# Development of a Submillimetric GNSS-Based Distance Meter for Length Metrology +
## 1 Introduction  
Absolute distance determination in the open air with an uncertainty of a few tenths of a millimetre is increasingly required in fields such as length metrology, high precision geodetic metrology, deformation monitoring at critical sites or local ties in Fundamental Geodetic Observatories (FGOs) [1, 2, 3]. In the present context, the term absolute refers to the fact that distances have to be consistent with the metre, the unit of length of the International System of Units (SI) which is currently defined as the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second [4]. This definition of SI-metre is realized by the National Metrology Institutes (NMIs) with a standard uncertainty \(U_{\{k=1\}}=10^{-12}\) by using laser interferometers with stabilised frequencies, though such a high accuracy can onlybe obtained for short distances, i.e., several metres, under laboratory conditions. Following the core concept of metrological traceability, those references or primary standards are subsequently transferred or disseminated from laboratories to outdoor metrological facilities that are also known as calibrations baselines. These calibration baselines, whose inter-pillar lengths usually range from 10 m to 1000 m, are then used as secondary and working standards for practical purposes [5; 6; 7]. The only calibration baseline that has proved stable with a relative standard uncertainty near \(u_{(k=1)}=10^{-8}\) for more than 70 years is the Nummela Standard Baseline (NSB) in Finland (864 m), and thus acknowledged as international standard in geodetic metrology. Such a high accuracy can only be obtained by using the Vaisala interferometer which has the additional metrologic advantage of being directly traced to SI-metre [8; 9; 10]. With this method being very demanding, the NSB inter-pillar distances are measured only every five years by the Finnish Geospatial Research Institute (FGI), although its accurate scale can be traceably transferred to other baselines of reference by using submillimetric Electronic Distance Meters (EDM) like the Kern Mekometer ME5000 (ME5000) which was manufactured in the late 1980s [11; 12]. Nevertheless, the use of the out-of-production ME5000 entails two problems. Firstly, only a few units of this type of EDM are still in use, and secondly, having only one carrier phase (0.628 nm), the air refractivity has to be determined with an accuracy better than 0.1 ppm by using meteorological sensors, which is rather difficult for distances longer than 1 km [12]. Consequently, new techniques such as multi-wave interferometry, two-wave laser telemeters or laser trackers are currently required to go beyond the ME5000 [13; 14; 15]. Yet the research effort is considerable, and it demands joint projects like the current 18 SIB01 GeoMetre--large-scale dimensional measurements for geodesy' which has received funding from the EMPIR programme co-financed by the participating states and from the European Union's Horizon 2020 research and innovation programme [16]. A possible alternative to those expensive techniques is the use of Global Navigation Satellite Systems (GNSS) to develop a GNSS-Based Distance Meter (GBDM). Some experiments that compare GNSS distances with EDM distances can be found in the literature, but being most of them based in the use of commercial GNSS software and EDM instruments, the differences between these two techniques can easily reach around 3 mm [17; 18]. The GBDM as a potential technique for length metrology was firstly analysed in the EMRP-JRP 3.1-TP 3 'Length' [19], and subsequently in the EMRP-JRP SIB60 'Surveying' [20]. Most of the studies were performed by using state-of-the-art geodetic software, i.e., the Bernese 5.2 [21], along with the most advanced geodetic products and models.