Research On The Algorithm Of Sinusoidal Frequency Estimation

With the development of communication technology and signal processing,frequency estimation has been widely applied to various fields of military and civilian.Because the position and speed of transmitter and receiver change or communication channel conditions change,the frequency of the received signal will change in different degrees.In order to obtain the information,the frequency of received signal must be estimated,then the required information can be demodulated.In this paper,the methods of frequency estimation under different communication conditions and applications are researched,and the problems of existed frequency estimation methods on complexity and accuracy are improved.The novel frequency estimation methods under certain conditions are proposed,and the performance is verified by simulation.For the non-real-time estimation of the fixed frequency of sine signal,the most important thing is to improve the estimated accuracy under low SNR.Compared with other methods,the periodogram method and the autocorrelation method outperform others under low SNR.Two-stage frequency estimation method based on periodogram and noise approximation is proposed,which can avoid the wrong interpolation direction of interpolation method and improve the accuracy of the periodogram method.Two-stage frequency estimation method based on linear prediction of autocorrelation and Taylor function is proposed,which solves the problem of phase ambiguity of multiple time delay correlation and improves the estimated accuracy through Taylor function.For the real-time estimation of the fixed frequency of sine signal,the main methods include linear prediction method and notch filter method.In most of the existed linear prediction methods,the first-order prediction equation is used,which results in a low accuracy under low SNR.While,the problems of notch filter method are the range of estimated frequency is limited and the speed of convergence is slow.Therefore,the high-order linear prediction combined with LMS filter is proposed to estimate the carrier frequency in this paper.High-order linear prediction can improve the estimated accuracy and the LMS filter can avoid the problems of notch filter.In this paper,the average phase method is used to estimate the carrier frequency from the linear prediction vector,which does not need to solve the high-order equation and reduces the complexity.The influence of the linear prediction order is researched in this paper,and the strategy of choosing the order is given,which can achieve frequency estimation in low complexity and guarantees certain accuracy.For the estimation of variable frequency of sine signal in the Gaussian noise environment,the main challenge is to estimate and track the non-linear variable frequency.In the Gaussian noise environment,the probability density distribution of the state vector and the measurement vector of the particle filter is known,so the particle filter is very suitable to estimate the non-linear variable parameters.The accuracy of particle filter is very high,even under the low SNR and the highly non-linear conditions.However,the high complexity limits the applications of particle filter.In this paper,how to reduce the complexity of particle filter is researched and the KLD particle filter method with low complexity is proposed.The proposed method alternates the resampling and the KLD sampling,which can eliminate the resampling process of unnecessary particles to reduce the complexity.Moreover,the adaptive length of KLD bin is proposed,which can automatically adjust the number of particles of KLD sampling.The proposed method can avoid the failure of KLD sampling caused by too many particles and the poor estimated accuracy caused by too few particles.For the estimation of variable frequency of sine signal in the unknown noise environment,some common frequency estimation methods,such as periodogram method,autocorrelation phase method,Kalman filter and particle filter,cannot be used,because the carrier frequency is non-linear variable and the information about noise is unknown.Therefore in this paper,the LMS filter is used to estimate frequency for LMS filter is very steady and it does not demand the noise information.Linear prediction can be implemented by LMS filter and the estimated frequency can be obtained from the prediction vector.When use linear prediction to estimate frequency,the accuracy and complexity is influenced by the length of linear prediction model,i.e.the filter tap-length.In this paper,variable tap-length LMS filter method based on adaptive parameters is proposed to search the optimal filter tap-length.By automatically adjusting the values of parameters,proposed method can not only improve the convergence speed but also reduce the steady-state error.By limiting the values of parameters using Arctangent function,the stability is improved.When use the LMS filter to estimate and track the non-linear variable frequency,the performance is deeply influenced by the filter step-size.Too large step-size will cause the huge fluctuation of estimated and then increase estimated error,while too small step-size will result in a large lagging error.In this paper,variable step-size LMS filter method based on optimal step-size is proposed.The optimal step-size can be found by adaptive algorithm,which solves the problem of setting parameters and avoids the poor estimated accuracy caused by unsuitable step-size.