GBDM+: an improved methodology for a GNSS-based distance meter

The determination of distances consistent with the definition of the base unit of length in the International System of Units (SI), the SI meter, with uncertainties of less than 1 ppm up to 5 km in the open air is a current challenge that is being increasingly required for different applications, including the determination of local ties, calibration baselines, and high precision geodetic metrology in singular scientific and engineering projects. The required knowledge of the index of refraction of the propagating medium at the same level of 1 ppm is a hard limit to the use of precise electronic distance meters (EDMs), which has motivated the recent development of new two-color, refractivity compensated, EDM prototypes. As an alternative, the use of global navigation satellite systems (GNSS) could benefit from their high scale stability although the lack of appropriate estimation of the uncertainties in their sources of error and their unknown propagation into the final result during the data processing has prevented a rigorous uncertainty analysis and, therefore, the use of GNSS for absolute distance determination. Stemming from our initial methodology for a GNSS-based distance meter (GBDM) that was restricted to relatively horizontal baselines and distances up to 1 km only, we have improved the method so that its application range is extended to baselines of up to 5 km with a possibly significant height difference so that it provides the final baseline distance with the corresponding uncertainty derived from the uncertainties in the different error sources rigorously propagated through the equations by which the distance is finally determined. This improved methodology, named as GBDM+, constitutes a significant step forward in the application of GNSS to open air length metrology.