The inertia of a power system is a key factor in determining the initial frequency decline after a disturbance. Low system inertia can allow large frequency declines to occur that could lead to violation of frequency security limits, particularly in smaller power systems, or play a key role in allowing cascading outages to occur. Future developments in power systems will mean that the system inertia will become highly variable and take values that would traditionally have been considered very low. Presented is a method for the robust estimation of the generator inertia available in the system during a disturbance. This method has been validated using simulations of the IEEE 39-bus system in DIgSILENTTM PowerFactory®. Inertia estimates for a variety of disturbance types and noise conditions have been made, and found to have a median error of 1.53% with inter-quartile range of 6.6%.