Tensor Decomposition Approach to Data Association for Multitarget Tracking

Bayesian methods employed in classical observation-to-track data-association problems in dense environments suffer from exponential growth in complexity with an increase in the number of targets. This paper employs tensor decomposition, which is a technique commonly used in high-dimensional applications to address the curse of dimensionality in the context of such data-association problems. The joint probabilistic data-association (JPDA) filter is developed in the framework of incremental tensor decomposition to curtail the computational burden caused by exponential growth in the number of feasible association events. Adynamic tensor analysis is employed to reduce each scan of measurements to a so-called core tensor, effectively reducing the number of feasible association events to be considered in the JPDA filter. Object tracks are obtained by reconstructing the updated decomposed tensor measurements at the end of the association algorithm. It is shown through numerical examples that employing the reduced core measurements instead of the full set can lead to an order of magnitude reduction in computational time for data association. Two case studies are presented to demonstrate the reduction in computational burden afforded by the new tensor JPDA: a benchmark image-processing problem involving pedestrian tracking, and a space debris tracking problem as a part of space situational awareness.