In this paper, we first consider a simple Bayesian fusion problem in a matrix Lie group, and propose to tackle it using the unscented transform. The method is then leveraged to derive two simple alternative unscented Kalman filters on Lie groups, for both cases of noisy partial measurements of the state, and full state noisy measurements of the state on the group. The general method is applied to a robot localization problem, and results based on experimental data combined with extensive Monte-Carlo simulations at various noise levels illustrate the superiority of the approach over the standard UKF.

In this paper we propose a novel accurate method for dead-reckoning of wheeled vehicles based only on an Inertial Measurement Unit (IMU). In the context of intelligent vehicles, robust and accurate dead-reckoning based on the IMU may prove useful to correlate feeds from imaging sensors, to safely navigate through obstructions, or for safe emergency stops in the extreme case of exteroceptive sensors failure. The key components of the method are the Kalman filter and the use of deep neural networks to dynamically adapt the noise parameters of the filter. The method is tested on the KITTI odometry dataset, and our dead-reckoning inertial method based only on the IMU accurately estimates 3D position, velocity, orientation of the vehicle and self-calibrates the IMU biases. We achieve on average a 1.10% translational error and the algorithm competes with top-ranked methods which, by contrast, use LiDAR or stereo vision. We make our implementation open-source at: https://github.com/mbrossar/ai-imu-drIndex Terms-localization, deep learning, invariant extended Kalman filter, KITTI dataset, inertial navigation, inertial measurement unit

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