Study On Prony Algorithm And Esprit Algorithm Under Parameter Estimation Algorithm Of Multi-sinusoidal Signal

The estimation of parameters of multi-sinusoidal signal under additive white Gaussian noise has become an important problem in signal processing and communications. Currently,multi-sinusoidal signal parameters estimation has been successfully applied in fields, such as control theory, radar application, biomedical engineering, the bridge vibration detection and electronic communications technology. Thus, the extracting parameters of the multiple sinusoids signal from the noisy sample data is of great theoretical significance and application value.This paper analyzes classical Prony algorithm and ESPRIT algorithm. Respectively on the basis of the principle algorithm and the corresponding simulation experiments, it is concluded that the relationship between the SNR and the parameters of the mean square error,have carried on summarize and made corresponding improvements. The main research work and conclusions are as follows:1. An improved algorithm based on Prony algorithm is proposed. Based on the iterative algorithm, the proposed algorithm constructs a new sequence, and establishes the relationship between the multi-sinusoids in time domain accumulation. It obtains the high-precision frequency estimation by constructing Prony polynomials. The simulation results show that this method improves the estimation precision. The improved algorithm is able to get better estimate parameters in the case of the low signal noise ratio (SNR)2. According to the time domain cumulative parameters algorithm, the multi-sinusoids amplitude and phase estimation algorithm is proposed. According to the equivalent relations of the multiple sinusoidal signals in time domain, the equations are obtained by using Euler transformation, and combined with the frequency values of the improved Prony algorithm,then using the least square method, the multiple sinusoidal signal amplitude and phase estimation values are obtained. This method can simplify, reduce the amount of calculation and time when some parameter is equal to zero. Simulation experiment shows that this algorithm has high estimation precision in high signal noise ratio (SNR).3. Based on the ESPRIT algorithm, using the algorithm calculates directly to the eigenvalues of the matrix pencil. A new amplitude and phase estimation algorithm is proposed combined with the amplitude and phase estimation of the time domain accumulation. This algorithm is effective to suppress the noise on the influence of amplitude and phase.Simulation results show that the proposed algorithm is better in the case of low SNR.