Application of artificial neural networks to height transformation

Abstract

Original scientific paperThe vertical positioning has two indispensable constituents: the height and the relevant reference surface. The definition of the height differs according to the appointed reference surface. Global Navigation Satellite Systems (GNSS) ensure ellipsoidal heights relative to a geodetic reference ellipsoid surface. However, many field applications require heights that are related to a physically meaningful surface (e.g. the geoid). Such physically meaningful heights often provided in terms of orthometric heights. The geoid undulation is the relation between the ellipsoidal and orthometric heights. The ellipsoidal heights can be transformed to orthometric heights via two principal approaches: a gravimetric geoid model, and geometrical interpolation between geoid undulations where GNSS observations have been collocated with benchmarks. The purpose of this study is investigating the applicability of a back propagation artificial neural network as a height transformation tool. Keywords: back propagation artificial neural networks; ellipsoidal height; orthometric height Primjena umjetnih neuronskih mreža na transformaciju visineIzvorni znanstveni članak Dvije su osnovne komponente vertikalnog pozicioniranja: visina i odgovarajuća referentna površina. Definicija visine se mijenja u skladu s odabranom referentnom površinom. Satelitski sustavi globalne navigacije (Global Navigation Satellite Systems -GNSS) daju elipsoidne visine razmjerne površini geodetski referentnog elipsoida. Međutim, mnoge aplikacije zahtijevaju visine koje su povezane s fizikalno značajnom površinom kao što je geoid. Takve visine su u obliku ortometrijskih (ili normalnih) visina. Veza između elipsoidnih i ortometrijskih visina je visina geoida iznad referentnog elipsoida, obično nazivana valovitim kretanjem geoida. Dva su osnovna pristupa kod pretvaranja elipsoidnih u ortometrijske visine: gravimetrijski model geoida i interpolacija između geometrijski deriviranih valovitih kretanja geoida gdje su GNSS mjerenja locirana uz nivelacijske točke. U ovom se radu istražuje korisnost umjetnih neuronskih mreža s unatražnim rasprostiranjem kao alternativni alat za transformaciju visine.Ključne riječi: elipsoidna visina; ortometrijska visina; umjetne neuronske mreže s unatražnim rasprostiranjem

Deriving a Geoid Undulation Network over Egypt by Merging Data of Different Global Geo-Potential Models

“…The relations between Ellipsoid height (h i ), orthometric height (H i ) and geoid undulation (N i ) (Yilmaz et al, 2017).…”

Correlation Relationship between Different GGMs Data over Egypt

“…Although the GPS (as one of space-based technology) is used recently as a widespread in the world for many reasons, Orthometric height (H i ) is still needed for many different projects of civil engineering area. Yilmaz et al (2017) presented the relation between the Geodetic height (h i ) and Orthometric height (H i ), which were linked mathematically by Geoid Undulation/Geoidal Height (Ni) of any point by equation (1) and graphically in figure (1). So, the orthometric height value (H) at point (i) can be calculated by knowing the ellipsoid height value (h i ) and undulation height value (Ni) in order to combine the advantages between both techniques and converting also.…”