A geometric extended Kalman filter using affine connections, parallel transport, and curvature to transform Gaussian covariances between coordinates improves state estimation on manifolds.
A Closed Formula for the Riemann Normal Coordinate Expansion
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We derive an integral representation which encodes all coefficients of the Riemann normal coordinate expansion, and also a closed formula for those coefficients.
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The Geometry of Extended Kalman Filters on Manifolds with Affine Connection
A geometric extended Kalman filter using affine connections, parallel transport, and curvature to transform Gaussian covariances between coordinates improves state estimation on manifolds.