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Traditional vision-based 3-D motion-estimation algorithms require given or calculated 3-D models while the motion is being tracked. We propose a high-speed extended-Kalman-filter-based approach that recovers camera position and orientation from stereo image sequences without prior knowledge, as well as the procedure for the reconstruction of 3-D structures. Empowered by the use of a trifocal tensor, the computation step of 3-D models can be eliminated. The algorithm is thus flexible and can be applied to a wide range of domains. The twist motion model is also adopted to parameterize the 3-D motion. It is minimal since it only has six parameters as opposed to seven parameters in quaternion and 12 parameters in matrix representation. The motion representation is robust because it does not suffer from singularities as Euler angles. Due to the fact that the number of parameters to be estimated is reduced, our algorithm is more efficient, stable, and accurate than traditional approaches. The proposed method has been applied to recover the motion from stereo image sequences taken by a robot and a handheld stereo rig. The results are accurate compared to the ground truths. It is shown in the experiment that our algorithm is not susceptible to outlying point features with the application of a validation gate.