Fast minor component extraction using Givens rotations

Elaboration is provided of a new version of the YAST-PGS algorithm for the extraction and tracking of the minor eigenvectors of a positive Hermitian covariance matrix associated with time series. The proposed algorithm, referred to as minor component-YAST-PGS (MC-YAST-PGS), estimates the minor eigenvectors (not only a random basis of the minor subspace) of the considered covariance matrix. Also, it guarantees the orthogonality of the weight matrix at each iteration and requires O(np) flops per iteration where n is the size of the observation vector and p<n is the number of eigenvectors to estimate. The estimation accuracy and tracking properties of MC-YAST-PGS are illustrated through simulation results and compared with the singular value decomposition and PASTd algorithms.