利用最小一乘法改进的灰色模型的导航卫星钟差预报

在卫星钟差波动较大的情况下，为了克服基于最小二乘法估计灰色模型参数对卫星钟差预报精度的不足，本文利用最小一乘法对传统灰色模型进行了改进。在建模的过程中，采用以误差绝对值之和最小为优化原则，针对目标函数不可微的特点，运用线性规划的方法对灰色预报模型的模型参数进行了估计。此外，将改进后的预报模型应用到卫星钟差波动较大情况下钟差的预报中，并将预报结果与传统灰色模型的预报结果进行了对比分析。结果表明：在卫星钟差波动较大的情况下，该方法相比传统灰色模型的预报结果有显著改善，为高精度的卫星钟差预报提供了一种新思路。

Navigation satellite clock bias prediction based on grey model improved by least absolute deviations

In order to overcome the shortcomings of satellite clock bias(SCB) forecasting accuracy based on the grey model(GM(1,1)) parameters of least squares estimation in the case of large SCB fluctuations, this paper uses the least absolute deviations(LAD) to improve the GM(1,1). During the modeling process, the principle of minimizing the absolute sum of errors is used as the optimization principle. Aiming at the non-differentiable characteristics of the objective function, the linear programming method is used to estimate the model parameters of the GM (1, 1). In addition, the improved forecasting model is applied to the forecast of the SCB when the SCB fluctuates greatly, and the forecast results are compared with the results predicted by GM (1, 1).The results show that the prediction results of the GM (1, 1)-LAD are significantly improved compared with the GM (1, 1) in the case of large fluctuations in the SCB, which provides a new idea for high-precision SCB prediction.