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The problem of inferring 3D orientation of a camera from video sequences has been mostly addressed by first computing correspondences of image features. This intermediate step is now seen as the main bottleneck of those approaches. In this paper, we propose a new 3D orientation estimation method for urban (indoor and outdoor) environments, which avoids correspondences between frames. The scene property exploited by our method is that many edges are oriented along three orthogonal directions; this is the recently introduced Manhattan world (MW) assumption. The main contributions of this paper are: the definition of equivalence classes of equiprojective orientations, the introduction of a new small rotation model, formalizing the fact that the camera moves smoothly, and the decoupling of elevation and twist angle estimation from that of the compass angle. We build a probabilistic sequential orientation estimation method, based on an MW likelihood model, with the above-listed contributions allowing a drastic reduction of the search space for each orientation estimate. We demonstrate the performance of our method using real video sequences.