Title: Localization Algorithm with Circular Representation in 2D and its Similarity to Mammalian Brains,
Abstract: Extended Kalman filter (EKF) does not guarantee consistent mean and
covariance under linearization, even though it is the main framework for
robotic localization. While Lie group improves the modeling of the state space
in localization, the EKF on Lie group still relies on the arbitrary Gaussian
assumption in face of nonlinear models. We instead use von Mises filter for
orientation estimation together with the conventional Kalman filter for
position estimation, and thus we are able to characterize the first two moments
of the state estimates. Since the proposed algorithm holds a solid
probabilistic basis, it is fundamentally relieved from the inconsistency
problem. Furthermore, we extend the localization algorithm to fully circular
representation even for position, which is similar to grid patterns found in
mammalian brains and in recurrent neural networks. The applicability of the
proposed algorithms is substantiated not only by strong mathematical foundation
but also by the comparison against other common localization methods.