Optimal Linear Attitude Estimator for Alignment of Point Clouds

This paper presents an approach to estimate the rigid transformation between two point clouds using a linear least squares solution termed as the optimal linear attitude estimator (OLAE). It is shown that by parameterizing the relative orientation between point clouds of interest using the Classical Rodrigues Parameters (CRP), the OLAE approach transforms the nonlinear attitude estimation problem into a linear problem. These linear equations are solved efficiently with closed form solution without any expensive matrix decomposition or inversion. This paper also shows that the 3 degree of freedom (DOF) special case of OLAE that is of interest for aligning point clouds sensed by road vehicles in self-driving car applications can be effectively solved as a linear function with only 1 unknown variable. This formulation enables the 1D RANSAC that can effectively remove outliers in the measurement.