Most automotive perception systems leverage radar sensors for their long-range measuring capability and weather robustness at eco-nomic costs. A downside is the rather low spatial resolution. It com-plicates the estimation of pose and size of an extended object. High-resolution sensors facilitate techniques like shape recognition based on a single measurement. But even these sensors only provide sparse measurements at larger distances, which makes instantaneous object detection highly ambiguous. We propose an approach that incorporates the current state estimate to probabilistically identify the true origin of a detection and thereby decreases its association ambiguity. It uses all given measurement data, including the radial speed. This improves the information gain for mass-market sensors with a high measurement uncertainty. We first perform a parametrization of the object using a set of components. They describe the characteristics of a detection in dependency of the current state estimate and various physical relations. Their superposition resembles the spatial detection likelihood of the entire object. Subsequently, we perform a computationally efficient state update that exploits the probabilistic association of the detection to the components. All steps take about 20 µs of computing time. In this article, we demonstrate this technique in an ap-plication that tracks vehicles with radar detections. Besides providing details on the algorithm and a formal description of the components, we also illustrate the probabilistic association with examples. Finally, we discuss the performance in real-world tracking scenarios and out-line interfaces to multi-hypotheses and multi-sensor fusion algorithms. This paper is accompanied by an exemplary MATLAB implementation and a demonstration video.