基于高斯样条函数的局部重力异常场解析重构

重力匹配辅助导航理论大都建立在离散场的基础上的，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。仿真实验中采用五组不同的参数对变化范围为-51.185mGal~86.1819mGal的重力异常场进行逼近。从最后的仿真实验结果可以看出采用最优参数时逼近绝对误差均值达到0.00069，相对误差均值更达到10-6级，能较好的满足了匹配导航要求，其逼近精度较采用其它非最优参数时均有较大提高，由此验证了文中提出的重构算法有效性。

The Reconstruction of Local Gravity Anomaly Field Based on Gauss Spline Function

The normal gravity aided navigation theories are based on grid discrete field in most cases. 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 1-D Gauss spline function interpolation and the algorithm to approximate the local grid gravity anomaly field with the 2-D Gauss spline function based on Fibonacci series search is put forward. To improve the searching speed, the 2-D criterion function was decoupled to two mutually independent 1-D criterion functions at the X and Y direction. Then, the optimal parameters were obtained from the Fibonacci number series searching of these two 1-D 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 were set in the simulation to approximate the gravity anomaly with the variation range -51.185mGal~86.1819mGal. The simulation results shows that approximation mean absolute error of the simulation with optimal parameters is 0.00069 and the mean relative error is to the level of 10-6 which is far less than the simulations with the other parameters. The effectiveness of the reconstruction algorithm was proved by the simulation results and the approximating precision can satisfy the need of matching navigation.