Estimation of Crustal Deformation Parameters in GPS Network with the Aid of Four-Dimensional Integrated Adjustment

Abstract

A special approach to adjust geodetic network in which GPS surveys are frequently repeated is performed with the aid of four-dimensional integrated adjustment technique. We take global Cartesian coordinate as a reference system, and assume not only coordinate unknowns but also rate of deformation signal linear with time. Observation equation for the repeated baseline measurements is proved to be a type of fundamental observation equation in least squares collocation. We deduced the solutions of deterministic approach for three cases in which (1) both design matrix and signal coefficient matrix are singular, (2) only design matrix is singular, and (3) signal coefficient matrix is singular. In solving the observation equation, we apply reduced normal equation for case (2) and (3). Further we discussed the solution of stochastic approach. In case of singular normal equation, we apply inner constrain matrix both for parameters and signals in order to obtain the unknowns. The adjusted results are transformed into the numerical values based on local Cartesian coordinate. Finally, horizontal strains are deduced from overdetermined horizontal displacement vectors at the GPS stations.