Abstract: In this paper, constrained minimization for the point of closest approach of two conic sections is developed. For this development, we considered the nine cases of possible conics, namely, (elliptic–elliptic), (elliptic–parabolic), (elliptic–hyperbolic), (parabolic–elliptic), (parabolic–parabolic), (parabolic–hyperbolic), (hyperbolic–elliptic), (hyperbolic–parabolic), and (hyperbolic–hyperbolic). The developments are considered from two points of view, namely, analytical and computational. For the analytical developments, the literal expression of the minimum distance equation (S) and the constraint equation (G), including the first and second derivatives for each case, are established. For the computational developments, we construct an efficient algorithm for calculating the minimum distance by using the Lagrange multiplier method under the constraint on time. Finally, we compute the closest distance S between two conics for some orbits. The accuracy of the solutions was checked under the conditions that L solution ≤ ɛ1; G solution ≤ ɛ2, where ɛ1,2 < 10−10. For the cases of (parabolic–parabolic), (parabolic–hyperbolic), and (hyperbolic–hyperbolic), we studied thousands of comets, but the condition of the closest approach was not met. PubDate: Fri, 08 Oct 2021 00:00:00 GMT

Abstract: The aim of this work is to explore, for the first time in Poland, the possibility of determining Earth’s crust movements from permanent observations at selected permanent stations using the GipsyX software for a period of 8 years (2011–2018) in the ITRF2014 reference frame. The data used in this work are from 15 Aktywna Sieć Geodezyjna (ASG)-EUPOS stations from 2011 to 2018, which are also European Permanent Network (EPN) stations. The stations Borowa Góra, Borowiec, Józefosław, Lamkówko, and Wroclaw are also International Global Navigation Satellite Systems (GNSS) Service (IGS) stations. Daily data, rinex files, for these stations have been made available for this work by the Main Office of Surveying and Cartography. The calculations were made using the GipsyX software in the ITRF14 reference frame. The tests performed have shown that daily solutions from 8-year-long time series give secular trends with an accuracy of 0.01 mm/yr. Our results suggest that there are small differences in horizontal and vertical velocities and in the accuracy estimated between our and EPN solutions. At some stations, for example, Łódź, the differences are much larger. The impact of additional GNSS observations on the accuracy of determination of horizontal and vertical movements of the Earth’s crust shows a submillimeter accuracy in computed coordinates of stations even at a relatively small time interval. It means that multi-GNSS Precise Point Positioning (PPP) processing can be used in the future for the estimation of geodynamic processes. PubDate: Fri, 08 Oct 2021 00:00:00 GMT

Abstract: To estimate Moho depth, geoid, gravity anomaly, and other geopotential functionals, gravity data is needed. But, gravity survey was not collected in equal distribution in Ethiopia, as the data forming part of the survey were mainly collected on accessible roads. To determine accurate Moho depth using Global Gravity Models (GGMs) for the study area, evaluation of GGMs is needed based on the available terrestrial gravity data. Moho depth lies between 28 km and 32 km in Afar. Gravity disturbances (GDs) were calculated for the terrestrial gravity data and the recent GGMs for the study area. The model-based GDs were compared with the corresponding GD obtained from the terrestrial gravity data and their differences in terms of statistical comparison parameters for determining the best fit GGM at a local scale in Afar. The largest standard deviation (SD) (36.10 mGal) and root mean square error (RMSE) (39.00 mGal) for residual GD and the lowest correlation with the terrestrial gravity (0.61 mGal) were obtained by the satellite-only model (GO_CONS_GCF_2_DIR_R6). The next largest SD (21.27 mGal) and RMSE (25.65 mGal) for residual GD were obtained by the combined gravity model (XGM2019e_2159), which indicates that it is not the best fit model for the study area as compared with the other two GGMs. In general, the result showed that the combined models are more useful tools for modeling the gravity field in Afar than the satellite-only GGMs. But, the study clearly revealed that for the study area, the best model in comparison with the others is the EGM2008, while the second best model is the EIGEN6C4. PubDate: Fri, 08 Oct 2021 00:00:00 GMT

Abstract: The release of low-cost dual-frequency (DF) global navigation satellite system (GNSS) modules provides an opportunity for low-cost precise positioning to support autonomous vehicle applications. The new GNSS modules support the US global positioning system (GPS) L1C/L2C or L5 civilian signals, the Russian GNSS Globalnaya Navigazionnaya Sputnikovaya Sistema (GLONASS) L1/L2, Europe’s GNSS Galileo E1/E5b, and Chinese GNSS BeiDou B1/B2 signals. The availability of the DF measurements allows for removal of the ionospheric delay, enhancing the obtained positioning accuracy. Unfortunately, however, the L2C signals are only transmitted by modernized GPS satellites. This means that fewer GPS DF measurements are available. This, in turn, might affect the accuracy and the convergence of the GPS-only precise point positioning (PPP) solution. Multi-constellation GNSS PPP has the potential to improve the positioning accuracy and solution convergence due to the high redundancy of GNSS measurements. This paper aims to assess the performance of real-time quad-constellation GNSS PPP using the low-cost u-blox Z9D-F9P module. The assessment is carried out for both open-sky and challenging environment scenarios. Static, simulated-kinematic, and actual field-kinematic trials have been carried out to evaluate real-time PPP performance. Pre-saved real-time precise orbit and clock products from the Centre National d’Etudes Spatiales are used to simulate the real-time scenario. It is shown that the quad-constellation GNSS PPP using the low-cost u-blox Z9D-F9P module achieves decimeter-level positioning accuracy in both the static and simulated-kinematic modes. In addition, the PPP solution convergence is improved compared to the dual- and triple-constellation GNSS PPP counterparts. For the actual kinematic trial, decimeter-level horizontal positioning accuracy is achieved through the GPS + GLONASS + Galileo PPP compared with submeter-level positioning accuracy for the GPS + GLONASS and GPS + Galileo PPP counterparts. Additionally, submeter-level vertical positioning accuracy is achieved through the GPS + GLONASS + Galileo PPP compared with meter-level positioning accuracy for GPS + GLONASS and GPS + Galileo PPP counterparts. PubDate: Fri, 08 Oct 2021 00:00:00 GMT

Abstract: Length-of-day (LOD) change, i.e., variations in Earth’s rotation rate, includes the long-term slowdown trend, as well as periodic and irregular fluctuations. The current continuous sequence of the LOD change covers a time span of <400 years. Using astronomical records in ancient historical documents, combined with a modern astronomical ephemeris, it is possible to obtain ancient LOD change. Some scholars have given a discontinuous LOD data series for the past 4000 years. In this paper, the author uses the Lomb–Scargle periodogram to study the LOD series and finds a significant quasi-1500-year-cycle signal. Furthermore, with weighted wavelet Z-transform, time-varying characteristics of the cycle in the LOD change are obtained. PubDate: Fri, 13 Aug 2021 00:00:00 GMT

Abstract: The precise point positioning (PPP) method has become more popular due to powerful online global navigation satellite system (GNSS) data processing services, such as the Canadian Spatial Reference System-PPP (CSRS-PPP). At the end of 2020, the CSRS-PPP service launched the ambiguity resolution (AR) feature for global positioning system (GPS) satellites. More reliable results are obtained with AR compared to the results with traditional ambiguity-float PPP. In this study, the performance of the modernized CSRS-PPP was comparatively assessed in terms of static positioning and zenith total delay (ZTD) estimation. Data for 1 month in the year 2019 obtained from 47 international GNSS service (IGS) stations were processed before and after modernization of the CSRS-PPP. The processes were conducted for GPS and GPS + GLONASS (GLObalnaya NAvigatsionnaya Sputnikovaya Sistema) satellite combinations. Besides, the results were analyzed in terms of accuracy and convergence time. According to the solutions, the AR feature of the CSRS-PPP improved the accuracy by about 50% in the east component for GPS + GLONASS configuration. The root-mean-square error (RMSE) of the ZTD difference between modernized CSRS-PPP service and IGS final troposphere product is 5.8 mm for the GPS-only case. PubDate: Fri, 13 Aug 2021 00:00:00 GMT

Abstract: Discussing the problem of the external gravitational potential of the rotating Earth, we have to consider the fundamental postulate of the finite speed of the propagation of gravitation. This can be done using the expressions for the gravitational aberration compared to the Liénard–Wiechert solution of the retarded potentials. The term gravitational counter-aberration or co-aberration is introduced to describe the pattern of the propagation of the gravitational signal emitted by the rotating Earth. It is proved that in the first approximation, the classic theory of the aberration of light can be applied to calculate this effect. Some effects of the gravitational aberration on the external gravity field of the rotating Earth may influence the orbit determination of the Earth artificial satellites. PubDate: Sun, 18 Apr 2021 00:00:00 GMT