## 2 DoV Estimation: Description of the Methods
### Determination of DoV Using the QDaedalus System  
The DoV components were also measured using QDaedalus, an instrument designed and built at the Institute of Geodesy and Photogrammetry of ETH Zurich [23].  
QDaedalus consists of a CCD camera clipped on a total station, in our case a Leica TCA2003 (\(\sigma=0.5\) arcsec), in replacement of the eye-piece, a pluggable front lens, a low cost u-blox LEA-6T GNSS receiver, and a laptop running the dedicated software for steering, imaging and processing [30].  
The instrument is able to automatically search the most relevant stars thanks to the internal star catalogue (FK6) [31] and it measures the local star vector by means of the embedded image recognition algorithm. For astro-geodetic applications, the centroid of the image of the stars is detected and tracked. The observation equation underlying the determination of the astronomical coordinates is the following [32]:  
\[\begin{array}{lcl}x_{topo}\left(t\right)&=&\mathbf{T}\left(\Lambda,\Phi \right)&x_{ITRS}\left(t\right)\\ &=&\mathbf{T}\left(\Lambda,\Phi\right)&\mathbf{R}_{2}\left(-x_{p}\right)& \mathbf{R}_{1}\left(-y_{p}\right)&\mathbf{R}_{3}\left(GAST\right)&\mathbf{N} \left(t\right)&\mathbf{P}\left(t\right)&x_{ICRS\bullet}\left(t\right)\end{array} \tag{6}\]  
where:  
\(\mathrm{x_{topo}}\left(\mathrm{t}\right)=\) star vector in the local topocentric Cartesian system;  
\(\mathrm{x_{ITRS}}\left(\mathrm{t}\right)=\) star vector in ITRS (International Terrestrial Reference System);  
\(\mathrm{x_{ICRS}}^{\ast}\left(\mathrm{t}\right)=\) star vector in ICRS (International Celestial Reference System) corrected for parallax, relativity and aberration;  
\(\mathbf{T}\left(\Lambda,\Phi\right)=\) transformation matrix from ITRS to the local topocentric system;  
\(\mathbf{R}_{2}\left(-\mathrm{x_{p}}\right)\)\(\mathbf{R}_{1}\left(-\mathrm{y_{p}}\right)=\) polar motion matrices;  
\(\mathbf{R}_{3}\left(\mathrm{GAST}\right)=\) Earth rotation matrix;  
\(\mathbf{N}\left(t\right)=\) nutation matrix;  
\(\mathbf{P}\left(t\right)=\) precession matrix; and  
\(\mathrm{t}=\) time of the observation.  
The star vector in ICRS is computed by means of NOVAS-C routines [33], while the parameters determining the matrices \(\mathbf{R}_{1}\), \(\mathbf{R}_{2}\), \(\mathbf{R}_{3}\), and \(\mathbf{N}\) are retrieved from the IERS Bulletin A [34].  
The astronomical coordinates \(\left(\Lambda,\Phi\right)\) are related to the ITRS ellipsoidal coordinates \(\left(\lambda,\varphi\right)\) measured with GNSS by the deflection of the vertical \(\left(\eta,\xi\right)\) according to Equation (3).  
The measurements were performed during nights with clear sky. The system allows to reach an accuracy in the order of 0.2-0.3 arcsec [30], and it depends on the number, the distribution and the apparent magnitude of the visible stars.  
In July 2014, the instrument was mounted on some existing pillars near the VLBI and permanent IGS-GNSS antennas of Medicina and Noto sites (see Figures 1 and 2), whose ellipsoidal coordinates were previously determined using geodetic GNSS receivers operated in static mode. Hence, the GPS receiver of QDaedalus was used for timing purposes only.  
When setting up at a new station, the approximate orientation of the instrument has to be established manually, by pointing to a known star such as Polaris.  
The robust adjustment of each set of measurements was directly performed in the field, enabling an immediate preliminary control of the results and avoiding gross errors in the instrumental set up and calibration.