We present the Dynamic Programming Projected Phase-Slope Algorithm (DYPSA) for automatic estimation of glottal closure instants (GCIs) in voiced speech. Accurate estimation of GCIs is an important tool that can be applied to a wide range of speech processing tasks including speech analysis, synthesis and coding. DYPSA is automatic and operates using the speech signal alone without the need for an EGG signal. The algorithm employs the phase-slope function and a novel phase-slope projection technique for estimating GCI candidates from the speech signal. The most likely candidates are then selected using a dynamic programming technique to minimize a cost function that we define. We review and evaluate three existing methods of GCI estimation and compare the new DYPSA algorithm to them. Results are presented for the APLAWD and SAM databases for which 95.7% and 93.1% of GCIs are correctly identified