Research And Application On Frequency Estimation Based On Linear Prediction

Frequency estimation algorithms can usually be classified into two categories based on frequency domain implementation and time domain implementation.Algorithm implemented in the frequency-domain is accurate,but it is complicated.However,based o time-domain algorithm is simple to implement and is widely used in fast real-time applications,especially linear prediction.This paper is mainly based on the unitconstrained least-squares criterion and concentrates on two aspects: a novel four-point linear prediction model and an arbitrary time interval-based linear prediction model.The main major contributions are as the following:The frequency estimation based on linear prediction is studied.Firstly,the basic knowledge of linear prediction is introduced.The three-point modified covariance(MC)algorithm and the improved Pisarenko harmonic decomposer(RPHD)algorithm are studied.The consecutive four-point linear prediction algorithm is introduced,and the limitations of the algorithm are analyzed.The frequency estimation algorithm of a novel consecutive four-point linear prediction model based on unit-constrained least squares is studied.In order to address the problem of the existing four-point algorithm,a novel time-series relationship between four consecutive real-valued single-frequency sinusoidal samples is proposed.In order to achieve asymptotic unbiased frequency estimation,based on the proposed four-point time-series relationship,a contrianed least squares cost function in minimized based on the unit-norm principle.Closed-form expressions for the variance and the asymptotic expression for the variance of the proposed frequency estimator are derived,facilitating a theoretical performance comparison with the existing RPHD algorithm.Based on the variance expression,the frequency advantage of the proposed frequency estimator based on the new consecutive four-point linear prediction is analyzed in detail.Computer simulations verify the accuracy of the proposed algorithm's theoretical variance and asymptotic variance.Compared with its three-point counterpart,the proposed four-point frequency estimation algorithm has obvious advantages for short observation sequences in the digital domain frequency bands which is minus0.5?,and is closer to the Cramer-Rao Lower Bound(CRLB).Thus,it is suitable for real-time frequency estimation applications.The frequency estimation algorithm of a linear prediction model with arbitrary time intervals based on the unit constraint least squares is studied.Firstly,the P estimator and the modified Pisarenko harmonic decomposer(MPHD)algorithm that improve the inconsistency of frequency estimation performance with high lags autocorrelation are introduced.In order to improve the inconsistent performance of existing frequency estimation algorithms based on continuous time series.With the help of high lags autocorrelation method,the linear prediction model based on arbitrary time intervals is preserved,including improved threepoint and four-point linear prediction based on arbitrary time intervals are proposed.The corresponding frequency estimator is derived based on the criterion of unit-norm constrainted least squares,and the asymptotic expression of the closed variance of the algorithm is derived.Based on the asymptotic variance expression,the closed expression of the optimal time interval for obtaining the best estimation performance can be obtained,which can be solved by traversing.Finally,summarize the three important steps of this type of frequency estimation algorithm.Computer simulations verify the validity of the frequency estimation algorithm and the correctness of the derived variance formula.The improved algorithm can indeed provide fairly consistent performance estimates over the entire frequency band.The simulation results indicate that the stability of the estimation performance of the four-point algorithm is better than the three-point algorithm,and the three-point algorithm is superior to the existing MPHD algorithm.The complexity of the frequency estimation algorithm based on the linear prediction model of any time interval is k times of the estimator based on the continuous time series model,thus this kind of frequency estimator is suitable for applications with higher accuracy requirements.