBM), which is a Bayesian MOT algorithm, to optimally estimate the set of vehicle trajectories. We have also developed a parameter estimation algorithm for the measurement model. We have tested the accuracy of the resulting TPMBM filter in synthetic and experimental data sets.

In this article, we propose a Poisson multi-Bernoulli (PMB) filter for extended object tracking (EOT), which directly estimates the set of object trajectories, using belief propagation (BP). The proposed filter propagates a PMB density on the posterior of sets of trajectories through the filtering recursions over time, where the PMB mixture (PMBM) posterior after the update step is approximated as a PMB. The efficient PMB approximation relies on several important theoretical contributions. First, we present a PMBM conjugate prior on the posterior of sets of trajectories for a generalized measurement model, in which each object generates an independent set of measurements. The PMBM density is a conjugate prior in the sense that both the prediction and the update steps preserve the PMBM form of the density. Second, we present a factor graph representation of the joint posterior of the PMBM set of trajectories and association variables for the Poisson spatial measurement model. Importantly, leveraging the PMBM conjugacy and the factor graph formulation enables an elegant treatment on undetected objects via a Poisson point process and efficient inference on sets of trajectories using BP, where the approximate marginal densities in the PMB approximation can be obtained without enumeration of different data association hypotheses. To achieve this, we present a particle-based implementation of the proposed filter, where smoothed trajectory estimates, if desired, can be obtained via single-object particle smoothing methods, and its performance for EOT with ellipsoidal shapes is evaluated in a simulation study.

This article shows that the Poisson multi-Bernoulli mixture (PMBM) density is a multi-target conjugate prior for general target-generated measurement distributions and arbitrary clutter distributions. That is, for this multi-target measurement model and the standard multi-target dynamic model with Poisson birth model, the predicted and filtering densities are PMBMs. We derive the corresponding PMBM filtering recursion. Based on this result, we implement a PMBM filter for point-target measurement models and negative binomial clutter density in which data association hypotheses with high weights are chosen via Gibbs sampling. We also implement an extended target PMBM filter with clutter that is the union of Poisson-distributed clutter and a finite number of independent clutter sources. Simulation results show the benefits of the proposed filters to deal with non-standard clutter.