## 1 Introduction  
Global Navigation Satellite Systems (GNSS) are nowadays extensively used to survey geodetic networks with different levels of precision. However, there are countless applications where satellite systems must be integrated with traditional three-dimensional terrestrial surveying techniques. These include, e.g., underground engineering surveying and any surveying application where equipotential surfaces are relevant, such as in the hydraulic infrastructure framework or during the construction of large instruments, (e.g., large-scale interferometers or particle accelerators, _etc._), where extended geoidal surfaces are often to be determined. For these applications, global geometric techniques, such as GNSS, must be combined with more traditional observation techniques and instruments (total stations, levels, gyroscopic theodolites, nadir/zenith levels, _etc._), whose set up and measurements depend on the local plumb line, _i.e._, on the tangent to the line of force of the terrestrial gravity field at the instrument [1; 2; 3]. In order to integrate the observations of GNSS and traditional instruments, it is necessary to know the Deflection of the Vertical (DoV), defined as the angle between the plumb line and the ellipsoidal normal in a given point. There are areas where the ellipsoid can considerably differ from the geoid surface, in particular for globally oriented geocentric ellipsoids [4]. The values of the DoV can be as large as several tens of arcseconds [5] and can exhibit significant variations in relation to the change of topography and to the spatial variation of the lithosphere density. The DoV values and spatial variations can well exceed the precision of the measurements and, often, its impact cannot be ignored when solely terrestrial technique based surveys are also concerned [4; 6]. In the 1980s and 1990s when satellite navigation systems became fully accessible for a geodetic use, the development of the adjustment theory to be applied to mixed three-dimensional networks surveyed by GPS and traditional techniques required the inclusion of the DoV values [7; 8; 9; 10; 11]. One striking example of the importance of the DoV is related to the alignment of the tie vectors for the combination of space geodetic solutions and the computation of the International Terrestrial Reference Frame (ITRF) [12]. In fact, the ITRF is realized combining the global solutions of GNSS, Very Long Baseline Interferometry (VLBI), Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) and Satellite Laser Ranging (SLR) and a key role is played by the co-location sites where two or more geodetic techniques are operated. At these sites, the connection between each single technique frame is realized measuring the tie vector, _i.e._, the reciprocal position of the reference points of each instrument. The tie vectors are generally measured using classic topographical (traditional) instruments and, therefore, are initially obtained in a local topocentric reference system. In the ITRF computation, the tie vectors must be aligned with the global reference frame before the combination process is realized. The alignment can be performed in various ways and it is always critical, as any misalignment could degrade the intrinsic precision of the tie vector and impact the ITRF solution. A comprehensive discussion about the role of the co-location sites in space geodesy and about the tie vectors and their alignment in the ITRF computation can be found in [13]. A common alignment procedure is based on the least-squares method: the tie vector is rotated and translated via a similarity transformation performed using common points, _i.e._, points surveyed using both terrestrial and GNSS techniques. However, this method might be insufficiently accurate for small networks: the limited accuracy of GNSS-derived ellipsoidal heights will certainly affect the positions of common points and will particularly reflect on the orientation accuracy of the shortest baselines (e.g., a couple of hundred meters or less).