Stepwise Parameter Estimations in a Time-Variant Similarity Transformation

Abstract

A classic seven-parameter similarity transformation is typically applied in reference frame transformations. For modern day global applications with a higher accuracy requirement, this model is extended to accommodate time-dependent positional variations. The time-variant transformation, however, also brings a new problem—rank deficiency—while performing parameter estimations. In this paper, a stepwise parameter estimation approach is proposed to overcome this problem and give a reliable solution. It also enables one to investigate different types of transformation parameters independently. To prove its feasibility on present day global datum applications, this approach is applied to the reference frame transformation between ITRF2000 and ITRF97 at epoch 1997.0. In addition, a simulation test is performed to show the advantages of the proposed approach against other parameter estimation approaches currently in use, for its wider range of applications in science and engineering.