Input estimation indicates a class of algorithms to estimate the input excitation of a dynamical system based on output measurements and a model of the system. The feasibility of the estimation is conditioned on the identifiability of input. Noteworthy, identifiability entails that the response of the dynamical system is sensitive to a specific variable, and its effect is distinguishable from those of all other variables. This work explores two methods for assessing the identifiability of the input using two benchmark dynamical systems, which are simulated numerically. One method is based on the calculation of Lie derivatives and the other method is based on the calculation of Empirical Gramians. To verify the outcomes of the identifiability analysis, joint input estimation is computed for both systems using the Augmented Extended Kalman Filter.