Dynamic models of industrial processes play an instrumental role in the operation of such processes from smart sensors, data reconciliation, to advanced control. For good performance, a precise model is normally required. The issue of improving models has received considerable critical attention. In this work, we consider the estimation of model parameters and initial states of a gas lifting oil well model, followed by filtering of its states. By utilizing information from both first-principle model and data, the results are presented to show the estimated values and their uncertainties. Julia is the main programming language used in this study. This research study provided an opportunity to advance the understanding of the optimization and estimation for the oil well operation.