时间尺度的分域递推模型

A SUBSECTIONAL RECURRENCE MODEL FOR THE TIME SCALE

建立时间尺度是时间测量的目的之一．实时原子时则要求对时间尺度进行必要的预测．小波分析是近年来迅速发展起来的一门学科，它可以对信号在不同的分辨率下进行分析，凡是传统的Fourier分析可以应用的地方，小波分析都可以得到应用．基于小波分析建立了一种时间尺度分域递推模型，这种方法既不同于ARMA（p，q）模型，又有别于卡尔曼滤波方法．ARMA模型要求过程是平稳随机的，而卡尔曼滤波方法虽然不要求过程是平稳的，但它预测的精度有限．分城递推模型将信号在不同的频率尺度进行正交分解，在各个尺度上对小波变换系数进行建模．最后根据陕西天文台守时实验室的实测数据，验证了分域递推模型，ARMA模型一步预测误差10ns，而分域递推模型五步预测误差平均为4．5ns．结果表明这种方法简单而切实可行，分域递推模型的预测精度优于其它方法．

The establishment of a time scale is one of the main aims of time measurementThe time scale prediction is necessary for the real atomic time. The wavelet theory is a new subjet which will be well developed in the near future. It can be used to analyze signals with different resolutions. Besides, it may be applied whenever the Fourier analysis is available. A subsectional recurrence model for time scale based on wavelet theory is put forward in this paper. It is different from the AREA(p,q) and the Kalman filter. The ARMA(p,q) model requires that the process should satisfy the stationary condition, while the Kalman filter is not so. The forecast step of our model is finite and the signals are orthogonally analyzed at different frequency scales. The wavelet coefficients are given for each frequency scale. Finally, our model is checked with data of CSAO. The forecast error of ARMA(p,q) is about 10ns in one step.That of the subsectional recurrence model is less than 4.5ns in 5 steps. Our model is simple and practicable. The results show that this method is better than the other in the accuracy of measurements.