On the physical meaning of geodetic networks’ over-constraints solutions

It is widely known that the geodetic networks (both terrestrial and space) suffer from the so-called rank deficiency. This is the algebraic expression of the weakness of the observations to sense all the necessary information for the reference system definition (in terms of origin scale and orientation). For example, the SLR technique is sensitive to the origin and scale, while the orientation can be only externally defined. On the other hand, the traditional quasar-based VLBI does not sense either origin and orientation but only scale. In general, the rank deficiency is remedied by the use of the so-called constraints. The constraints can be divided into two major categories: a. The minimum constraints, where they just treat the rank deficiency problem (as the word minimum dictates) and do not interfere with the shape of the network, and b. the over-constraints, which do not only solve the rank deficiency but alter the shape of the geodetic network. While the minimum constraint solutions are widely discussed in the geodetic literature, regarding their nature, the over-constraints' physical meaning is not so clear (if not vague). The present study aims to provide a physical meaning of the over-constraints solution, under the prism of its stochastic interpretation.