The paper presents the results of the studies on the determination of the degree of dependence between the adjusted observations, on the basis of the levels of their coexistence in a network. An approximate model is proposed making it possible to estimate that dependence without the necessity to perform the adjustment procedure. This model can be applied in the procedures of gross error detection in observations. Additionally, a supplementary algorithm to determine the coexistence levels for the observations on the grounds of the matrix of coefficients in the observation equations is presented.

The present work deals with continuum mechanical considerations for deformable and rigid solids as well as for fluids. A common finite element framework is used to approximate all systems under considerations. In particular, we present a standard displacement based formulation for the deformable solids and make use of this framework for the transition of the solid to a rigid body in the limit of infinite stiffness. At last, we demonstrate how to immerse a discretized solid into a fluid for fluid-structure interaction problems.

The paper presents the results of research on the DiSTFA method (Displacements and Strains using Transformation and Free Adjustment) for the determination of displacement and strains of a surface determined in unstable reference systems. Additionally, covariance matrices were introduced to assess the accuracy of estimation results. The theoretical discussion includes an example of its application in a simulated, three-dimensional geodetic network. The obtained results encourage further, more detailed analysis of real geodetic networks.