Abstract: We present a novel technique for estimating initial 3D poses in the context of localization and Visual SLAM problems. The presented approach can deal with noise, outliers and a large amount of input data and still performs in real time in a standard CPU. Our method produces solutions with an accuracy comparable to those produced by RANSAC but can be much faster when the percentage of outliers is high or for large amounts of input data. On the current work we propose to formulate the pose estimation as an optimization problem on Lie groups, considering their manifold structure as well as their associated Lie algebras. This allows us to perform a fast and simple optimization at the same time that conserve all the constraints imposed by the Lie group SE(3). Additionally, we present several key design concepts related with the cost function and its Jacobian; aspects that are critical for the good performance of the algorithm.