Results of comparing astronomical-geodetic and navigational-geodetic methods of determining the components of the deflection of vertical

The authors present the results of comparing the components of deflection of vertical obtained through astronomical-geodetic and navigational-geodetic methods. The first one is based on comparing astronomical and geodetic coordinates of a location. This method has recently been widely implemented in a digital zenith camera systems using a small-sized digital telescope with an astronomical camera based on CCD or CMOS technologies, a high-precision inclinometer and satellite navigation system receiver. In this case, the combination of a telescope, an astronomical camera and an inclinometer enables determining the local direction of the plumb line, expressed by astronomical coordinates, from observations of stars at the zenith and using high-precision star catalogs. The navigational-geodetic method is based on comparing the results of the normal heights’ increments, defined through geometric leveling, and geodetic heights, computed with the relative method of satellite coordinate determinations. For each method, random and systematic components of the error and its confidence bounds were calculated; the absolute values of the deflection of vertical components at two geographically separated points were compared.

Calculation of Deflection of Vertical and Gravity Anomalies Over the South China Sea Derived from ICESat-2 Data

The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2) satellite uses a synchronized multi-beam photon-counting method to collect data from three pairs of synchronous ground tracks. The sampling rate along the ground tracks is designed to be ∼0.7 m, much smaller than that used in conventional radar altimeters. Hence, it is reasonable to expect an improvement in marine gravity recovery over coastal zones using ICESat-2 data. ICESat-2 provides valid sea surface height (SSH) measurements and a standard data product (ATL12) over ocean areas. This led us to consider the possibility of investigating its ability to calculate the deflection of vertical (DOV) and marine gravity anomalies. We processed ATL12 data about 22 months over the South China Sea (0°–23°N, 103°–120°E) and verified the ability of ICESat-2 SSH measurements to be used in calculating directional components of DOV. The results show that the ICESat-2 SSH data have a similar centimeter-magnitude accuracy level as data from the Jason-2 satellite. Furthermore, the accuracy of cross-track deflection of vertical (CTDOV) calculations between non-identical side beams is lower. For along-track points, the difference in accuracy between the solution of the prime component and the meridional component is significantly reduced, the prime component accuracy is significantly better than the directional components of the gridded deflection of vertical (GDOV), although the enhancement is weak for the meridional component. We also implemented the inversion of the ICESat-2 single mission based on the inverse Vening Meinesz formula, and verified the capability of ICESat-2 gravity field detection using shipborne gravity measurements and XGM2019 gravity field model, and found that the accuracy is 1.35 mGal and 2.47 mGal, respectively. ICESat-2 deserves the attention of the altimetry community, and its advantages are expected to make it an alternative data source for multi-mission fusion inversion of the ocean gravity field in the future.

Analysis of Deflection of Vertical Compensation for Inertial Navigation System

With the development of high-precision inertial navigation systems, the deflection of vertical (DOV), gravity disturbance, is still one of the main error sources that restrict navigation accuracy. For the DOV compensation of the Strapdown Inertial Navigation System (SINS) problem, the influences of the calculation degree of the spherical harmonic coefficient and the calculation error of the DOV on the compensation effect were studied. Based on the SINS error model, the error propagation characteristics of the DOV in SINS were analyzed. In addition, the high-precision global gravity field spherical harmonic model EIGEN-6C4 was established and the influence comparative analysis of the calculation degree of the spherical harmonic coefficient on the DOV compensation of SINS in different regions was carried out. Besides, the influence of the calculation error of the DOV on the compensation was emphatically analyzed. Finally, the vehicle experiment verified the feasibility of compensation in SINS based on the gravity field spherical harmonic model. The simulation and experiment results show that it is necessary to consider the influence of the calculation degree and the calculation error of the DOV on the compensation for long-time high-precision SINS with the position accuracy of 0.3 nm/h, while the SINS with general requirements for position accuracy can ignore the impact.

Theoretical Considerations about the Influence of the Work Environment and of Mixer Hydrodynamic Mass on the Deformations and Implicitly on the Shaft Own Pulsation

Loading shaft of the mixing device is complex. Because the operating regime is characterized by a random variation of the regime parameters, it is difficult to determine an exact theoretical approach, from the point of view of calculation of the shaft. The stress shaft of a mixing device takes into account only partally of the real state of loading. At present, there is no unitary methodology for calculating of shaft for mixing devices. Although the effect of the mixer weight on the own frequency, has been partially taken into account when the shaft-mixer system rotates in the air, it must be reconsidered if the shaft-mixer system rotates in a liquid. The calculation presented in this paper will take into account "hydrodynamic mass" mam of liquid, corresponding to the mixer that actually vibrates with it. This contributes to an increase of its inertia, and to reducing of the own frequency (respectively of the critical speed). In this paper, the influence of the working environment on the deflection of vertical cantilever shaft will be considered, and calculation relations for own pulsation of the shaft equipped with a mixer will be set, with consideration of mixer hydrodynamic mass. For this purpose, it is calculated hydrodynamic mass mh attached to the mixer, and the reduction factor of pulsation due to hydrodynamic mass.

ANALYSIS OF THE IMPACT OF CELESTIAL BODIES ON DIFFERENCES IN MEASURED HEIGHT / DANGAUS KŪNŲ ĮTAKOS IŠMATUOTAM AUKŠČIŲ SKIRTUMUI TYRIMAS / АНАЛИЗ ВЛИЯНИЯ НЕБЕСНЫХ ТЕЛ НА ИЗМЕРЕННУЮ РАЗНИЦУ ВЫСОТ

Under the effect of celestial bodies, the deflection of vertical induces changes in the levelled height difference. Therefore, it is necessary to evaluate the produced effect on high-precision levelling data. The article analyses the dependency of lunisolar correction on the lunar phase and azimuth of the levelling line and correction rate of changes. The paper also revises formulas for calculating lunisolar correction derived from using tide generating potential. Santrauka Straipsnyje analizuojama vertikalės nuokrypio dėl dangaus kūnų įtaka išmatuotam aukščių skirtumui. Šią įtaką būtina įvertinti apdorojant precizinės niveliacijos matavimų duomenis. Įvertinta potvynio pataisos priklausomumas nuo Mėnulio fazių ir niveliacijos linijos azimuto bei pataisos kitimo greitis. Taikant potvynio potencialo išraišką, gautos patikslintos išmatuoto aukščių skirtumo vertinimo formulės. Резюме Под влиянием небесных тел отклонение вертикали вызывает изменения в разнице высот, полученной нивелированием. Необходимо оценить этот эффект в данных высокоточной нивеляции. Были проанали зированы зависимость лунно-солнечных поправок от лунных фаз, азимута линии нивеляций и скорости изменения поправки. Получены уточненные формулы для расчета лунно-солнечной поправки с использованием приливного потенциала.