4D millimeter-wave (mmWave) radars are sensors that provide robustness against adverse weather conditions (rain, snow, fog, etc.), and as such they are increasingly used for odometry and SLAM (Simultaneous Location and Mapping). However, the noisy and sparse nature of the returned scan data proves to be a challenging obstacle for existing registration algorithms, especially those originally intended for more accurate sensors such as LiDAR. Following the success of 3D Gaussian Splatting for vision, in this paper we propose a summarized representation for radar scenes based on global simultaneous optimization of 3D Gaussians as opposed to voxel-based approaches, and leveraging its inherent Probability Density Function (PDF) for registration. Moreover, we propose optimizing multiple registration hypotheses for better protection against local optima of the PDF. We evaluate our modeling and registration system against state of the art techniques, finding that our system provides richer models and more accurate registration results. Finally, we evaluate the effectiveness of our system in a real Radar-Inertial Odometry task. Experiments using publicly available 4D radar datasets show that our Gaussian approach is comparable to existing registration algorithms, outperforming them in several sequences. Copyright 2026 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.