Study On Parameter Estimation Algorithms For Multiple Sinusoidal Signal Based On Matrix Pencil And Prony Methods

The parameter estimation of multiple sinusoidal signal has been widely applied in electronic communications technology,earthquake detection and biomedical engineering detection,etc.Under the influence of noise,the received signal is different from the source signal.Therefore,getting rid of the noise in the signal and accurately estimating the signal parameters have important theoretical and application value.This dissertation analyzes the parameter estimation principle of generalized Prony algorithm,classical Prony algorithm and classical Matrix Pencil algorithm in detail.The parameter estimation performance of corresponding algorithms is analyzed by numerical experiment.And it shows that estimation precision of these classical algorithms is easily affected by noise.Therefore,for the problem that parameters estimation precision of classical algorithms is insufficient,this dissertation proposes the improved Matrix Pencil algorithm and the Prony algorithm based on time domain cumulative.The research work is as follows:(1)This dissertation proposes an improved Matrix Pencil algorithm.On the basis of remaining the arrangement redundancy of matrix element unchanged,it makes a cumulative sampling for each element,and makes new sequence values as matrix elements.Compared to classical Matrix Pencil algorithm,the improved Matrix Pencil algorithm achieves the double antinoise performance on theory,which can more accurately estimate the frequency of the signal.According to the frequency values,estimated values of the amplitude and phase are obtained through the least squares principle and the relationship between the parameters.At the same time,it makes comparison between the improved algorithm and the classical algorithm by making the simulation experiment.And the experimental results show that parameters estimation precision of the improved Matrix Pencil algorithm improves compared with the classical Matrix Pencil algorithm.(2)A time domain cumulative Prony algorithm of multiple sinusoidal signal frequency estimation is proposed.Through establishing a new equivalent relationship,the algorithm constructs a different Prony polynomials and deduces a new system of linear equations.And then a high precision of frequency estimation algorithm is obtained.At the same time,itmakes comparison between the improved algorithm and the classical algorithm by making the simulation experiment.And the experimental results show that both antinoise ability and parameters estimation precision of the improved algorithm improve.(3)An improved amplitude and phase estimation algorithm is proposed.On the basis of time domain cumulative Prony algorithm,according to the relationship between parameters and cumulative relationship,estimated expressions of the amplitude and phase are obtained.It makes comparison between the improved algorithm and the classical algorithm by making the simulation experiment.And the experimental results show that estimation precision of the improved algorithm improves for amplitude and phase estimation of multiple sinusoidal signal containing noise.