Gaussian Process on the Product of Directional Manifolds

We present a principled study on establishing Gaussian processes over variables on the product of directional manifolds. As a basic functional component, a manifold-adaptive kernel is presented based on the von Mises distribution for Gaussian process regression on unit circles. Afterward, a novel hypertoroidal von Mises kernel is introduced to enable topology-aware Gaussian processes on hypertori with consideration of correlational circular components. Based thereon, we enable multi-output regression for learning vector-valued functions on hypertori using intrinsic coregionalization model and provide analytical derivatives in hyperparameter optimization. The proposed multi-output hypertoroidal Gaussian process is further embedded to a data-driven recursive estimation scheme for learning unknown range sensing models of angle-of-arrival inputs. Evaluations on range-based localization show that the proposed scheme enables superior tracking accuracy over parametric modeling and common Gaussian processes.

Continuous-Time Ultra-Wideband-Inertial Fusion

We present a novel continuous-time online state estimation framework using ultra-wideband and inertial sensors. For representing motion states continuously over time, quaternion-based cubic B-splines are exploited with efficient solutions to kinematic interpolations and spatial differentiations. Based thereon, a sliding-window spline fitting scheme is established for asynchronous multi-sensor fusion and online calibration. We evaluate the proposed system, SFUISE (spline fusion-based ultra-wideband-inertial state estimation), in real-world scenarios based on public data set and experiments. The proposed spline fusion scheme is real-time capable and delivers superior performance over state-of-the-art discrete-time schemes. We release the source code and own experimental data set at https://github.com/KIT-ISAS/SFUISE.

Towards High-Performance Solid-State-LiDAR-Inertial Odometry and Mapping

We present a novel tightly-coupled LiDAR-inertial odometry and mapping scheme for both solid-state and mechanical LiDARs. As frontend, a feature-based lightweight LiDAR odometry provides fast motion estimates for adaptive keyframe selection. As backend, a hierarchical keyframe-based sliding window optimization is performed through marginalization for directly fusing IMU and LiDAR measurements. For the Livox Horizon, a newly released solid-state LiDAR, a novel feature extraction method is proposed to handle its irregular scan pattern during preprocessing. LiLi-OM (Livox LiDAR-inertial odometry and mapping) is real-time capable and achieves superior accuracy over state-of-the-art systems for both LiDAR types on public data sets of mechanical LiDARs and in experiments using the Livox Horizon. Source code and recorded experimental data sets are available on Github.

Improved Pose Graph Optimization for Planar Motions Using Riemannian Geometry on the Manifold of Dual Quaternions

We present a novel Riemannian approach for planar pose graph optimization problems. By formulating the cost function based on the Riemannian metric on the manifold of dual quaternions representing planar motions, the nonlinear structure of the SE(2) group is inherently considered. To solve the on-manifold least squares problem, a Riemannian Gauss-Newton method using the exponential retraction is applied. The proposed Riemannian pose graph optimizer (RPG-Opt) is further compared with currently popular optimization frameworks using public planar pose graph datasets. Evaluations show that the proposed method gives equivalently accurate results as the state-of-the-art frameworks and shows better convergence robustness under large uncertainties of odometry measurements.