# Experimental Validation of a GNSS Receiver Antenna Absolute Field Calibration System
## 2 Materials and Methods
### LMMT Robotic Calibration System  
The LMMT robotic calibration system comprises a six-axis industrial robot Mitsubishi MELFA RV-4 FLM-Q, its corresponding controller Mitsubishi MELFA CR750, GNSS receivers with antennas, a personal computer (laptop), and the necessary wiring. An overview of the system components is shown in Figure 2, with the on-site calibration setup illustrated in Figure 3.  
Figure 1: Conceptual definition of the standard GNSS receiver antenna phase center correction (PCC) model; APC—actual phase center; MPC—mean phase center; ARP—antenna reference point; PCV—phase center variation; PCO—phase center offset [17]. As the most prominent hardware component of the system, the industrial robot is employed to precisely and efficiently sample the entire upper hemisphere of the AUT, ensuring homogeneous coverage in accordance with the concepts of absolute receiver antenna calibration. The robot is a multiple-joint-type robot arm of vertical structure and six degrees of freedom, with a rated load of 4 kg [37]. Communication between the robot controller and the personal laptop is facilitated via the TCP/IP protocol, enabling two-way data exchange. Prior to antenna calibration, the industrial robot is installed at the calibration field, i.e., the position and orientation of the robot base frame (RBF) in the global geocentric frame (e.g., ITRF2020) is determined according to the defined setup methodology and is based on a precise total station survey. The calibration field of the LMMT calibration facility consists of two concrete pillars (part of the Calibration Baseline of the Faculty of  
Figure 3: An on-site calibration setup of the antenna calibration system at LMMT. Figure 2: Overview of LMMT robotic antenna calibration system components [32]. Geodesy [38]), thus forming a 5 m long short-baseline. From a software perspective, the LMMT system operates through three independent modules, each custom-built in-house using Python (version number 3.10): the Antenna Calibration Module (ACM), the PCC Estimation Module (PEM), and the Time Synchronization module (TiSy) [17; 32]. Time synchronization is an important issue according to the receiver antenna robotic calibration method. This is mainly because carrier-phase observations registered during AUT rotations, i.e., robot travel time, must be temporally filtered and removed from further data processing and PCC estimation. Within LMMT's calibration system, the one pulse-per-second signal (1 PPS) and the corresponding _TimeTag_ message, which are outputted by the receiver, are utilized. This time synchronization method ensures that the computer's internal clock is disciplined and aligned with GPS Time (GPST). During system development, a comprehensive time synchronization test has been conducted, within which time differences between the computer's internal clock and Coordinated Universal Time (UTC), generated by the GNSS receiver, have been calculated. The duration of the synchronization test was 8000 epochs (seconds), i.e., approximately 2 h and 13 min, and was divided into three phases based on the working status of TiSy: TiSy OFF, TiSy ON, and TiSy OFF. Corresponding computer clock errors have been calculated and are depicted in Figure 4. Blue lines at epochs \(t=1900\) and \(t=7300\) indicate the change in TiSy's working status. Based on the obtained synchronization test results, and a comprehensive analysis of other influential factors, the time synchronization uncertainty of the developed calibration system has been experimentally estimated to be 1.02 ms [32]. The resulting data largely fulfill the requirements of the robotic calibration system. To estimate the PCC model of the AUT, the antenna is positioned by the industrial robot in a total of 2088 distinct spatial orientations with 2.5 s stationary at every single attitude.