Gaussian Belief Propagation for Tracking With Unresolved Measurements

Augustin A. Saucan, Florian Meyer, Peter Willett

Unresolved measurements occur in many inference problems where two or more hidden processes may, at times, jointly generate a single measurement. For instance, such phenomena are encountered in multiobject tracking owing to the limited resolution capabilities of practical sensors; or in camera-aided autonomous driving due to shadowing or occlusions. Substantial performance degradation, such as track losses, are incurred when unresolved measurements are not accounted for. In this paper, we address multiobject tracking under a generalized unresolved measurement model, where any subset of objects may generate a single unresolved measurement according to a probabilistic model. Our innovation lies both in modeling and algorithm-design directions. First, we develop a probability distribution for object partitions based on a model of pairwise coupling of objects and subsequently a probability distribution for object-to-measurement association variables. This generic model incorporates sensor resolution capabilities, sensor detection, and sensor noise characteristics for object groups. Second, a generic Loopy Belief Propagation (LBP) method as well as a specialized Gaussian-LBP (GLBP) algorithm are proposed that perform object state inference under the aforementioned model. In contrast to direct marginalization methods, which involve a computational complexity of $O(m^n)$, for $m$ measurements and $n$ objects, the proposed GLBP algorithm achieves a computational complexity on the order of $O(m n 2^{n})$. Numerical results demonstrate the effectiveness of our proposed GLBP, with estimation performance that closely matches that of exact marginalization for only a fraction of the computational resources.