Optimization of least squares method to determine the harmonic coefficients on the sphere

: pp. 13-18
Department of Geodesy, Institute of Geodesy, Lviv Polytechnic National University
Lviv Polytechnic National University

Knowledge of the gravity field takes significance place in today's world. Such information is very important for performing of a number of contemporary problems related to satellite technologies. Such problems include: the launch of launch vehicles, satellites orbit prediction, the study of the surface of the oceans, transformation of normal and geodetic heights and more. Goal: Each year, data on the Earth's gravitational field appears more and more that complicates the task of optimal using and joint processing, so it is important to use algorithms that would allow simultaneously to process the largest possible number of input data. But, it is not easy task, even with performing of computing cluster. The increasing tendency to space mission launches, will causing growing of the number of data. Method: based on the above it is represented in the modified least squares method used to determine the harmonic coefficients based on gravity anomalies DTU 10. This input information is provided by array of free air gravity anomalies, arranged in a regular grid points with a resolution of 5 '× 5'. Scientific novelty and practical significance: article describes the principles of antipodean-uniform grid and its division into 8 parts for use of orthogonal properties that arise in this points situation. Results: Thus defined set of harmonic coefficients up to 720 order / degree, and were compared with the model EGM 2008 in terms of spectral characteristics. Was built quasigeoid based on the obtained model. To build quasigeoid used Bruns formula, which includes normal gravity (normal gravitational acceleration) is calculated approximately, because it almost does not affect the final result. Moreover the main objective is to optimize the methodology for determining of the harmonic coefficients, instead of the construction of high-precision geoid. Was performed comparison quasigeoid heights defined in the GNSS-leveling at the site New-Mexico for confirmation of the results.

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