Analysis of Measurements Based on the Singular Value Decomposition

Abstract

The problem of maintaining quality control of manufactured parts is considered. This involves matching points on the parts with corresponding points on a drawing. The difficulty in this process is that the measurements are often in different coordinate systems. Using the assumption that the relation between the two sets of coordinates is a certain rigid transformation, an explicit least squares solution is obtained. This solution requires the singular value decomposition of a related matrix. Other topics in the paper include an appropriate angular representation of the resulting orthogonal transformation matrix, and a computational algorithm for the various required quantities.