Kalman filters can be formulated on any manifold with an affine connection, unifying the Lie-group and Riemannian approaches.
Notes on Kalman Filter (KF, EKF, ESKF, IEKF, IESKF)
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A geometric perspective of state estimation using Kalman filters
Kalman filters can be formulated on any manifold with an affine connection, unifying the Lie-group and Riemannian approaches.