A Scalable Algorithm for Tracking an Unknown Number of Targets Using Multiple Sensors

We propose a method for tracking an unknown number of targets based on measurements provided by multiple sensors. Our method achieves low computational complexity and excellent scalability by running belief propagation on a suitably devised factor graph. A redundant formulation of data association uncertainty and the use of "augmented target states" including binary target indicators make it possible to exploit statistical independencies for a drastic reduction of complexity. An increase in the number of targets, sensors, or measurements leads to additional variable nodes in the factor graph but not to higher dimensions of the messages. As a consequence, the complexity of our method scales only quadratically in the number of targets, linearly in the number of sensors, and linearly in the number of measurements per sensors. The performance of the method compares well with that of previously proposed methods, including methods with a less favorable scaling behavior. In particular, our method can outperform multisensor versions of the probability hypothesis density (PHD) filter, the cardinalized PHD filter, and the multi-Bernoulli filter.Comment: 13 pages, 8 figur

Multisensor CPHD filter

The single sensor probability hypothesis density (PHD) and cardinalized probability hypothesis density (CPHD) filters have been developed in the literature using the random finite set framework. The existing multisensor extensions of these filters have limitations such as sensor order dependence, numerical instability or high computational requirements. In this paper we derive update equations for the multisensor CPHD filter. The multisensor PHD filter is derived as a special case. Exact implementation of the multisensor CPHD involves sums over all partitions of the measurements from different sensors and is thus intractable. We propose a computationally tractable approximation which combines a greedy measurement partitioning algorithm with the Gaussian mixture representation of the PHD. Our greedy approximation method allows the user to control the tradeoff between computational overhead and approximation accuracy

Decentralized Gaussian Filters for Cooperative Self-localization and Multi-target Tracking

Scalable and decentralized algorithms for Cooperative Self-localization (CS) of agents, and Multi-Target Tracking (MTT) are important in many applications. In this work, we address the problem of Simultaneous Cooperative Self-localization and Multi-Target Tracking (SCS-MTT) under target data association uncertainty, i.e., the associations between measurements and target tracks are unknown. Existing CS and tracking algorithms either make the assumption of no data association uncertainty or employ a hard-decision rule for measurement-to-target associations. We propose a novel decentralized SCS-MTT method for an unknown and time-varying number of targets under association uncertainty. Marginal posterior densities for agents and targets are obtained by an efficient belief propagation (BP) based scheme while data association is handled by marginalizing over all target-to-measurement association probabilities. Decentralized single Gaussian and Gaussian mixture implementations are provided based on average consensus schemes, which require communication only with one-hop neighbors. An additional novelty is a decentralized Gibbs mechanism for efficient evaluation of the product of Gaussian mixtures. Numerical experiments show the improved CS and MTT performance compared to the conventional approach of separate localization and target tracking.Comment: 16 pages, 7 figure