With the increasing presence of renewable energy sources in power grids, inertia estimation has become a pivotal problem in ensuring stable energy distribution. Inertia estimation during normal operating conditions of the network is still an open problem, since most algorithms rely on post-fault data or injection of probing signals in the grid. Here we extend a previously proposed algorithm for online inertia estimation to account for the presence of turbine governors in the power grid. The algorithm was tested on the IEEE-14-bus power system and it was successful in tracking the inertia of generators with and without turbine governors.