Let z1, ..., zn, denote vectors of coordinates of n points that describe some object in p-dimensional Euclidean space, . Suppose the object undergoes rigid motion T= (a,B) where a is a p-vector and B is a p x p orthonormal matrix. The points are measured to be at coordinate vectors
, where
, is an error vector,
. We give a simple formula for the least-squares estimate of T. For independent
identically distributed as p-variate normal
positive definite, we obtain maximum likelihood estimators or T (
known) and of (T,
(
unknown). The distribution of the estimate of T and of prediction error are: discussed and in the case p=2 asymptotic (large n) distributions are calculated. This problem arose in a production Iine manufacturing ceramic substrates for silicone chips.
By: Arthur Nadas
Published in: RC6945 in 1978
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