Closed form least-squares solution to 3D symmetric Helmert transformation with rotational invariant covariance structure

Abstract

Least-squares (LS) solutions to the 3D Helmert and symmetric Helmert transformations with rotational invariant covariance structure are studied in a unified framework. This is an extension of the 3D Helmert transformation with naive identity covariance and the counterpart of the 2D symmetric Helmert transformation with rotational invariant covariance. It is found that the closed form LS solution still exists and that the rotation parameters are still the same between the Helmert and symmetric Helmert transformations.