一种基于插值和卡尔曼滤波的接收机钟差预测方法

针对多模多频接收机面临同时处理大量数据的压力，提出了一种基于插值和卡尔曼滤波的接收机钟差预测方法。插值方法分别用拉格朗日和三次样条，三次样条端点的一阶导数采用“差分法代替求导法”来确定。首先由插值方法得出每隔1s的卫星坐标、速度、钟差、频漂和伪距测量值，然后基于单星授时方法计算出静止接收机钟差，接着用卡尔曼滤波算法对接收机钟差和频漂进行预测，最后将预测的接收机钟差与加拿大空间参考系统( CSRS )提供的精密接收机钟差数据进行比较。结果表明，拉格朗日插值由于存在龙格效应，其接收机钟差的抖动幅度比三次样条略大，它们与CSRS钟差数据相比，均方根误差在3 ns之内。

A method for receiver clock bias prediction based on interpolation and Kalman filter

To reduce the burden of multi-mode multi-band receiver to handle a large number of data at the same time,a method for the receiver clock bias prediction based on the interpolation and Kalman filter is proposed. Lagrange interpolation and cubic spline are used in this paper. The first derivative of the cubic spline is determined by the difference instead of derivation. First satellite coordinates,satellite speed,satellite clock bias,satellite frequency drift and pseudo-range measurements every one second are obtained by interpolation,and then the stationary receiver clock biases are calculated by single satellite timing method,the receiver clock bias and frequency drift are predicted by Kalman filter,finally the predictive value is compared with the precision receiver clock error provided by the Canada Space Reference System(CSRS) company. The results show that the jitter of Lagrange interpolation clock bias is slightly larger than a cubic spline due to the Runge effect,and compared with the CSRS data,the root-mean-square error(RMSE) is in about 3 nanoseconds.