Precise and real-time estimation of the robotic arm's position on the patient's side is essential for the success of remote robotic surgery in Tactile Internet (TI) environments. This paper presents a prediction model based on the Transformer-based Informer framework for accurate and efficient position estimation. Additionally, it combines a Four-State Hidden Markov Model (4-State HMM) to simulate realistic packet loss scenarios. The proposed approach addresses challenges such as network delays, jitter, and packet loss to ensure reliable and precise operation in remote surgical applications. The method integrates the optimization problem into the Informer model by embedding constraints such as energy efficiency, smoothness, and robustness into its training process using a differentiable optimization layer. The Informer framework uses features such as ProbSparse attention, attention distilling, and a generative-style decoder to focus on position-critical features while maintaining a low computational complexity of O(L log L). The method is evaluated using the JIGSAWS dataset, achieving a prediction accuracy of over 90 percent under various network scenarios. A comparison with models such as TCN, RNN, and LSTM demonstrates the Informer framework's superior performance in handling position prediction and meeting real-time requirements, making it suitable for Tactile Internet-enabled robotic surgery.