Research On Modeling Method Of Spatial Gridded Disturbing Gravity Field

Nowadays, the existing high-accuracy methods of disturbing gravity assignment mainly include Stokes integral method, single-layer density method, fictitious point-mass method, fictitious compress-recuperation method, continuation method, potential coefficient method, pole-changed spherical harmonic method and gradient method. Yet, because of the enormous calculation and the considerable time which will be consumed, it might cause a large delay to obtain the disturbing gravity value when they are used on high-speed moving vehicles at low altitude such as missils, rockets and some man-made satellites, probably making the carriers deviate from the established tracking trial in the end. There still exist some high-efficiency methods:spline function method, BP-nerve net method, finite element anylasis and wide-area polynomial approximation. These methods could provide great efficiency, however it is usually applied with the trajectory of objects in the field meaning that it could not meet the need of vehicles well, which have to be fast maneuvered and to transfer orbit occationally. This paper conducts researches in order to construct a kind of spatial grided disturbing gravity field model allowed to calculate the disturbing value of any position with extreme efficiency regardless of the track of the objects forehead. Main work and innovation points are listed below:1. Stokes and Molodensky boundary value theories were studied as well as several equivalent virtual thoughts represented by Bjerhammar theory, including single-layer density method, fictitious point-mass method and fictitious compress-recuperation method; the basic approaches to calculating the disturbing gravity value such as Stokes integral, virtual mass point and potential coefficient model were mainly focused on, which will provide therotical support for the calculation of panel points’ value in gridded space disturbing gravity field.2. The principel and calculation steps of the finite element analysis and wide-are polynomial approximation method were studied. In terms of finite element, figurate functions of spatial hexahedron with different orders were studied. When it comes to the other one, the effect of different term numbers were stistically analyzed. It was pointed out that when the highest term number reached 4, Runge phenomenon would appear. These two space approximation methods were compared in experiment, where accuracy and efficiency were mainly focused, only to find that the accuracy level of wide-area polynomial approximation was 4 times as great as the other one, also the calculation efficiency was one magnitude order higher than it. Thus wide-area polynomial became the main research target.3. The relationship between shape of unit area and the accuracy of approximation was studied. By comparing the accuracy of 6 different shapes in some certain area, the spatial approximative hexahedron unit, which pocesses the highest accuracy level as well as facilitates the division, was finally selected as the main research object.4. The earth exterior space disturbance variation characteristics of gravitational field were statistically analyzed and 3D layered maps were used to present the variance of disturbing gravity value for the first time. Gradient of disturbing gravity was considered as the sign of fierceness, according which the outer space was divided into 4 regions.5. Criterion of space gridded disturbing gravity field model based on wide-area polynomial approximation (the term number and unit shape have already settled in the former experiments) was established, at the same time some detailed problems, which might occur when the criterion was applied, were discussed so that there would not be any overlap or interspace during establishment. During the research into the criterion, units of 6 kinds of definations and polynome of 4 different patterns were chose to compare the approximation accuracy and efficiency in different height regions. The optimal match would act as the basis of the criterion.6. Methods of spherical harmonic coefficients and Stokes intergral calculation of the gravity disturbance were studied, and calculation method of spherical harmonic coefficients based on FFT was studied. Stokes integral method based on FFT to calculate disturbing gravity was deduced for the first time. And the two advanced methods were compared with traditional methods respectively and it was found that the efficiency of spherical harmonic coefficient method with FFT technology was one time better than the traditional one, while the advanced Stokes method was 20-255 times better; meanwhile, no decline of accucacy was witnessed.7. In terms of integral radius and the order selection of low-order model, which are the basic parameters in Stokes method based on FFT, experiments were conducted to analyze accuracy situation changing with height, in which 5 different integral radiuses(30’,1°,1°30’,2°,5°) and 4 different models(the highest orders of models were 360,180,36,18 respectively) were considered.8. The modeling method based on gridding criterion was studied, and the corresponding process was designed; also the output data format of the model was put forward with detailed description; finally the concrete steps of disturbing gravity calculation was brought out.