Accurately estimating the position of a patient's side robotic arm in real time in a remote surgery task is a significant challenge, particularly in Tactile Internet (TI) environments. This paper presents a Kalman Filter (KF) based computationally efficient position estimation method. The study also assume no prior knowledge of the dynamic system model of the robotic arm system. Instead, The JIGSAW dataset, which is a comprehensive collection of robotic surgical data, and the Master Tool Manipulator's (MTM) input are utilized to learn the system model using System Identification (SI) toolkit available in Matlab. We further investigate the effectiveness of KF to determine the position of the Patient Side Manipulator (PSM) under simulated network conditions that include delays, jitter, and packet loss. These conditions reflect the typical challenges encountered in real-world Tactile Internet applications. The results of the study highlight KF's resilience and effectiveness in achieving accurate state estimation despite network-induced uncertainties with over 90\% estimation accuracy.