Methods tackling multi-object tracking need to estimate the number of targets in the sensing area as well as to estimate their continuous state. While the majority of existing methods focus on data association, precise state (3D pose) estimation is often only coarsely estimated by approximating targets with centroids or (3D) bounding boxes. However, in automotive scenarios, motion perception of surrounding agents is critical and inaccuracies in the vehicle close-range can have catastrophic consequences. In this work, we focus on precise 3D track state estimation and propose a learning-based approach for object-centric relative motion estimation of partially observed objects. Instead of approximating targets with their centroids, our approach is capable of utilizing noisy 3D point segments of objects to estimate their motion. To that end, we propose a simple, yet effective and efficient network, AlignNet-3D, that learns to align point clouds. Our evaluation on two different datasets demonstrates that our method outperforms computationally expensive, global 3D registration methods while being significantly more efficient. We make our data, code, and models available at https://www.vision. rwth-aachen.de/page/alignnet.