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This paper deals with the inertia estimation of power systems in presence of significant contribution provided by renewable energy sources. The efforts to decommission conventional power plants and replace them with renewable resources could affect the robust and reliable operation of future power systems. The main issue related to the integration of renewable-based generation in the networks deals with the substitution of conventional synchronous generators connected to the grid and equipped by rotating masses, with converter-based generator which have not rotating masses, or they are decoupled by the grid due to the presence of interfacing power converters. Since the system inertia is the inherent ability of the online synchronous machines to oppose sudden changes in generation or load, the increasing share of renewable generators, such as wind and solar, the overall system inertia could decrease. This leading network operators to introduce new tools for monitoring the system inertia values, to contain them within admissible values, and to better prepare for different kinds of operational scenarios with undesired reduction of the system inertia. At this purpose, in this paper a tool for the analysis and prediction of inertia is proposed. The proposed method is based on a minimum variance harmonic finite impulse response and can consider the actual penetration of renewable energy sources. The proposed approach is tailored for online monitoring and exploits the real time measurements of relevant features of the network. The method is tested with actual data of the Italian Transmission Network and its effectiveness is studied by comparisons with some popular and well-established method of analysis and prediction.