Study On Frequency Estimators For Noisy Sinusoid Signals

Parameter estimation of a tone in noise is important in many fields such as radar,sonar,communications,and speech signal processing.Frequency is the most important parameter and the most essential feature,so its estimation is a classical issue in the field of signal processing.The methods of frequency estimation can be divided into two categories,the time-domain and frequency-domain.The time-domain methods are based on the sample autocorrelation or the linear prediction property,while the frequency-domain methods need Discrete Fourier Transform(DFT).The mean square error and estimation bias are two most important measuresfor the performance of different algorithms.In practice,the computational complexity,the range of signal-to-noise ratio(SNR)and the sample data's length are also consideredfrequently.The Cramer Rao Low Bound(CRLB)is considered as the theoretical boundary,so efficient estimators which approach the CRLB and have less computation demanding as well are the key point in the study of frequency estimation.Since the sample autocorrelation sequence has the same frequency as the original signal,but with less noise effect.Two frequency estimators for real sinusoid signals have been designed based on the autocorrelation in this dissertation,the theoretical derivations are proposed as well.Computation simulations suggest new estimators approach the CRLB in low and median SNR environment.Based on two steps method,this dissertation offersaresearch for complex signal.The two steps method: the coarse search and a fine search.The coarse search finds the peak magnitude of the Discrete Fourier Transform(DFT).The fine search algorithms are designed for approaching the true frequency.Using the ratio of the magnitude of the DFT coefficients,a series of equations with the fine search factors aresettled.Using different skills to solve the equations can lead to several estimators which some of them are proposed separately before.However,the new estimator establishes a unified framework which can explain a lot of estimator.Someuseful requirements are laid out,which will be helpful for future estimation designing work.The content of research and innovation are the following aspects:A new frequency estimator based on equations for high lags autocorrelations is proposed to solve the problem of poor estimation precision of the short sequence.Based on thegood performance of the autocorrelation in denoising and frequency keeping,the autocorrelations are used for establishing a equation.By solving the equation,the frequency estimator isproposed.The computational complexity of the frequency estimator are given as well.The effects of White Gaussian noise on the performance is derived by using the Taylor expansion,so that atheoretical performances bound and its approximation formulaare obtained.The theoretical bound can approach the simulation results well.However,the theoretical bound expressionsis much too complex.In case of long sequence and median SNR,the approximation formula can take place of the accurate expression.The new estimator can reach a compromise between the estimation performance and the computation speed.Computer simulations areincluded to show the performance of the proposed estimator via comparison with Cramer-Rao lower bound(CRLB)and several conventional frequency estimators.The results show the proposed estimator is superior over other methods,especially for the short data length and median SNR.To solve the problem of the lack using of high lags autocorrelation and the frequency unwrapping issue,a improved estimator is designed.The new frequency estimators of real sinusoid signal in additive white Gaussian noise is based on recursive formula for the first kind Chebyshev polynomials.By the recursive formula,the estimation can be expressed as the nonzero solution to a homogeneous systems of linear equations.Using algebraic and numerical methods,the algorithm of frequency isbuilt.The frequency estimation problem is transformed as rooting problem for a polynomial function of degree-n.Eventually,the problem is done as the minimization problem of the polynomial function by proving to benonnegative.Although the high lags autocorrelations are involved,the new estimator do not need to do the phase unwrapping.The theoretical derivationsare given for the properties of estimation and the equivalence form.Computer simulations results showed the proposed estimator is superior over other methods,especially for the short data length and low SNR.At last,the acoustic release transponder experiment data is used to test the performance of estimators and other algorithms.Also,the best data length is provide for real-time environment.Based on two steps method,a framework of the fine search estimation and the its analysis for single tone complex sinusoid are proposed.First of all,the principle of the two steps method are introduced in order to explain the difference between the true frequency and the magnitude of the DFT coefficients.After that the Fourier transform coefficients expression with the peak magnitudeis deduced.Using the ratio of the magnitude of the DFT coefficients,a series of equations with the fine search factors aresettled.Using different skills to solve the equations can lead to several estimators which some of them are proposed separately before.The new estimator establishs a unified framework which can explain a lot of estimators.Than,the theoretical derivations and computer simulations are given for the estimator properties.At the end,someuseful requirements for designing this kind of estimators are laid out,which will be helpful for future researches.