Estimation of the Shift between Parameters of Functional Models of Geodetic Observations by Applying Msplit Estimation

Abstract

This paper presents a new method of estimating a shift between parameters of a functional model of observations. The method in question is based on the theory of Msplit estimation and assumes that design matrices of functional models may not have full column rank. Thus, this alternative method, which is called Shift-Msplit(+) estimation, can be applied to analyze deformations of free geodetic networks. The shift of the parameters can then be regarded as a shift between the coordinates of the network points at two different measurement epochs. Such an application is illustrated using a numerical example, and the results are compared with the results of R-estimation and with a conventional free adjustment of the least squares. This paper presents the theory of Shift-Msplit(+) estimators and ways to compute them. The procedures in question are based on the general principles of Msplit estimation and practical application of the Moore–Penrose inverses.