# Development of a Submillimetric GNSS-Based Distance Meter for Length Metrology +
## 2 GNSS Data Processing Approach
### Initial Assumptions  
Our approach to investigate the capabilities of GNSS for length determination with submillimetric accuracy relies on four initial assumptions: First, modern receivers provide carrier phase observations with submillimetre level noise. Secondly, distances determined by GNSS are highly stable at a global scale. Thirdly, the modulus of a vector between two GNSS receiver antennas can be more precisely determined than its corresponding components. Finally, the increasing number of operational GNSS satellites allows one to optimise the selection of satellites to improve length determination. These four assumptions are discussed below. Regarding the noise of the GNSS carrier phase signal, it used to be assumed as a random error of 1% of the carrier wavelength, but recent literature shows that modern GNSS receivers can provide enhanced performance [26; 27]. The random noise of a GNSS signal depends on the electronics of the receivers, but also on the quality of the signal. Therefore, a different noise should be expected for each constellation and even for each individual satellite. A standard method to assess the overall random noise of a GNSS receiver is to perform a zero baseline test, which consists of processing the double differences of phase observations of two receivers that are connected to the same antenna by means of a signal splitter (see Figure 1). Figure 2 shows the double difference residuals obtained using two multi-constellation Leica GS10 receivers. The overall root mean square (RMS) value obtained for L1 double difference residuals was 0.7 mm, thus confirming our first initial assumption that they are currently below 1 mm \(\times\) 2, that is, as we assumed, less than 1 mm of standard error for a carrier phase observation amplified by a factor of 2 due to the double difference combination (see e.g., expression (20.67) in Reference [28]). Figure 1: Global Navigation Satellite System (GNSS) measurement at the Universitat Politècnica de Valencia (UPV) calibration baseline using a 3D choke-ring antenna equipped with a signal splitter and two receivers collecting the same signals. Concerning the GNSS scale stability, it is maintained worldwide at the level of 1 ppb = 10\({}^{-9}\), which is to say 1 mm over 1000 km. Nonetheless, some open questions still remain as to whether this high absolute scale accuracy is also applicable to short distance determination in the existing metrological infrastructures. Moreover, the GNSS scale stability relies on the accuracy of the precise ephemeris and ultimately on the International Terrestrial Reference Frame (ITRF) which is used for their determination. Since the ITRF scale is determined by a combination of Satellite Laser Ranging (SLR) and Very Long Baseline Interferometry (VLBI) observations whose scale differs by about 10\({}^{-9}\)[29], the linkage between the centre of the instruments used by SLR, VLBI and GNSS at Fundamental Geodetic Observatories (FGO), also known as local ties, should be performed with submillimetric accuracy [2]. Thus, an additional benefit of submillimetric length determination with an appropriate metrological uncertainty evaluation based on traceable instruments and methods would be to improve the ITRF scale and consequently the accuracy of the precise ephemeris of GNSS satellites. The third assumption is that GNSS distance may be better determined than the individual components of the corresponding vector.