Frequency estimator by combination of phase difference method and interpolation algorithm

Abstract

In the traditional time-shifting based phase difference method, considerable errors may be introduced by wrapped phase problem as long as translation coefficient tends to one even in a small-scale turbulence noise. In this paper, an improved frequency estimator is proposed to overcome the problem of wrapped phase by combination of phase difference method and interpolation algorithm. Compared with the traditional method of phase difference based on time-shifting, the improved algorithm can obtain an accurate estimate when translation coefficient exceeds one. Comparative studies were done by means of root-mean-square error over Cramer–Rao lower bound. According to the computer simulations, it is demonstrated that root-mean-square errors can cross Cramer–Rao lower bound if the translation coefficient is properly selected even in the case of the low signal-to-noise ratio, which implies that the proposed algorithm has a strong noise immunity. Finally, the advantage of the proposed algorithm is illustrated for the simulation signal which contained strong local random noise.