Labeled multi-Bernoulli filtering methods for efficient multi-object tracking

Abstract

Multi-object tracking aims to estimate the time-dependent number and states of multiple objects from measurements provided by one or more sensors. Potential applications include surveillance, autonomous driving, indoor localization, robotics, and biomedical analytics. All these applications require accurate object state estimates computed by efficient and reliable multi-object tracking algorithms. The framework of labeled random finite sets (RFSs) provides a versatile mathematical tool for modeling the multi-object tracking problem and moreover enables track continuity, i.e., the consistent identification of objects over consecutive time steps. However, the practical application of many RFS- based multi-object tracking algorithms is limited by their high computational complexity. Therefore, to leverage the potential of labeled RFSs, there is a need for efficient yet accurate approximations and implementations.This thesis presents three contributions to the field of RFS-based multi-object tracking. All of them involve a type of high-performing RFS-based multi-object tracking methods generically known as the labeled multi-Bernoulli (LMB) filter as well as the belief propagation (BP) algorithm for iterative Bayesian inference. First, we propose a new fast LMB filter that uses BP for probabilistic data association. The complexity of this filter is significantly smaller than that of existing LMB filters and scales only linearly in the number of Bernoulli components and the number of measurements. This scaling behavior is due to a new fast BP-based algorithm for probabilistic data association. The use of this algorithm within the LMB filter is enabled by a new derivation of the original LMB filter. In this derivation, the generalized LMB posterior probability density function (PDF) is reformulated in terms of a joint object-measurement association distribution, which is approximated by the product of its marginals. The new LMB filter is then obtained by an approximate marginalization using the proposed BP-based algorithm. Contrary to traditional LMB filter implementations based on a ranked assignment algorithm or a Gibbs sampler, our BP-based LMB filter does not prune any association information in the update step, which results in an improved tracking performance.As a second contribution, we propose an eficient RFS-based algorithm for multi- object tracking, referred to as LMB/P filter, that exhibits an even better performance in challenging scenarios, e.g., in scenarios with a high number of objects and/or clutter measurements. The LMB/P filter is based on a new system model for tuples of labeled/unlabeled state RFSs as well as a description of the multi-object state by the tuple of an LMB RFS, i.e., a labeled RFS, and a Poisson RFS, i.e., an unlabeled RFS. The LMB/P filter tracks objects that are unlikely to exist within the less computationally demanding Poisson part and objects that are likely to exist within the more accurate but also more computationally demanding LMB part. Here, only if a quantity characterizing the plausibility of object existence is above a threshold, a new labeled Bernoulli component is created and the object is transferred from the Poisson part to the LMB part. Conversely, a labeled Bernoulli component is transferred back to the Poisson part if the corresponding existence probability falls below another threshold. The fact that unlikely objects are tracked within the less computationally demanding Poisson part combined with additional complexity-reducing approximations and modifications results in a low computational complexity of the LMB/P filter, especially in challenging scenarios.Finally, we propose a distributed multi-sensor LMB filter that uses the generalized covariance intersection (GCI) technique to fuse the local LMB posterior PDFs. A critical aspect of such filters is to correctly associate labeled Bernoulli components describing the same object at difierent sensors. Instead of using a hard association of labeled Bernoulli components, which is done in current state-of-the-art distributed GCI-based LMB filters, we propose a soft (probabilistic) label association scheme. To develop this scheme, we first derive a formulation of the fused multi-object PDF that involves a label association distribution. We then show that approximating the label association distribution by the product of its marginals results in a fused multi-object PDF that is again of LMB form. We finally obtain an efficient implementation of the distributed LMB filter by using a BP-based algorithm for fast approximate marginalization and a Gaussian approximation of the spatial PDFs.