摘要
通过分析比较标准前向列推、标准前向行推、跨阶次递推和Belikov列推4种缔合勒让德递推算法的精度、稳定性以及计算速度,提出了选取Belikov列推法来解算超高阶重力场模型高程异常;研究探讨了基于严密球谐级数展开、保留泰勒级数展开的零阶项和保留至泰勒级数展开一阶项计算模型高程异常的三种算法,并进行了实验计算分析。结果表明,保留至泰勒级数一阶项的模型高程异常既能保证计算速度也能达到足够的精度,可满足大区域高分辨率高程异常建模的需求。
Four recursion methods of computing the ultra-high degree and order fully normalized associated Legendre functions such as standard forward column method, standard forward row method, recursive method between every other order and degree and Belikov column method, were analyzed and compared to the advantages and disadvantages from three aspects of numerical precision, numerical stability and numerical efficiency in this paper. The Belikov column method was chosen to calculate the height anomaly of the earth＇ s gravity field model. Then three different algorithms for calculating model height anomaly based on strict spherical harmonic expansion formula, retaining the formula＇ s function of Taylor series about geocentric radius vector unfolded to zero order term and retaining the formula＇ s function of Taylor series unfolded to one order term were discussed, and some experiments were conducted. The result showed that unfolding to first order Taylor series of formula about geocentric radius vector to calculate height anomaly of the earth＇ s gravity field model could both ensure good computing speed and reach enough precision, meeting the requirement of building the large area high-resolution height anomaly model.
出处
《海洋测绘》
2014年第4期5-8,16,共5页
Hydrographic Surveying and Charting
基金
国家自然科学基金(41274029)
国家863计划(2013AA122502)
关键词
缔合勒让德函数
超高阶地球重力场模型
高程异常
泰勒级数展开
associated Legendre function
ultra-high degree and order earth gravity field model
heightanomaly
Taylor series expansion
