The estimation of the instantaneous Angular speed of rotating machines is a crucial issue that has to be tackled before any analysis or diagnosis of a machine operating under non-stationary conditions. This operation is generally carried out thanks to a tachometer, or an angle encoder, but in some cases this information can be missing for different reasons. The aim of this work is to propose a new method, based on the a priori knowledge of the kinematics of the machine, that extracts from a vibration signal the most probable instantaneous rotation frequency without focusing on one specific order, under some a priori constraints. The efficiency of the approach is illustrated on two cases that have been distributed to the community in the frame of contests organized during two international conferences (CMMNO 2014 and Surveillance 8). The two application cases concern very different systems, the first one is a wind turbine and the second one an aircraft engine.