In this paper, we study the correlated neuronal activity caused by afferent inputs from distinct and common population of pre-synaptic neurons. We present a method based on the integration of the expectation-maximization algorithm, Kalman filtering and backward smoothing in order to estimate the parameters associated with pre-synaptic activity and the latent common inputs from post-synaptic measurements. We provide simulation results that validate the performance of the proposed methodology in terms of parameter estimation and tracking the dynamics of the common pre-synaptic inputs.