Sinusoidal Signal Parameter Estimation Algorithm Based On Prony Model

Based on the theory of Fourier series,the signal can be seen as that made up of multiple sinusoids.In the reality it is unavoidable that the signal was polluted by noise in the process of acquisition and transmission.Thus,the problem of extracting parameters from the noisy sample data of the multiple sinusoids is becoming an important research direction.The classical Prony algorithm which is extended on Prony model use the complex sinusoids to fit the samples.It can estimate the frequencies,amplitudes and phases precisely from finite noisy sample data.But once the signal mixed of noise,classic Prony algorithm would lead to serious deviation of calculated results because of the ill-condition feature in the numerical computation.To solve this problem,many domestic and foreign scholars have made improvement to Prony method.Among them,Coluccio et al use the property of continuous sinusoids to transform the signal,and the CEF algorithm is proposed based on the Prony model.In high SNR condition,the algorithm can get an accurate estimation of sinusoidal signal,but in low SNR condition,its performance is not so good.This paper studies the multiple sinusoids parameter estimation algorithm based on Prony model,the main research work is as follows:Proposed an improved CEF algorithm(MCEF)based on CEF algorithm,take the third order autocorrelation on the samples,then take Laplace transform and the inverse transform on the new sequence,thus the estimated frequencies were obtained by constructing a new prediction equations and Prony polynomials.Simulation experiment show that noise resistance of this algorithm is stronger than CEF in noise resistance,and MCEF can estimate the multi-sinusoids effectively in the relative low signal-to-noise ratio.Establish a new multi-sinusoids frequency estimation algorithm based on time domain cumulate.Based on the linear property of the sinusoidal,build a new cumulative relationship in time domain between the multi-sinusoids samples.According to the relationship and the theory of the Prony algorithm,estimate the frequencies of the multi-sinusoids.The simulation results show that this method is effective in low signal noise ratio(SNR),and more stability.According to the new time domain cumulative frequency algorithm,this section propose a new multi-sinusoids amplitude and phase estimation algorithm.Use the frequencies obtained in the new cumulative frequency estimation algorithm and the relationship in timedomain between the multi-sinusoids samples,found a new amplitude and phase estimation algorithm of multi-sinusoids based on time domain cumulate.Simulation experiment shows that this algorithm has high estimate precision in high signal noise ratio(SNR).