Arithmetic Average Density Fusion -- Part II: Unified Derivation for Unlabeled and Labeled RFS Fusion

As a fundamental information fusion approach, the arithmetic average (AA) fusion has recently been investigated for various random finite set (RFS) filter fusion in the context of multi-sensor multi-target tracking. It is not a straightforward extension of the ordinary density-AA fusion to the RFS distribution but has to preserve the form of the fusing multi-target density. In this work, we first propose a statistical concept, probability hypothesis density (PHD) consistency, and explain how it can be achieved by the PHD-AA fusion and lead to more accurate and robust detection and localization of the present targets. This forms a both theoretically sound and technically meaningful reason for performing inter-filter PHD AA-fusion/consensus, while preserving the form of the fusing RFS filter. Then, we derive and analyze the proper AA fusion formulations for most existing unlabeled/labeled RFS filters basing on the (labeled) PHD-AA/consistency. These derivations are theoretically unified, exact, need no approximation and greatly enable heterogenous unlabeled and labeled RFS density fusion which is separately demonstrated in two consequent companion papers.Comment: 13 pages, 4 figures, 1 tabl

Linear Complexity Gibbs Sampling for Generalized Labeled Multi-Bernoulli Filtering

Generalized Labeled Multi-Bernoulli (GLMB) densities arise in a host of multi-object system applications analogous to Gaussians in single-object filtering. However, computing the GLMB filtering density requires solving NP-hard problems. To alleviate this computational bottleneck, we develop a linear complexity Gibbs sampling framework for GLMB density computation. Specifically, we propose a tempered Gibbs sampler that exploits the structure of the GLMB filtering density to achieve an $\mathcal{O}(T(P+M))$ complexity, where $T$ is the number of iterations of the algorithm, $P$ and $M$ are the number hypothesized objects and measurements. This innovation enables an $\mathcal{O}(T(P+M+\log(T))+PM)$ complexity implementation of the GLMB filter. Convergence of the proposed Gibbs sampler is established and numerical studies are presented to validate the proposed GLMB filter implementation

Information-Theoretic Active Perception for Multi-Robot Teams

Multi-robot teams that intelligently gather information have the potential to transform industries as diverse as agriculture, space exploration, mining, environmental monitoring, search and rescue, and construction. Despite large amounts of research effort on active perception problems, there still remain significant challenges. In this thesis, we present a variety of information-theoretic control policies that enable teams of robots to efficiently estimate different quantities of interest. Although these policies are intractable in general, we develop a series of approximations that make them suitable for real time use. We begin by presenting a unified estimation and control scheme based on Shannon\u27s mutual information that lets small teams of robots equipped with range-only sensors track a single static target. By creating approximate representations, we substantially reduce the complexity of this approach, letting the team track a mobile target. We then scale this approach to larger teams that need to localize a large and unknown number of targets. We also examine information-theoretic control policies to autonomously construct 3D maps with ground and aerial robots. By using Cauchy-Schwarz quadratic mutual information, we show substantial computational improvements over similar information-theoretic measures. To map environments faster, we adopt a hierarchical planning approach which incorporates trajectory optimization so that robots can quickly determine feasible and locally optimal trajectories. Finally, we present a high-level planning algorithm that enables heterogeneous robots to cooperatively construct maps