GPS卫星轨道插值及拟合研究

基于GPS广播星历,采用拉格朗日插值、切比雪夫多项式拟合及埃尔密特插值3种算法进行卫星轨道插值、拟合研究,然后把运算结果与卫星轨道外推结果进行对比分析.结果表明,3种算法在相同阶数条件下,切比雪夫多项式拟合可以达到最好的拟合精度,拉格朗日插值算法次之,埃尔米特插值精度最低;但从运算时间量分析,拉格朗日插值算法运算速度最快,而切比雪夫多项式拟合次之,埃尔米特插值最慢.

Interpolation and Fitting for the Orbit of GPS

The paper has used the fitting methods of Lagrange interpolation,Chebyshev polynomials fitting and Hermite interpolation these three algorithms to fitting the orbit based on the broadcast ephemeris,and then has compared these results with the orbit of extrapolation,which indicates that the Chebyshev polynomials fitting can get the best precision,the Lagrange interpolation takes the second place and the Hermite interpolation takes the third in the condition of same order.But in consideration of operation time,the Lagrange interpolation can get the fast the result in these three algorithms,the Chebyshev polynomials fitting takes the second place,and the Hermite interpolation gets the largest computation.