Bing Yang's PAST and PASTD Algorithms for Signal Subspace Tracking with MUSIC-Based DOA Estimation

This paper presents the implementation of Bing Yang's Projection Approximation Subspace Tracking (PAST) and PAST with Deflation (PASTD) algorithms for dynamic signal subspace tracking, coupled with Multiple Signal Classification (MUSIC) algorithm for Direction of Arrival (DOA) estimation. These algorithms represent fundamental methods in signal processing for analyzing and processing various signal types. The PAST algorithm employs an approximate projection approach to recursively update the signal subspace with O(nr) computational complexity, where n is the input dimension and r is the subspace dimension. PASTD extends this capability by incorporating deflation techniques to handle multiple subspaces simultaneously. The MUSIC algorithm leverages the estimated signal subspace to perform high-resolution spectral estimation through eigenvalue decomposition of the covariance matrix, generating pseudospectrum peaks that correspond to signal source directions. Implementation typically involves covariance matrix computation, eigenvalue decomposition, and pseudospectrum generation using orthogonal complement projections. This integration enables robust signal analysis and processing, yielding accurate results for source localization and subspace identification applications.