When tracking maneuvering targets, model-driven approaches encounter difficulties in comprehensively delineating complex real-world scenarios and are prone to model mismatch when the targets maneuver. Meanwhile, contemporary data-driven methods have overlooked measurements' confidence, markedly escalating the challenge of fitting a mapping from measurement sequences to target state sequences. To address these issues, this paper presents a deep maneuvering target tracking methodology based on target state space projection. The proposed methodology initially establishes a projection from the target measurement sequence to the target state space by formulating the probability density function of measurement error and samples the distribution information of measurement noise within the target state space as a measurement representation. Under this representation, the sequential regression task of target state estimation can be transmuted into a task of detecting the target location in the state space. Subsequently, a deep detection network is devised to accomplish target location detection in the target state space. Finally, a loss function is designed to facilitate the network's training for attaining the desired network performance. Simulation experiments suggest that the proposed method can maintain satisfactory tracking performance even when the target maneuvers, and can rapidly converge and achieve higher estimation accuracy compared with existing methods after the target maneuvers.