Towards calibration of GNSS receiver hardware delays for improving geodetic reference systems through clock ties. A requirements analysis for developing a GNSS pseudolite transmission chain

The growing demand for Earth science applications poses challenges in improving geodetic reference frames. Systematic errors currently restrict the accuracy of these frames because the classical geometric ties between multiple geodetic techniques fall short of sufficiency. Our objective is to identify and analyze the impact of variable GNSS receiver hardware delays (incl. antenna-hardware delays) on carrier-phase time transfer with an accuracy of picoseconds/millimeters. We propose using a ground-based GNSS pseudolite system synchronized to an optical timing system (clock tie) developed at the Geodetic Observatory Wettzell to calibrate the variable hardware delays and facilitate a closure in time between multiple geodetic techniques. This study analyzes the requirements for developing a GNSS pseudolite and its transmission chain. We reformulate the classic iono-free Precise Point Positioning (PPP) mathematical theory to incorporate pseudolite data, separating the known receiver clock error from unknown transceiver hardware delays. The analysis suggests a preference for highly directive and mechanically stable Right Hand Circularly Polarized (RHCP) log periodic or helix transmission antennae. Calibration for Phase Center Offset (PCO), Phase Center Variations (PCVs) and careful installation to minimize multipath are crucial. This results in a carrier-phase observation model with three unknowns: transceiver hardware delays (our focus), frequency-dependent ambiguity terms, and low tropospheric delay influence. Utilizing a USRP-based transmission procedure, we successfully tracked an E1B Galileo signal replica with an in-house developed GNSS software-defined receiver (SDR). The transmission was implemented using two approaches: over-the-air and loopback. The over-the-air transmission was carefully planned using a link budget calculation to ensure that it did not exceed the allowed free-air transmission constraints. Empirical validation ensured a carrier-to-noise ratio (C/N0) below 30dB/Hz near critical public areas. In the loopback approach, the transmitted GNSS signal was fed into the local SDR within the pseudolite, sharing the same Analog-Digital-Converter (ADC)/ Digital-Analog-Converter (DAC)ADC/DAC, clock and local oscillators. In a future stage, this signal is supposed to be compared to a reference signal derived from the optical timing system.  In our analysis, we also assessed the stability of the USRP frequency synthesizer, known as Phase Lock Loop (PLL), in the context of high-precision applications, such as real-time kinematic (RTK) positioning. We found that tuning the synthesizer in integer-n mode is crucial in maintaining a stable carrier frequency and achieving a 100% real-time kinematic positioning fixing rate.