226 C. Kotsakis Anatomy of minimum constraints in geodetic network adjustment C. Kotsakis Department of Geodesy and Surveying, Aristotle University of Thessaloniki Abstract. The scope of this paper is to investigate the influence of the minimum constraints (MCs) on the reference frame parameters in a free-net solution. The non-estimable part of these parameters is analyzed in terms of its stability under a numerical perturbation of the constrained datum functionals. In practice, such a perturbation can be ascribed either to hidden errors in the known coordi- nates/velocities participating in the MCs, or to a simple change of their a priori values due to a datum switch on a different fiducial dataset. In addition, a perturba- tion of this type may cause a nonlinear variation to the estimable part of the refer- ence frame parameters, since it theoretically affects the adjusted observations that are implied by the network's nonlinear observational model. The aforementioned effects have an impact on the quality of a terrestrial reference frame that is estab- lished via a minimum-constrained adjustment, and our study shows that they are both controlled through a characteristic matrix which is inherently linked to the MC system. 1. Introduction The establishment of terrestrial reference frames (TRFs) is a fundamental task in geodesy, closely related to the zero-order design or datum choice problem of net- work optimization theory (Grafarend 1974, Teunissen 1985). Due to the inherent datum deficiency in all types of geodetic measurements, a set of external condi- tions is always required to obtain a unique and well defined TRF realization from a geodetic network adjustment. The use of minimum constraints signifies an optimal choice of such conditions in the sense that they provide the required information for the datum definition without interfering with the network’s estimable character- istics. As a result, a minimum-constrained network is theoretically free of any geometrical distortion that could originate from the external datum conditions, while its estimable TRF parameters (if any) are determined solely from the avail- able measurements without being affected by the user’s minimum constraints. The latter affect only the non-estimable part of the reference frame parameters which is not reduced by the data, yet they influence the quality of the entire coordinate- based representation of the adjusted network (e.g. the covariance matrix of the es- timated positions and their external reliability level). A realized TRF through a network adjustment is subject to quality limitations