#### Technical Report USC-SIPI-118

“3-D Motion Estimation Using a Sequence of Noisy Stereo Images Part I: Models and Motion Estimation”

by Gem-Sun Young and Rama Chellappa

We discuss a kinematic model based approach for the estimation of 3-D motion parameters from a sequence of noisy stereo images. The approach is based on representing the constant acceleration translational motion, and constant angular velocity or constant precession rotational motion in the form of a bilinear state space model using standard rectilinear state for translational and quaternions for rotation. Closed form solutions of the state transition equations are obtained to propagate to quaternions in both constant angular velocity and constant precession models. The measurements are noisy perturbations of 3-D feature points represented in an inertial coordinate system. It is assumed that the 3-D feature points are extracted from the stereo images and matched over the frames. Owing to the nonlinearity in the state model, nonlinear filters are designed for the estimation of motion parameters. A performance bound for the motion parameters is calculated. Simulation results are included. In a companion report [19], uniqueness of motion parameter estimates is established.

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