NBS Internal Report 74-532; 25p. July 26, 1974.
Calibration; convergence criterion; Gauss-Seidel method; incomplete model; least squares estimation; measurement algorithm; nonlinear mathematical model; sparse matrix algorithm; standard deviation; systematic erros; two-dimensional reference plates.
With the acquisition of a three coordinate measuring machine the Dimensional Technology Section began investigating the problem of precisely measuring two-dimensional reference plates. The algorithm which was developed for this measurement process is highly redundant and incorporates a nonlinear mathematical model. Both the mean and standard deviation of the relative (x,y) coordinates of the points on the reference plates are estimated.
The long term goal of the investigation is to use this algorithm as a tool in developing a measurement process which is under statistical control. On the way to that goal certain problems and pitfalls associated with two-dimensional measurements are sure to arise and will be examined. It is hoped that some light will be shed on areas such as long term stability of measuring performance, measuring machine characterization, temperature problems, and the stability of two-dimensional standards.