Research Of Signal Frequency And Phase Estimation Based On Double Sub-segment Algorithm

Frequency estimation and phase estimation is essential in the fields of radar communications, voice processing, fault diagnosis and so on. Complex exponential signal superimposed with white noise is usually chosen as the mathematical model to solve this problem, whose solution is closely related to spectral analysis. For the purpose of realizing high-accuracy estimation, existing estimators(for example Candan estimator, CO estimator) require additional measures such as interpolation, iteration to correct the DFT result. However, these estimators can hardly achieve a good tradeoff in accuracy, computational complexity and variance forecasting, etc. Specifically speaking, the disadvantages are as follows:(1) The majority of the interpolation based estimators are biased even in noiseless case because most of them are theoretically derived from some mathematical approximation;(2) A lot of DFT bins are required to be synthesized together in frequency estimation, i.e., for most of these estimators, high computational complexity has to be consumed to achieve a high estimation accuracy;(3) It is difficult to derive the theoretic closed-form expression of frequency and phase estimation variance from these estimators;(4) For the existing estimators, the phase estimate is on the premise that the frequency estimate is obtained in advance, which also gives rise to error diffusion.To solve the problems above, this dissertation puts forward one novel frequency and phase estimator based on double sub-segment. In this estimator, the frequency estimate can be directly extracted from the phase difference at the peak FFT bins of these two sub-segments, which are actually the first and the last sub-segment in all-phase FFT. Furthermore, similar to apFFT phase measurement, accurate phase estimate can also be simply acquired through performing symmetric compensation on the peak DFT bins of these forward and backward sub-segments. To improve performance, frequency shift compensation and iteration can also be applied to the proposed estimator.In this dissertation, we also give theoretical derivation and numerical simulation for the proposed frequency and phase estimator. Consequently, we find that the proposed estimator possesses the following advantages:(1) Both the proposed frequency estimator and the phase estimator are unbiased, since the derivation process does not introduce any mathematical theory approximation;(2) The computation complexity consumed in the proposed estimator is low, since only the single peak bins of the two sub-segments are utilized to calculate the frequency estimate and phase estimate;(3) The proposed estimator can also provide a closed-form theoretic expression of the frequency and phase estimation variance, which is derived from the rigorous parameter variance at each step. Moreover, this closed-form variance approximates the Cramer-Rao Lower bound of two-parameter mathematical model and can also provide a basis for accuracy prediction;(4) Error diffusion does not exist in the proposed phase estimator, since it is derived by symmetry compensation and thus it is indispensable of frequency estimate. In general, the proposed estimator overcomes the major drawbacks of the existing estimators.Numerical results not only verify the correctness of the closed-form expression, but also prove that the proposed frequency estimator's mean square error is closer to the Cramer-Rao Lower bound compared to that of apFFT/FFT phase difference estimator and Candan estimator in most cases of frequency offset. Moreover, the proposed phase estimator's mean square error also approximates the Cramer-Rao Lower bound of the two-parameter model, verifying that the proposed estimator has a high measurement accuracy.