Deploying automated ground vehicles beyond the confines of sunny and dry climes will require sub-lane-level positioning techniques that use radio waves, rather than near-visible light radiation. Like human sight, LiDAR and optical cameras perform poorly in low-visibility conditions. We present and demonstrate a novel technique for robust, sub-50-cm, urban ground vehicle positioning based on all-weather sensors. The technique incorporates a computationally-efficient, globally-optimal radar scan registration algorithm within a larger estimation pipeline that fuses data from commercially-available, low-cost, automotive radars, low-cost inertial sensors, vehicle motion constraints, and, when available, precise GNSS measurements. We evaluate the performance of the presented technique on an extensive and realistic urban dataset derived from all-weather sensors. Comparison against ground truth shows that during 60 min of GNSS-denied driving in the urban center of Austin, TX, the technique maintains 95th-percentile errors below 50 cm in horizontal position and 0.5 in heading.