基于Powell法的GNSS卫星轨道拟合算法

针对GNSS导航信号模拟源中卫星轨道计算的高精度实时性要求,提出了一种基于Powell最优化理论的卫星轨道拟合算法。该算法将有限点卫星位置拟合问题转化为无约束极小值问题,使用最优化理论求解卫星轨道模型参数,从而可以方便计算任意时刻的卫星速度、加速度等高阶量。算例结果表明计算卫星星历时,位置误差小于1×10-4m,速度误差小于1×10-6m/s,计算量为广播星历直接计算的1/3;计算精密星历时,位置精度在2cm左右,拟合精度较拉格朗日插值算法提高了大约1倍。通过实际应用,充分验证了算法的有效性。

A Fitting Method for Satellite Orbit in GNSS Based on Powell Optimization Theory

Aiming at the high precise and real-time computation of the satellite orbit in GNSS (Global Navigation Satellite System) simulator with satellite orbit, a fitting method based on Powell optimization theory is proposed in this paper. The method converts the fitting method for satellite position to the non-restraint least method, and we can find the parameters of the satellite orbit model by the optimization theory, which is easy to compute the velocity, acceleration and so on. The computation examples show that the new method speed up computation three times than the direct ephemeris calculation, when fitting the satellite ephemeris, the position error is less than 1?10_-4 m and the velocity error 1?10_-6m/s. When fitting the GPS precise ephemeris, the new method increases precise two times than the ephemeris Lagrange interpolation.