Variance Factor Estimation for Two-Step Analysis of Deformation Networks

Abstract

This paper reconsiders the two-step analysis method in an attempt to show how correct processing of both steps will ensure results identical to those obtained when using the one-step method and moreover may result in improved variance-covariance estimation of the deformation parameters. The approach for solving a vector of parameters indirectly from the measurement vector by using a vector of pseudomeasurements is referred to as a two-step analysis. In deformation networks, the first step is processing the geodetic measurements sequentially without modeling the variation in the network geometry. The results of this first step are sets of network point coordinates pertaining to the specific epochs of the measurements. In the second step the variation in network geometry is modeled. The result of this step is a set of deformation model parameters. It is argued that a proper processing of the two-step method will ensure a correct estimation of the variance-covariance matrix of the deformation parameters, which is a critical value in the overall deformation analysis scheme.