Piezoelectric actuators exhibit hysteresis between the driving voltage and the displacement, impacting the positioning accuracy. This nonlinear behavior poses challenges for system identification and control. In this paper, we implement and test several filtering techniques to estimate the system states using a set of available noise-corrupted measurements. We present the estimation of the system states via numerical simulations and Monte Carlo analysis. These insights contribute to identifying the most effective state estimator for the nonlinear system model.