We address ego-motion estimation for automated parking, where centimeter-level accuracy is crucial due to tight spaces and nearby obstacles. Traditional methods using inertial-measurement units and wheel encoders require calibration, making them costly and time-consuming. To overcome this, we propose a radar-based simultaneous localization and mapping (SLAM) approach that leverages the robustness of radar to adverse weather and support for online calibration. Our robocentric formulation fuses feature positions and Doppler velocities for robust data association and filter convergence. Key contributions include a Doppler-augmented radar SLAM method, multi-radar support and an information-based feature-pruning strategy. Experiments demonstrate high-accuracy localization and improved robustness over state-of-the-art methods, meeting the demands of automated parking.