Bin Yang's PAST Algorithm: Projection Approximation Subspace Tracking

This text presents a translation of Bin Yang's original work on the PAST algorithm (Projection Approximation Subspace Tracking Algorithm), an efficient method widely used in signal processing applications. The core concept involves projecting signals onto adaptive subspaces and performing real-time tracking and approximation within these subspaces. From an implementation perspective, PAST typically utilizes recursive updates to maintain subspace estimates, employing optimization techniques like gradient descent or RLS (Recursive Least Squares) for efficient computation. The algorithm's key functions include dimensionality reduction through orthogonal projections and adaptive subspace maintenance using forgetting factors to handle non-stationary signals. This approach not only enhances computational efficiency but also effectively processes high-dimensional data streams, making it particularly valuable for real-time applications. The algorithm's practical implementation often involves matrix decomposition techniques (e.g., QR or SVD) for numerical stability and efficient memory management through rank-one updates. Due to these advantages, PAST has gained extensive adoption and continued research in signal processing domains such as array processing, spectral analysis, and system identification.