Reduced Equations for K UTM Scale Factor and GNSS Usage in Chilean Cadastral Environments

Abstract

Topographic distances from global navigation systems (GNSS) equipment are being progressively involved in legal land parcel registration applications (Bramanto et al., 2019; Dabove, 2019; Pullar and Donaldson, 2022; Roberts, 2005; Tamrakar, 2013), a practice not entirely reliable from the surveying point of view of legal land registration. GNSS observations expressed as Universal Transverse Mercator (UTM) coordinates, are cartographic projection data and are not exactly what horizontal ground topographic distances indicate, which are valid for land tenure, deeds, rights purposes. A method for converting GNSS positions to horizontal topographic distances in cadastral environments preserving metric accuracy standards fixed for parcel registration according to Chilean authorities, is presented here. Complex equations to determine scale factor K from the UTM projection have been reduced to a set of constant coefficients, allowing replicating electronic distance measurement (EDM) performance in horizontal distances used in other experiences as Australia, by just providing coordinates and observed accuracies. All assumptions are aimed to simplify the property registration procedures in singular geographic environments like Chile, where urban settlements can be found at heights 2,000 m or more, being of utmost relevance to bear in mind differences between projected and ground coordinates. Applied experiences performed near Santiago de Chile at heights of 600 m over the MSL, yielded 3 mm difference in 500 m distance compared to measurements carried out by means of GNSS equipment in static mode.