基于双精度与四精度的重力场解算精度分析

Accuracy Analysis of the Double Precision and Quadruple Precision Gravity Field Solution

基于动力学方法比较分析了双精度与四精度模式下重力场模型的解算精度,主要包括缔合勒让德函数计算、数值积分器及重力场反演结果。结果显示,在勒让德函数计算方面,部分角度在双精度模式下计算至1900阶以后会出现溢出问题,而在四精度模式下任何角度都满足精度要求,并且计算结果比双精度模式高8个量级。数值积分器Adams预测校正法积分1 d的位置和速度误差,在四精度模式下比在双精度模式下高4个量级。在精密轨道反演重力场计算方面,动力学方法在双精度及四精度模式下反演结果一致,统计其计算至60阶的累计大地水准面误差为1.29×10^-5 m,这是因为动力学方法的线性误差相对计算误差而言是主要误差;非线性动力学方法在四精度模式下比在双精度模式下高7个量级,其大地水准面误差分别为8.92×10^-15 m和8.16×10^-8 m。

In this paper,the precision of gravity field model under double precision and quadruple precision mode is compared and analyzed based on dynamics method,including the calculation of associated Legendre function,numerical integrator and gravity field inversion results.In terms of Legendre function calculation,part of the angle can be calculated in the double accuracy mode to the 1900 order and overflow problems occur beyond this order.However,in quadruple precision mode any angle satisfies the accuracy requirement and the result is 8 orders of magnitude higher relative to the double precision mode.The quadruple precision model of numerical integrator Adams predictive correction method is 4 orders of magnitude higher than the double precision model.In terms of gravity field inversion,the inversion results of dynamic method are consistent in double and quadruple precision mode,and the accumulated geoid error calculating to order 60 is statistically 1.29×10^-5 m,mainly because the linearized error of the dynamics method dominates the calculation error.The nonlinear dynamics method is 7 orders of magnitude higher than the double precision model in the quadruple precision model,and its accumulated geoid errors are respectively 8.92×10^-15 m and 8.16×10^-8 m.