一种GNSS卫星轨道高精度实时插值方法

A high-precision and real-time interpolation method for satellite orbit in GNSS

针对GNSS导航信号模拟源中多星座轨道计算实时性问题,从计算效率、精度等角度分析和对比了牛顿多项式和埃尔米特多项式插值算法的性能,通过对牛顿插值的加"窗"改进,使得卫星位置、速度的插值精度显著提高。算例结果表明,该方法能够在等间距时间点上多个卫星位置已知、速度未知的条件下,高精度实时地内插出卫星的位置和速度,其中卫星位置插值精度为mm级,速度插值精度小于1e-5m/s,计算量为广播星历直接计算的1/7,位置和速度的拟合精度均优于三阶埃尔米特插值结果。

Aiming at solving the real-time computation of the satellite orbit in GNSS（Global Navigation Satellite System） emulator with multiple constellations,the Newton and Hermite polynomial interpolation algorithms were analyzed and compared by computing efficiency and accuracy.The precision of the satellite position and velocity（PV） performed better by adding ＂window＂ in the Newton algorithm.The computation examples show that the real-time and high-precision computation of the satellite PV is achieved with position at the equation interval epoch known and velocity unknown.The results also show that the new method speeds up the computation seven times faster than the direct ephemeris calculation,and yeilds better performance in orbit precision than the 3-order Hermite Interpolation,for the position error is less than millimeter and the velocity error 1e-5 m/s.