Mountain peaks and their altitude have been of interest to researchers across disciplines. Measurement methods and techniques have changed and developed over the years, leading to more accurate measurements and, consequently, more accurate determination of peak altitudes. This research transpired due to the frequency of misstatements found in existing sources including books, maps, guidebooks and the Internet. Such inaccuracies have the potential to create controversy, especially among peak-baggers in pursuit of climbing the highest summits. The Polish Sudetes Mountains were selected for this study; 24 summits in the 14 mesoregions were measured. Measurements were obtained employing the global navigation satellite system (GNSS) and light detection and ranging (LiDAR), both modern and highly precise techniques. Moreover, to determine the accuracy of measurements, several of the summits were measured using a mobile phone as an additional method. We compare GNSS vs. LiDAR and verify the level of confidence of peak heights obtained by automatic methods from LiDAR data alone. The GNSS receiver results showed a discrepancy of approximately 10 m compared with other information sources examined. Findings indicate that the heights of peaks presented in cartographic materials are inaccurate, especially in lesser-known mountain ranges. Furthermore, among all the mountain ranges examined, the results demonstrated that five of the summits were no longer classed as the highest, potentially impacting tourist perceptions and subsequent visitation. Overall, due to the topographical relief characteristics and varying vegetation cover of mountains, we argue that the re-measuring procedure should comprise two steps: (1) develop high-resolution digital elevation models (DEMs) based on LiDAR; (2) assumed heights should be measured using precise GNSS receivers. Unfortunately, due to the time constraints and the prohibitive costs of GNSS, LiDAR continues to be the most common source of new altitude data.
The paper presents a combined analysis of terrestrial laser scanning (TLS) and structure from motion (SfM) photogrammetric measurement to determine an accurate model of the surface shape of a thin-walled dome. The analysis takes into account several factors that may affect the accuracy of measurement. In TLS measurements, these are related to scattering of the beam and its penetration into the structure of objects. Penetration of the beam into a synthetic structure changes the measured length. Shell moisture, caused by rainfall or dew effect, similarly affects the measured length, but the changes are dispersed. In the first case, it will change the size of the object, and in the second one, it generates measurement noise. SfM photogrammetric problems, such as object gloss and ambient reflection, lack of detail, and different results from software creating point clouds were also analyzed. An interesting observation was the significant influence of atmospheric pollution, sedimented on the lower half of the glossy dome, on increasing the accuracy of photogrammetric measurement. The analyses contain a number of cases that take into account the complex problems of obtaining and processing data of such facilities: periodic measurement, TLS and SfM photogrammetric measurement, measurement outside and inside the object, determination of the wall thickness, comparison with the project and free-sphere fitting, and use of dome rotation during TLS.
A geoid or quasigeoid model allows the integration of satellite measurements with ground levelling measurements in valid height systems. A precise quasigeoid model has been developed for the city of Krakow. One of the goals of the model construction was to provide a more detailed quasigeoid course than the one offered by the national model PL-geoid2011. Only four measurement points in the area of Kraków were used to build a national quasigeoid model. It can be assumed that due to the small number of points and their uneven distribution over the city area, the quasigeoid can be determined less accurately. It became the reason for developing a local quasigeoid model based on a larger number of evenly distributed points. The quasigeoid model was based on 66 evenly distributed points (from 2.5 km to 5.0 km apart) in the study area. The process of modelling the quasigeoid used height anomalies determined at these points on the basis of normal heights derived through levelling and ellipsoidal heights derived through GNSS surveys. Height anomalies coming from the global geopotential model EGM2008 served as a long-wavelength trend in those derived from surveys. Analyses showed that the developed height anomaly model fits the empirical data at the level of single millimetres – mean absolute difference 0.005 m. The developed local model QuasigeoidKR2019, similar to the national model PL-geoid2011, are models closely related to the reference and height systems in Poland. Such models are used to integrate GNSS and levelling observations. A comparison of the local QuasigeoidKR2019 and national PL-geoid2011 model was made for the reference frame PL-ETRF2000 and height datum PL-KRON86-NH. The comparison of the two models with respect to GNSS/levelling height anomalies shows a triple reduction in the values of individual quartiles and a mean absolute difference for the developed local model. These summary statistics clearly indicate that the accuracy of the local model for the city of Krakow is significantly higher than that of the national one.
Precise data processing from the Global Navigation Satellite Systems (GNSS) reference station network is mainly based on a combination of double-differenced carrier phase and code observations. This approach allows most of the measurement errors to be removed or reduced and is characterized as the most accurate method. However, creating observation differences between two receivers and two satellites increases the measurement noise of the observations by a factor of 2. As a result, it increases the impact of the incorrect definition of the noise characteristic on the results of the estimation of the unknowns in the positioning model. This is especially important in Multi-GNSS solutions, which integrate measurements from different systems, for which the stochastic parameters of observation may differ significantly. In this paper, the authors prepared a complex analysis of the noise type in double-differenced GNSS (GPS, GLONASS and Galileo) observations, both carrier phase and code ones, with a 1 s sampling interval. The Autocorrelation Function (ACF) method, the Lomb–Scargle (L-S) periodogram method, and the Allan variance (AVAR) method were used. The results that were obtained for the weekly set of measurement data showed that, depending on the system and type of observation, the noise level and its type are significantly different. Among the code measurements, the lowest noise levels were obtained for the GPS C5Q and Galileo C7Q/C8Q observations, with the standard deviations not exceeding ±10 cm, while the noisiest observations were for the GLONASS C1C and C2C signals, which had standard deviations of about ±90 cm and ±45 cm, respectively. For the carrier phase observations, each signal type was characterized by very similar noise levels of ±1.5–3.5 mm. The ACF analysis showed that 1 Hz double-differenced GNSS data can only be treated as being not correlated to time for carrier phase observations; for code observations, an irrelevant autocorrelation may be considered for measurement intervals greater than 20 s. Depending on the GNSS signals, the spectral index k varies in a range from −1.3 to −0.2 for code data and k = 0.0 in the case of phase data. Using the modified Allan deviation (MDEV) allows for specific noise types for each signal and GNSS system to be determined. All of the code observations were characterized by either flicker PM or white PM. In the case of the phase observations, they were all uniquely characterized by white PM (GPS and Galileo or by white PM and flicker PM (GLONASS).
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