Invariant Smoothing on Lie Groups
This work addresses estimation challenges in robotics, such as localization, but appears incremental as it builds on existing smoothing methods with specific structural improvements.
The paper tackles the problem of non-linear smoothing for group-affine observation systems on Lie groups by proposing an algorithm based on maximum a posteriori estimation, and it demonstrates validation through robot localization simulations and real data.
In this paper we propose a (non-linear) smoothing algorithm for group-affine observation systems, a recently introduced class of estimation problems on Lie groups that bear a particular structure. As most non-linear smoothing methods, the proposed algorithm is based on a maximum a posteriori estimator, determined by optimization. But owing to the specific properties of the considered class of problems, the involved linearizations are proved to have a form of independence with respect to the current estimates, leveraged to avoid (partially or sometimes totally) the need to relinearize. The method is validated on a robot localization example, both in simulations and on real experimental data.