Accurate local site response analysis allows for assessing the response of sites nearby an active seismic zone, and consequently modeling the expected earthquake behavior at the surface level. However, the modeling of this non-linear behavior is always accompanied with high uncertainty and variability that could lead to either an unsafe or a very conservative design. One way to overcome these challenges is by relying on site specific instrumentation techniques. In this study a sequential data assimilation technique is employed for real time calibration of the adopted soil model by relying on a measurement data array from different soil layers in the site of interest. The dynamic model parameters are updated in an optimal probabilistic framework using Ensemble Kalman Filter and therefore minimizing the mismatch between the measured and the predicted response of the site of interest. Due to complexities associated with inverting and updating a non-linear soil model, limited number of studies used monitoring techniques to calibrate a non-linear hysteretic soil model while incorporating different sources of uncertainties. Therefore, in this study monitored data are coupled with a non-linear dynamical model in a probabilistic setting to accurately simulate the vertical wave propagation through the soil layers of a given site. This study uses simulated vertical arrays measurements to assess the validity of the framework and to determine several practical concerns such as convergence and robustness of the presented non-linear scheme.