Biological agents still outperform the artificial counterparts in navigating the first-visited environments, even with the advance of deep neural networks nowadays. To bridge this gap, by taking the localization problem as the initial step, we investigate the localization principles in mammalian brains to establish the common localization framework in both biological and artificial systems. Furthermore, inspired by the grid cells discovered in mammalian brains, a localization algorithm with circular representation is proposed. Compatible with bearing-and-distance measurement, the proposed algorithms avoid the linearization inconsistency which remains a severe problem in conventional extended Kalman filter algorithms. As the effectiveness of the proposed algorithms shown in simulation results, this paper indicates a novel localization method that is promising to further tackle the simultaneous localization and mapping (SLAM) problem .
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 .
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Biological agents still outperform the artificial counterparts in navigating the first-visited environments, even with the advance of deep neural networks nowadays. To bridge this gap, by taking the localization problem as the initial step, we investigate the localization principles in mammalian brains to establish the common localization framework in both biological and artificial systems. Furthermore, inspired by the grid cells discovered in mammalian brains, a localization algorithm with circular representation is proposed. Compatible with bearing-and-distance measurement, the proposed algorithms avoid the linearization inconsistency which remains a severe problem in conventional extended Kalman filter algorithms. As the effectiveness
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
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shown in simulation results, this paper indicates a novel localization method that is promising to further tackle the simultaneous localization and mapping (SLAM) problem
is substantiated not only by strong mathematical foundation but also by the comparison against other common localization methods