tract: We present unsupervised parameter learning in a Gaussian variational inference setting that combines classic trajectory estimation for mobile robots with deep learning for rich sensor data, all under a single learning objective. The framework is an extension of an existing system identification method that optimizes for the observed data likelihood, which we improve with modern advances in batch trajectory estimation and deep learning. Though the framework is general to any form of parameter learning and sensor modality, we demonstrate application to feature and uncertainty learning with a deep network for 3D lidar odometry. Our framework learns from only the on-board lidar data, and does not require any form of groundtruth supervision. We demonstrate that our lidar odometry performs better than existing methods that learn the full estimator with a deep network, and comparable to state-of-the-art ICP-based methods on the KITTI odometry dataset. We additionally show results on lidar data from the Oxford RobotCar dataset.