The method that is proposed in the present paper is a special case of squared M split estimation. It concerns a direct estimation of the shift between the parameters of the functional models of geodetic observations. The shift in question may result from, for example, deformation of a geodetic network or other non-random disturbances that may influence coordinates of the network points. The paper also presents the example where such shift is identified with a phase displacement of a wave. The shift is estimated on the basis of wave observations and without any knowledge where such displacement took place. The estimates of the shift that are proposed in the paper are named Shift- M split estimators.

The present paper consists of two parts. The first part presents theoretical foundations of Msplit, estimation with reference to the previous author's paper (Wiśniewski, 2009). This time, some probabilistic assumptions are described in detail. A new quantity called f-information is also introduced to formulate the split potential in more general way. The main aim of this part of the paper is to generalize the target function of Msplit estimation that is the basis for a new formulation of the optimization problem. Such problem itself as well as its solution are presented in this part of the paper. The second part of the paper presents some special case of Mspli, estimation called squared Mspli, estimation (also with reference to the mentioned above paper of the author). That part presents a new solution and development in the theory of this version of M,plit estimation and some numerical examples that show properties of the method and its application scope.

This part of the paper presents particular case of Msplit estimation called a squared Msplit estimation whose target function is based on convex squared functions. One can find here theoretical foundations and algorithm of the squared Msplit estimation as well as some numerical examples.