Subspace Tracking Algorithm PAST for Moving Target Tracking

This article introduces the Projection Approximation Subspace Tracking (PAST) algorithm, designed for tracking multiple moving targets using circular array configurations. The algorithm operates by recursively estimating the signal subspace through rank-1 updates, enabling efficient tracking of dynamic targets. Key implementation features include: eigenvalue decomposition avoidance through approximate projection methods, computational efficiency with O(nr) complexity (where n is dimension and r is subspace rank), and adaptive subspace updates using exponential weighting for time-varying scenarios. The PAST algorithm maintains robust tracking performance even under significant signal noise conditions, making it particularly valuable for practical applications such as video surveillance systems, UAV tracking, and radar signal processing. Implementation typically involves initial covariance matrix estimation followed by iterative subspace refinement using forgetting factors to prioritize recent observations.