北斗三号卫星位置插值研究

针对北斗精密星历只能提供离散的三维坐标,而无法提供任意时刻卫星位置的问题,本文提出插值法计算任意时刻的卫星位置,即分别采用拉格朗日插值法、多项式拟合法、分段线性插值法及径向基函数拟合法对北斗三号卫星精密星历进行内插。试验结果表明,拉格朗日插值法和多项式拟合法能够较好地内插BDS-3的位置坐标。搭载CZ-3A运载火箭的卫星X方向位置和搭载CZ-3C运载火箭的卫星Z方向位置均采用拉格朗日插值法解算效果最优;其余位置方向采用多项式拟合法解算效果最优。

Research on position interpolation of BDS-3 satellite

In view of the problem that BeiDou precise ephemeris can only provide discrete three-dimensional coordinates and can not provide satellite position at any time, this paper proposes to use interpolation method to calculate the satellite position at any time, which includes Lagrange interpolation method, polynomial fitting method, piecewise linear interpolation method and radial basis function fitting method to interpolate the precise ephemeris of BDS-3 satellite. The experimental results show that, Lagrange interpolation method and polynomial fitting method can well interpolate the position coordinates of BDS-3. The X-direction position of the satellite carrying CZ-3A launch vehicle and the z-direction position of the satellite carrying the CZ-3C launch vehicle are solved by Lagrange interpolation method, and the other position directions are solved by polynomial fitting method.