Deployment of automated ground vehicles beyond the confines of sunny and dry climes will require sub-lane-level positioning techniques based on radio waves rather than near-visible-light radiation. Like human sight, lidar and cameras perform poorly in low-visibility conditions. This paper develops and demonstrates a novel technique for robust sub-50-cm-accurate urban ground vehicle positioning based on all-weather sensors. The technique incorporates a computationally-efficient globally-optimal radar scan batch registration algorithm into 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. Performance is evaluated on an extensive and realistic urban data set. Comparison against ground truth shows that during 60 minutes 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 degrees in heading.