## 4 New TIRA System Design
### Access to the Global Reference Frame and Time Scale  
The radar measurements of the TIRA instruments are acquired in their native coordinates given by signal delay and Doppler frequency or (pseudo)-range and range rate,  
Figure 17: Illustration of the digital twin and model-based design concepts using TIRA’s high-precision position control as an example. Figure 18: Principle integration of system models into the operational software of TIRA utilizing the open FMI standard. respectively, and the monopulse direction of arrival (DOA) estimates of the targets echoes. Besides these measurements, the azimuth and elevation of the mechanical pointing as axis positions of the reflector are logged by the antenna positioning system. On the other hand, the targets' motion, usually that of space objects, have to be modeled in a global inertial reference system like the International Celestial Reference System (ICRS). To obtain the measurements in the respective ICRS realization, the International Celestial Reference Frame (ICRF), we have to transform the acquired data with the help of auxiliary measurements and through intermediate systems. TIRA maintains a local time scale operating a cesium beam primary clock to which timestamps and frequencies of the system are tied to give coherent measurements. This local time is attached to coordinated universal time (UTC) via common-view GNSS time transfer or precise point positioning (PPP). As the local clock is clocking a time-transfer global navigation satellite system (GNSS) receiver in the same setup as that maintained by metrology institutions, we can directly tie the local time scale to the UTC (PTB) which is realized in Braunschweig by jointly processing the GNSS raw data of both stations. Measurements of the radar are given in their respective feed's fixed coordinate frames. The measured propagation time is represented as pseudo-range and referenced to the intersection of the antenna rotational axes. Doppler frequencies are interpreted as range rates. To obtain the geometric range of the target, multiple effects of signal propagation, for example, from special relativity, troposphere, and ionosphere, have to be taken into account. The estimation of the respective models is supported by a meteorological measurement as well as observations of the GNSS permanent station. The monopulse system is calibrated and aligned along with measurements of the one-way and two-way antenna patterns using a terrestrial remote station at a distance of 23 km. Further calibration and validation are established through the in-orbit measurement of suitable objects with known precise ephemerides. The derived target position in the feed's coordinate system is then transformed to the antenna coordinates with knowledge of the reflectors' pointing vector. In order to access this vector, the mechanical boresight reference of the antenna is given by an optical mirror which was used to align the parabolic reflector panels during initial setup. The orientation of that mirror and thus the pointing of the antenna is measured by encoders on the axes. Measurements on the elevation angles are referenced to the local tangent plane by autocollimation with an automatic level towards the reference mirror; the azimuth encoders are referenced by transferring the normal of the reference mirror to a theodolite on the north monument outside the radome structure via collimation, which then measures the horizontal angle towards a marker on the GNSS station. As this baseline is known by astronomical optical measurements, a direct relation between the azimuth reading and true north is established. As indicated in Figure 19, three vectors are involved to find the relation between the reflector system and the global terrestrial system. The true orientation of the azimuth axis, the local vertical as normal to the geoid, which is accessed by leveling, and the normal to the ellipsoid as reference in the global system.