  In this paper we revisit the well-known constrained projection approximation
subspace tracking algorithm (CPAST) and derive, for the first time,
non-asymptotic error bounds. Furthermore, we introduce a novel sparse
modification of CPAST which is able to exploit sparsity in the underlying
covariance structure. We present a non-asymptotic analysis of the proposed
algorithm and study its empirical performance on simulated and real data.
