This study develops a two-axis gimbal system designed to maintain a target within its field of view by compensating for motion of either the target or the platform. The focus is on inertial stabilization platforms (ISPs), where accurate, real-time tracking is essential for applications such as surveillance, navigation, and scientific observation. The research prioritizes the design and optimization of inverse kinematics algorithms to enhance system performance. A detailed analysis of mathematical models underpins the development, addressing challenges in real-time processing with advanced optimization techniques to minimize latency and maximize accuracy. The proposed algorithms achieve a mean tracking error of 0.002 m and a mean convergence time of 2.12 seconds, surpassing traditional methods in precision and efficiency. Performance is evaluated within a simulation framework using Simscape Multibody, testing the algorithms under various conditions. Validation extends to real-world scenarios to ensure robustness and practical applicability. The results demonstrate significant improvements in tracking accuracy and responsiveness, offering a reliable solution for dynamic environments. This work paves the way for more efficient gimbal systems, contributing to advancements in technologies requiring stable and precise tracking in dynamic and challenging settings.