Wavelet model for the time scale

The establishment of a time scale is one of the main aims of time measurement. The time scale prediction is necessary for real atomic time. The wavelet theory is a new subject which will be developed in the near future. It can be used to analyze signals with different resolution. 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 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 scales. Finally, our model is checked with data of CSAO. The forecast error of ARMA(p,q) is about 10 ns in one step. That of the subsectional recurrence model is less than 4.5 ns in 5 step. Our model is simple and practicable. The results show that this method is better than the other in the accuracy of measurement.