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This paper proposes a new Bayesian online learning method on a Riemannian manifold for video objects. The basic idea is to consider the dynamic appearance of an object as a point moving on a manifold, where a dual model is applied to estimate the posterior trajectory of this moving point at each time instant under the Bayesian framework. The dual model uses two state variables for modeling the online learning process on Riemannian manifolds: one is for object appearances on Riemannian manifolds, another is for velocity vectors in tangent planes of manifolds. The key difference of our method as compared with most existing Riemannian manifold tracking methods is to compute the Riemannian mean from a set of particle manifold points at each time instant rather than using a sliding window of manifold points at different times. Next to that, we propose to use Gabor filter outputs on partitioned sub-areas of object bounding box as features, from which the covariance matrix of object appearance is formed. As an application example, the proposed online learning is employed to a Riemannian manifold object tracking scheme where tracking and online learning are performed alternatively. Experiments are performed on both visual-band videos and infrared videos, and compared with two existing manifold trackers that are most relevant. Results have shown significant improvement in terms of tracking drift, tightness and accuracy of tracked boxes especially for objects with large pose changes.