The Helmert Transformation Approach in Network Densification Revisited

Abstract

The mapping problem of an adjusted network from its initial frame to another target frame through the Helmert transformation (HT) is discussed in this paper. We present an optimal solution which can be easily computed by a closed-form expression in terms of appropriate corrections to the standard HT solution that is often used in geodetic practice. Its advantage is the minimization of the propagated noise from the initial network coordinates to their estimated values in the target frame, both at the reference and non-reference stations. This is accomplished by an additional filtering step within the transformation procedure which exploits the known covariance structure of the underlying network in both frames. The presented approach is a suitable tool for aligning an existing network solution to a secular frame such as the ITRF and, as shown in the paper, it can be unequivocally related to the constrained network adjustment directly in the target frame. Nevertheless, any unmodeled non-secular signals hidden in the initial coordinates will be affected by the aforementioned filtering step, and thus the frame alignment methodology presented herein is not tuned for geophysical loading studies with respect to a secular reference frame.