The recently introduced matrix group$\mathbf {SE_2(3)}$provides a 5$\mathbf {\times }$5 matrix representation for the orientation, velocity, and position of an object in the 3-D space, a triplet we call “extended pose.” In this article, we build on this group to develop a theory to associate uncertainty with extended poses represented by 5$\mathbf {\times }$5 matrices. Our approach is particularly suited to describe how uncertainty propagates when the extended pose represents the state of an inertial measurement unit (IMU). In particular, it allows revisiting the theory of IMU preintegration on manifold and reaching a further theoretic level in this field. Exact preintegration formulas that account for rotating earth, that is, centrifugal force and Coriolis force, are derived as a byproduct, and the factors are shown to be more accurate. The approach is validated through extensive simulations and applied to sensor fusion where a loosely coupled fixed-lag smoother fuses IMU and LiDAR on 1-h-long experiments using our experimental car. It shows how handling rotating earth may be beneficial for long-term navigation within incremental smoothing algorithms.

The present paper introduces a novel methodology for Unscented Kalman Filtering (UKF) on manifolds that extends previous work by the authors on UKF on Lie groups. Beyond filtering performance, the main interests of the approach are its versatility, as the method applies to numerous state estimation problems, and its simplicity of implementation for practitioners not being necessarily familiar with manifolds and Lie groups. We have developed the method on two independent open-source Python and Matlab frameworks we call UKF-M, for quickly implementing and testing the approach. The online repositories contain tutorials, documentation, and various relevant robotics examples that the user can readily reproduce and then adapt, for fast prototyping and benchmarking. The code is available at https://github.com/CAOR-MINES-ParisTech/ukfm.

Odometry techniques are key to autonomous robot navigation, since they enable self-localization in the environment. However, designing a robust odometry system is particularly challenging when camera and LiDAR are uninformative or unavailable. In this paper, we leverage recent advances in deep learning and variational inference to correct dynamical and observation models for state-space systems. The methodology trains Gaussian processes on the residual between the original model and the ground truth, and is applied on publicly available datasets for robot navigation based on two wheel encoders, a fiber optic gyro, and an Inertial Measurement Unit (IMU). We also propose to build an Extended Kalman Filter (EKF) on the learned model using wheel speed sensors and the fiber optic gyro for state propagation, and the IMU to update the estimated state. Experimental results clearly demonstrate that the (learned) corrected models and EKF are more accurate than their original counterparts.

This paper proposes a real-time approach for long-term inertial navigation based only on an Inertial Measurement Unit (IMU) for self-localizing wheeled robots. The approach builds upon two components: 1) a robust detector that uses recurrent deep neural networks to dynamically detect a variety of situations of interest, such as zero velocity or no lateral slip; and 2) a state-of-the-art Kalman filter which incorporates this knowledge as pseudo-measurements for localization. Evaluations on a publicly available car dataset demonstrates that the proposed scheme may achieve a final distance error of 20 m for a 21 km long trajectory of a vehicle driving for over an hour, equipped with an IMU of moderate precision (the gyro drift rate is 10 deg/h). To our knowledge, this is the first paper which combines sophisticated deep learning techniques with state-of the-art filtering methods for pure inertial navigation on wheeled vehicles and as such opens up for novel data-driven inertial navigation techniques. Moreover, albeit taylored for IMU-only based localization, our method may be used as a component for self-localization of wheeled robots equipped with a more complete sensor suite.

Combining visual information with inertial measurements is a popular approach to achieve robust and autonomous navigation in robotics, specifically in GPS-denied environments. In this paper, building upon both the recent theory of Unscented Kalman Filtering on Lie Groups (UKF-LG) and more generally the theory of invariant Kalman filtering (IEKF), an innovative UKF is derived for the monocular visual simultaneous localization and mapping (SLAM) problem. The body pose, velocity, and the 3D landmarks' positions are viewed as a single element of a (high dimensional) Lie group SE2+p(3), which constitutes the state, and where the accelerometers' and gyrometers' biases are appended to the state and estimated as well. The efficiency of the approach is validated both on simulations and on five real datasets.

Fusing visual information with inertial measurements for state estimation has aroused major interests in recent years. However, combining a robust estimation with computational efficiency remains challenging, specifically for low-cost aerial vehicles in which the quality of the sensors and the processor power are constrained by size, weight and cost. In this paper, we present an innovative filter for stereo visual inertial odometry building on: (i) the recently introduced stereo multistate constraint Kalman filter; (ii) the invariant filtering theory; and (iii) the unscented Kalman filter (UKF) on Lie groups. Our solution combines accuracy, robustness and versatility of the UKF. We then compare our approach to state-of-art solutions in terms of accuracy, robustness and computational complexity on the EuRoC dataset and a challenging MAV outdoor dataset.

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.