基于方差递推法的Kalman滤波在钟差预报中的应用

Clock Bias Prediction by Application of Kalman Filter Based on Recursive Variance Method

卫星导航系统中星载原子钟的钟差预报对于导航、定位及授时具有重要的作用。为了提高卫星钟差预报的精度,设计了一种两步确定卫星钟噪声协方差矩阵的Kalman滤波钟差预报模型。该方法首先基于Hadamard总方差确定卫星钟噪声协方差矩阵的初值,然后,使用方差递推法得到滤波过程中卫星钟的噪声协方差矩阵。使用GPS系统的星载铷钟数据进行短期预报,并与常用的二次多项式模型、灰色模型进行对比,结果表明:本文中提出的方法可以实现高精度的卫星钟差预报且预报效果优于两种常用模型,同时,该方法能够在一定程度上弥补预报误差随预报时间增加而不断变大的不足。

Satellite clock bias（ SCB） prediction plays important roles in navigation,positioning and time service for satellite navigation system. In order to improve the accuracy of SCB prediction,a Kalman filter model used for SCB prediction is designed based on a two- step method to determine the noise covariance matrix of satellite atomic clock. Firstly,the designed model adopts the Hadamard total variance to calculate the initial values of the satellite clock’s noise covariance matrix,and then a recursive variance method is used to obtain the matrix’s values in the process of filtering. Using rubidium atomic clock data of GPS satellite conducts short- term prediction tests for the designed model,simultaneously comparing with the two frequently- used prediction methods such as quadratic polynomial model and grey model. The results show that the proposed Kalman filter model can accurately predict SCB and get better prediction results than that of the frequently- used models. Moreover,the new model can also restrain the divergent trend of prediction errors growing with prediction interval increment.