Sparse Gaussian Processes for Continuous-Time Trajectory Estimation on Matrix Lie Groups
This work addresses trajectory estimation for robotics and SLAM systems, but it is incremental as it builds directly on prior research without new experiments.
The authors tackled the problem of continuous-time trajectory estimation in SLAM by extending sparse Gaussian processes to matrix Lie groups, enabling probabilistic non-parametric representations for practical applications, though experimental results are deferred to future work.
Continuous-time trajectory representations are a powerful tool that can be used to address several issues in many practical simultaneous localization and mapping (SLAM) scenarios, like continuously collected measurements distorted by robot motion, or during with asynchronous sensor measurements. Sparse Gaussian processes (GP) allow for a probabilistic non-parametric trajectory representation that enables fast trajectory estimation by sparse GP regression. However, previous approaches are limited to dealing with vector space representations of state only. In this technical report we extend the work by Barfoot et al. [1] to general matrix Lie groups, by applying constant-velocity prior, and defining locally linear GP. This enables using sparse GP approach in a large space of practical SLAM settings. In this report we give the theory and leave the experimental evaluation in future publications.