基于高斯样条函数的局部重力异常场解析重构

摘要

It is indispensable to build the local continuous gravity anomaly field model with high precision and good analytic property before the study on gravity matching algorithm based on continuous field. Fibonacci series searching is applied to optimize the 1D Gauss spline function interpolation and the algorithm to approximate the local grid gravity anomaly field with the 2D Gauss spline function based on Fibonacci series search is put forward. To improve the searching speed, the 2D criterion function is decoupled to two mutually independent 1D Criterion functions at the X and Y directions. Then, the optimal parameters are obtained from the Fibonacci number series searching of these two lD criterion functions. Finally, a local continuous gravity anomaly field analytic model which can approximate to local grid data with high precision is attained. Five different parameters are set in the simulation to approximate the gravity anomaly with the variation range -51. 185~86. 181 9 reGal(1 mGal=1 cm/S^2). The simulation results show that approximation mean absolute error of the simulation with optimal parameters is 0. 000 69 reGal and the mean relative error is to the level of 10^-6 which is far less than the simulations with the other parameters. Furthermore, the approximation methods with Gaussspline function and B-spline function are applied to approximate the 4′× 4′gravity anomaly data base from satellite altimetry inversion for comparative analysis. The effectiveness of Gauss spline function approximation can be verified by the results of pilot calculation and its approximating precision can satisfy the need of matchina navioation.%为了研究基于连续场重力匹配算法以克服传统匹配算法的局限，必须建立精度高且具有良好解析性质的局部重力异常场解析模型。利用斐波那契数列寻优方法对一维高斯样条函数插值进行最优化，在此基础上提出了基于斐波那契数列寻优的二维高斯样条函数逼近局部重力异常场方法。为了提高寻优算法运算速度，将二维准则函数解耦为x方向和y方向两个独立的一维准则函数，分别采用斐波那契数列寻优方法对这两个准则函数进行寻优以获取X方向和y方向最优参数，最终得到高精度逼近局部离散格网数据的局部重力异常场连续解析模型。在仿真试验部分，首先采用5组不同的参数对变化范围为-51．185～86．1819mGal（1mGal-1cm／S^2）的模拟重力异常数据进行逼近。从最后的仿真试验结果可以看出采用最优参数时逼近绝对误差均值达到0．00069mGal，相对误差均值更达到10^-6级，其逼近精度较采用其他非最优参数时均有较大提高。然后分别采用高斯样条函数逼近法和B样条函数逼近法对4′×4′卫星测高反演重力异常数据进行逼近试算和对比分析。试算结果表明了高斯样条函数逼近算法的有效性，其逼近精度能较好地满足匹配导航要求。