Localization Algorithm with Circular Representation in 2D and its Similarity to Mammalian Brains
This addresses inconsistency in robotic localization, offering a probabilistic solution with potential insights into brain-like navigation, though it appears incremental as it builds on existing filter methods.
The paper tackles the inconsistency problem in robotic localization by proposing a new algorithm that combines von Mises filter for orientation with Kalman filter for position, ensuring consistent mean and covariance estimates. It extends this to a fully circular representation, showing similarity to mammalian brain patterns and achieving substantiated applicability through mathematical foundation and comparisons against other methods.
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.