Methods for Precise Determination of Geopotential from Satellite Missions

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The major new results of this research project can be briefly summarized as follows: (i) As a first step to use GPS satellites in the determination of the gravitational field, we have to precisely determine the positions of a low satellite by using carrier phase observables. In order to correctly and quickly resolve the GPS integer ambiguity unknowns, we have proposed a new GPS integer decorrelation method and a new random simulation approach to scientifically compare different methods of correlation. The results have indicated that the new method is currently the best and showed that Gaussian integer decorrelation is not the best; (ii) We have investigated the nonlinear filter for precise orbit determination as well. The new results include proposing an unbiased predictor of second order and a truncated and unbiased filter of second order. We have also derived the coupled differential equations of the filter and its covariance matrix in the case of nonlinear continuous system. The new … More results imply that forty years of nonlinear filtering of continuous nonlinear systems may have a fundamental defect in the foundation; (iii) By means of simulation, we have tested the improvement of spatial and temporal resolution in gravity field by sampling more than one satellite at the same attitude but at different rates. We have also investigated the effect of the sampling rates of ECMWF surface pressure data and aliasing on the time varying gravity field. The results have confirmed the effectiveness of simulation; and (iv) Since the determination of the gravitational field from space observations is nonlinear, and keeping in mind that simulated annealing and genetic algorithms --- two most widely used global optimization methods are actually not capable of correctly producing the global optimal solution in general, we have focused on new non-random algorithms and proposed a new hybrid global optimization method for nonlinear nonconvex geo-inversion. The theoretical results have been established and practical applicability confirmed through the demonstration of examples. Less