The paper focuses on the estimation of the rotor speeds of synchronous machines by means of phasor measurement units. This estimation is aimed at on-line monitoring of electro-mechanical transients and transient stability analysis. The proposed technique is based on the concept of frequency divider formula recently published by the first two authors in these Transactions. The dynamic state estimation is formally stated as a convex optimization problem and a thorough discussion of the sensitivity analysis of the optimal solution is provided. The case study considers a dynamic 1,479-bus model of the all-island Irish system and discusses the effect of bad data, noise and latency on the proposed estimation technique.