Combining Global Geopotential Models, Digital Elevation Models, and GNSS/Leveling for Precise Local Geoid Determination in Some Mexico Urban Areas: Case Study

This work shows improvements of geoid undulation values obtained from a high-resolution Global Geopotential Model (GGM), applied to local urban areas. The methodology employed made use of a Residual Terrain Model (RTM) to account for the topographic masses effect on the geoid. This effect was computed applying the spherical tesseroids approach for mass discretization. The required numerical integration was performed by 2-D integration with 1DFFT technique that combines DFT along parallels with direct numerical integration along meridians. In order to eliminate the GGM commission error, independent geoid undulations values obtained from a set of GNSS/leveling stations are employed. A corrector surface from the associated geoid undulation differences at the stations was generated through a polynomial regression model. The corrector surface, in addition to the GGM commission error, also absorbs the GNSS/leveling errors as well as datum inconsistencies and systematic errors of the data. The procedure was applied to five Mexican urban areas that have a geodetic network of GNSS/leveling points, which range from 166 to 811. Two GGM were evaluated: EGM2008 and XGM2019e_2159. EGM2008 was the model that showed relatively better agreement with the GNSS/leveling stations having differences with RMSE values in the range of 8–60 cm and standard deviations of 5–8 cm in four of the networks and 17 cm in one of them. The computed topographic masses contribution to the geoid were relatively small, having standard deviations on the range 1–24 mm. With respect to corrector surface estimations, they turned out to be fairly smooth yielding similar residuals values for two geoid models. This was also the case for the most recent Mexican gravity geoid GGM10. For the three geoid models, the second order polynomial regression model performed slightly better than the first order with differences up to 1 cm. These two models produced geoid correction residuals with a standard deviation in one test area of 14 cm while for the others it was of about 4–7 cm. However, the kriging method that was applied for comparison purposes produced slightly smaller values: 8 cm for one area and 4–6 cm for the others

Combining Global Geopotential Models, Digital Elevation Models, and GNSS/Leveling for Precise Local Geoid Determination in Some Mexico Urban Areas: Case Study

This work shows improvements of geoid undulation values obtained from a high-resolution Global Geopotential Model (GGM), applied to local urban areas. The methodology employed made use of a Residual Terrain Model (RTM) to account for the topographic masses effect on the geoid. This effect was computed applying the spherical tesseroids approach for mass discretization. The required numerical integration was performed by 2-D integration with 1DFFT technique that combines DFT along parallels with direct numerical integration along meridians. In order to eliminate the GGM commission error, independent geoid undulations values obtained from a set of GNSS/leveling stations are employed. A corrector surface from the associated geoid undulation differences at the stations was generated through a polynomial regression model. The corrector surface, in addition to the GGM commission error, also absorbs the GNSS/leveling errors as well as datum inconsistencies and systematic errors of the data. The procedure was applied to five Mexican urban areas that have a geodetic network of GNSS/leveling points, which range from 166 to 811. Two GGM were evaluated: EGM2008 and XGM2019e_2159. EGM2008 was the model that showed relatively better agreement with the GNSS/leveling stations having differences with RMSE values in the range of 8–60 cm and standard deviations of 5–8 cm in four of the networks and 17 cm in one of them. The computed topographic masses contribution to the geoid were relatively small, having standard deviations on the range 1–24 mm. With respect to corrector surface estimations, they turned out to be fairly smooth yielding similar residuals values for two geoid models. This was also the case for the most recent Mexican gravity geoid GGM10. For the three geoid models, the second order polynomial regression model performed slightly better than the first order with differences up to 1 cm. These two models produced geoid correction residuals with a standard deviation in one test area of 14 cm while for the others it was of about 4–7 cm. However, the kriging method that was applied for comparison purposes produced slightly smaller values: 8 cm for one area and 4–6 cm for the others

Short Baseline Calibration using GPS and EDM Observations

Una investigación fue conducida para establecer y comparar una línea base de calibración a partir de mediciones realizadas a los GPS (Sistemas de Posicionamiento Global) y de taquímetro electrónico o EDM (Medición Electrónica de Distancia). El experimento se realizó en el campus de la Universidad Autónoma de Sinaloa (UAS) en Culiacán, México. El objetivo principal recae en la necesidad de establecer una línea base de calibración (∼125 m), que permita la realización continua y permanente de mediciones con receptores geodésicos GPS y con EDM para garantizar y validar las precisiones especificadas por los fabricantes de tales instrumentos. Dentro de los instrumentos de medición de diferente tipo y marca comercial utilizados y comparados se encuentran tres tipos de receptores geodésicos GPS: Topcon Hiper Lite +, Ashtech Z-Xtreme y Leica SR500 y tres tipos de EDM: Topcon GTS-236W, Pentax R-326EX y Leica TC-407. Para el experimento, los componentes de la línea base de calibración fueron calculados usando las observaciones GPS de fase de diferencias dobles libres de ionosfera y procesadas utilizando el software científico PAGES (Program for the Adjustment of GPS EphemerideS). Las mediciones GPS fueron procesadas considerando intervalos de medición de 1 segundo, un ángulo de elevación de 10 grados, y órbitas precisas GPS diseminadas por el IGS (International GNSS Service). Por otra parte, la longitud de la línea base de calibración también fue directamente determinada con base en el promedio de 20 mediciones realizadas con cada EDM sobre los monumentos BASE1 y BASE2. Resultados obtenidos con GPS concuerdan entre las diferentes marcas de equipos con diferencias de ±2 mm, en contraste con los resultados obtenidos con EDM, los cuales difieren entre ±3 mm. doi: https://doi.org/10.1016/j.gi.2015.04.01