An exploration of a Transformer's behavior is proposed in the context of object tracking, with a particular emphasis on maneuvering targets. We compare the performance of our Transformer-based approach against established tracking methods, including the Kalman filter, Extended Kalman Filter, and Unscented Kalman Filter. The first experiment examines its performance in single-target maneuvering scenarios, revealing heightened reactivity without compromising accuracy during abrupt maneuvers and straight-line trajectory. In a second experiment, we showcase the method's multi-target associative capability. By leveraging the attention mechanisms inherent in Transformers, we capitalize on both spatial and temporal de-pendencies for accurate tracking. We introduce specific training strategies and modifications to the original Transformer archi-tecture. Our proposed method underscores the Transformer's potential in maneuvering and multi-target scenarios, providing valuable insights into its efficacy for dynamic object motion estimation. We discuss the comparative results, highlighting performance gains over traditional approaches and addressing potential limitations.