Development of a Submillimetric GNSS-Based Distance Meter for Length Metrology

Absolute distance determination in the open air with an uncertainty of a few tenths of a millimetre is increasingly required in many applications that involve high precision geodetic metrology. No matter the technique used to measure, the resulting distances must be proven consistent with the unit of length (SI-metre) as realized in the outdoor facilities traditionally used in length metrology, which are also known as calibration baselines of reference. The current calibration baselines of reference have distances in the range of 10 to 1000 m, but at present there is no solution on the market to provide distances with submillimetric precision in that range. Consequently, new techniques such as multi-wave interferometry, two-wave laser telemeters or laser trackers are being developed. A possible alternative to those sophisticated and expensive techniques is the use of widely used Global Navigation Satellite Systems (GNSS) in order to provide a GNSS-Based Distance Meter (GBDM). The use of a GBDM as a potential technique for length metrology has been thoroughly analysed in several European research projects by using the state-of-the-art geodetic software, such as Bernese 5.2, but no definite conclusions have been drawn and some metrological questions are considered still open. In this paper, we describe a dedicated approach to build up a submillimetric GBDM able to be applied in the current calibration baselines of reference, as well as possible methods to cope with the multipath error of the GNSS signals which is the major limitation for the practical uptaking of the technique in metrology. The accuracy of the proposed approach has been tested following the length metrology standards in four experiments carried out in the Universitat Politècnica de València (UPV). The results demonstrate that the proposed GBDM can provide an accuracy of a few tenths of a millimetre in the current calibration baselines of reference.

Kalkayotl: A cluster distance inference code

Context. The high-precision parallax data of the Gaia mission allows for significant improvements in the distance determination to stellar clusters and their stars. In order to obtain accurate and precise distance determinations, systematics such as parallax spatial correlations need to be accounted for, especially with regard to stars in small sky regions. Aims. Our aim is to provide the astrophysical community with a free and open code designed to simultaneously infer cluster parameters (i.e., distance and size) and distances to the cluster stars using Gaia parallax measurements. The code includes cluster-oriented prior families and it is specifically designed to deal with the Gaia parallax spatial correlations. Methods. A Bayesian hierarchical model is created to allow for the inference of both the cluster parameters and distances to its stars. Results. Using synthetic data that mimics Gaia parallax uncertainties and spatial correlations, we observe that our cluster-oriented prior families result in distance estimates with smaller errors than those obtained with an exponentially decreasing space density prior. In addition, the treatment of the parallax spatial correlations minimizes errors in the estimated cluster size and stellar distances, and avoids the underestimation of uncertainties. Although neglecting the parallax spatial correlations has no impact on the accuracy of cluster distance determinations, it underestimates the uncertainties and may result in measurements that are incompatible with the true value (i.e., falling beyond the 2σ uncertainties). Conclusions. The combination of prior knowledge with the treatment of Gaia parallax spatial correlations produces accurate (error < 10%) and trustworthy estimates (i.e., true values contained within the 2σ uncertainties) of cluster distances for clusters up to ∼5 kpc, along with cluster sizes for clusters up to ∼1 kpc.