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We present a new algorithm for tracking the signal subspace recursively. It is based on an interpretation of the signal subspace as the solution of a constrained minimization task. This algorithm, referred to as the constrained projection approximation subspace tracking (CPAST) algorithm, guarantees the orthonormality of the estimated signal subspace basis at each iteration. Thus, the proposed algorithm avoids orthonormalization process after each update for postprocessing algorithms which need an orthonormal basis for the signal subspace. To reduce the computational complexity, the fast CPAST algorithm is introduced which has O(nr) complexity. In addition, for tracking the signal sources with abrupt change in their parameters, an alternative implementation of the algorithm with truncated window is proposed. Furthermore, a signal subspace rank estimator is employed to track the number of sources. Various simulation results show good performance of the proposed algorithms.