The RANdom SAmple Consensus (RANSAC) is one of the most powerful tools for the reconstruction of ground structures from point cloud observations in many applications. The algorithm utilizes iterative search techniques for a set of inliers to find a proper model for the given data. Despite its successful performances in many fields, the RANSAC is not repeatable, i.e, the optimal solution is not guaranteed by its repeated run. In this article, we propose a new algorithm for the reconstruction, called the Iterative Update SAmple Consensus (IUSAC), which is repeatable to get the optimal estimation for the model parameters. The main idea behind the IUSAC is the iterative update, which makes the estimated parameters converge to the optimal solution. The proposed algorithm is analyzed for convergence. It has been numerically verified that the IUSAC is repeatable, simple to implement, and more efficient than the RANSAC. Various numerical experiments incorporating synthetic datasets and the KITTI dataset validate the performance of the IUSAC. The KITTI dataset is a public domain dataset to serve for R&D activities on autonomous vehicle tracking in GPS-denied environments.