For autonomous ground vehicles (AGVs) deployed in suburban neighborhoods and other human-centric environments the problem of localization remains a fundamental challenge. There are well established methods for localization with GPS, lidar, and cameras. But even in ideal conditions these have limitations. GPS is not always available and is often not accurate enough on its own, visual methods have difficulty coping with appearance changes due to weather and other factors, and lidar methods are prone to defective solutions due to ambiguous scene geometry. Radar on the other hand is not highly susceptible to these problems, owing in part to its longer range. Further, radar is also robust to challenging conditions that interfere with vision and lidar including fog, smoke, rain, and darkness. We present a radar-based localization system that includes a novel method for highly-accurate radar odometry for smooth, high-frequency relative pose estimation and a novel method for radar-based place recognition and relocalization. We present experiments demonstrating our methods' accuracy and reliability, which are comparable with \new{other methods' published results for radar localization and we find outperform a similar method as ours applied to lidar measurements}. Further, we show our methods are lightweight enough to run on common low-power embedded hardware with ample headroom for other autonomy functions.