This work addresses the critical lack of precision in state estimation in the Kalman filter for 3D multi-object tracking (MOT) and the ongoing challenge of selecting the appropriate motion model. Existing literature commonly relies on constant motion models for estimating the states of objects, neglecting the complex motion dynamics unique to each object. Consequently, trajectory division and imprecise object localization arise, especially under occlusion conditions. The core of these challenges lies in the limitations of the current Kalman filter formulation, which fails to account for the variability of motion dynamics as objects navigate their environments. This work introduces a novel formulation of the Kalman filter that incorporates motion dynamics, allowing the motion model to adaptively adjust according to changes in the object's movement. The proposed Kalman filter substantially improves state estimation, localization, and trajectory prediction compared to the traditional Kalman filter. This is reflected in tracking performance that surpasses recent benchmarks on the KITTI and Waymo Open Datasets, with margins of 0.56\% and 0.81\% in higher order tracking accuracy (HOTA) and multi-object tracking accuracy (MOTA), respectively. Furthermore, the proposed Kalman filter consistently outperforms the baseline across various detectors. Additionally, it shows an enhanced capability in managing long occlusions compared to the baseline Kalman filter, achieving margins of 1.22\% in higher order tracking accuracy (HOTA) and 1.55\% in multi-object tracking accuracy (MOTA) on the KITTI dataset. The formulation's efficiency is evident, with an additional processing time of only approximately 0.078 ms per frame, ensuring its applicability in real-time applications.