Abstract: Several algorithms of subspace tracking are investigated. The eigenvalue decomposition (EVD) and singular value decomposition (SVD) are not suited for engineering implementation because of their high computation complexities, while the PASTd algorithm brings about very slow convergence rate because of the non-orthogonality of estimated eigenvectors though its computation complexity is low. An improved PASTd subspace tracking algorithm is therefore proposed to be applied to the subspace-based semi-blind multi-user detector for adaptive subspace estimation. The algorithm proposed can insure the orthogonality of the eigenvectors, thus quickening its convergence rate. Simulation results show that the proposed algorithm is superior to both the PASTd semi-blind multi-user detection and OPAST semi-blind multi-user detection in convergence rate, bit error rate (BER) and output signal interference to noise ratio (SINR), and approaches to the SVD semi-blind multi-user detection with relatively low computing speed kept.