  This paper presents a radar odometry method that combines probabilistic
trajectory estimation and deep learned features without needing groundtruth
pose information. The feature network is trained unsupervised, using only the
on-board radar data. With its theoretical foundation based on a data likelihood
objective, our method leverages a deep network for processing rich radar data,
and a non-differentiable classic estimator for probabilistic inference. We
provide extensive experimental results on both the publicly available Oxford
Radar RobotCar Dataset and an additional 100 km of driving collected in an
urban setting. Our sliding-window implementation of radar odometry outperforms
most hand-crafted methods and approaches the current state of the art without
requiring a groundtruth trajectory for training. We also demonstrate the
effectiveness of radar odometry under adverse weather conditions. Code for this
project can be found at: https://github.com/utiasASRL/hero_radar_odometry
