Overdetermined Yule-Walker estimation of the frequencies of multiple sinusoids: Accuracy aspects

Abstract The estimation of sinusoidal frequencies by the overdetermined Yule-Walker (OYW) method is considered. An explicit expression is derived for the asymptotic covariance matrix of the estimation errors. The effect of increasing the number of Yule-Walker equations on estimation accuracy is analyzed. The optimally weighted OYW method is also briefly discussed. The asymptotic estimation accuracy of the OYW method is compared to the best achievable accuracy corresponding to the Cramer-Rao bound.

[1]  Torsten Söderström,et al.  An efficient linear method for ARMA spectral estimation , 1994, ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[2]  Petre Stoica,et al.  Optimization with respect to covariance sequence parameters , 1985, Autom..

[3]  R. R. Boorstyn,et al.  Multiple tone parameter estimation from discrete-time observations , 1976, The Bell System Technical Journal.

[4]  Torsten Söderström,et al.  Asymptotic properties of high-order Yule-Walker estimates of frequencies of multiple sinusoids , 1986, ICASSP '86. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[5]  U. Grenander,et al.  Statistical analysis of stationary time series , 1957 .

[6]  M. Bartlett.  On the Theoretical Specification and Sampling Properties of Autocorrelated Time‐Series , 1946 .

[7]  J. Cadzow,et al.  High performance spectral estimation--A new ARMA method , 1980 .

[8]  R. Kumaresan,et al.  Estimation of frequencies of multiple sinusoids: Making linear prediction perform like maximum likelihood , 1982, Proceedings of the IEEE.

[9]  J. Cadzow,et al.  Spectral estimation: An overdetermined rational model equation approach , 1982, Proceedings of the IEEE.

[10]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[11]  T. W. Anderson,et al.  On the Asymptotic Distribution of the Autocorrelations of a Sample from a Linear Stochastic Process , 1964 .

[12]  U. Grenander,et al.  Toeplitz Forms And Their Applications , 1958 .

[13]  Yiu-Tong Chan,et al.  Spectral estimation via the high-order Yule-Walker equations , 1982 .

[14]  S.M. Kay,et al.  Spectrum analysis—A modern perspective , 1981, Proceedings of the IEEE.

[15]  Petre Stoica,et al.  Maximum likelihood estimation of the parameters of multiple sinusoids from noisy measurements , 1989, IEEE Trans. Acoust. Speech Signal Process..

[16]  B. Friedlander.  The overdetermined recursive instrumental variable method , 1983 .

[17]  E. J. Hannan,et al.  Multiple time series , 1970 .

[18]  Petre Stoica,et al.  On instrumental variable estimation of sinusoid frequencies and the parsimony principle , 1986 .

[19]  B. Friedlander,et al.  The Modified Yule-Walker Method of ARMA Spectral Estimation , 1984, IEEE Transactions on Aerospace and Electronic Systems.

[20]  T. Söderström,et al.  Optimal instrumental variable estimates of the AR parameters of an ARMA process , 1985 .