Robust and Optimal Alignment of High-Dimensional Data Using Maximum Likelihood Estimation through a Random Sample Consensus Framework

Correcting spatial orientations of groups of high-dimensional data sets such that they are all in a consistent coordinate system is often a time consuming and error-prone process. Automation of this process can be accomplished by using Generalized Procrustes Analysis to estimate the relative orientations among a population of high-dimensional data sets. A least squares Procrustes solution is applied through a maximum likelihood estimation and random sample consensus framework for robustness. The likelihood model is comprised of a mixture distribution where inliers are assumed to originate from a Student's t- distribution and outliers from a uniform distribution. Applications will focus on a synthetic data set that emulates tri-axial acceleration data from a population of accelerometers. Outliers represent either non-rigid body responses, data acquisition, and/or sensor issues. The intended application for the methodology is to robustly automate the rotation of populations of experimentally collected tri-axial accelerometer data sets to a single global coordinate system.