Newton algorithms for conditional and unconditional maximum likelihood estimation of the parameters of exponential signals in noise

The authors present polynomial-based Newton algorithms for maximum likelihood estimation (MLE) of the parameters of multiple exponential signals in noise. This formulation can be used in the estimation, for example, of the directions of arrival of multiple noise-corrupted narrowband plane waves using uniform linear arrays and the frequencies of multiple noise-corrupted complex sine waves. The algorithms offer rapid convergence and exhibit the computation efficiency associated with the polynomial approach. Compact, closed-form expressions are presented for the gradients and Hessians. Various model assumptions concerning the statistics of the underlying signals are considered. Numerical simulations are presented to demonstrate the algorithms' performance. >

[1]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[2]  J. Cadzow,et al.  Signal processing via least squares error modeling , 1990, IEEE ASSP Magazine.

[3]  Arthur Jay Barabell,et al.  Improving the resolution performance of eigenstructure-based direction-finding algorithms , 1983, ICASSP.

[4]  Thomas Kailath,et al.  On spatial smoothing for direction-of-arrival estimation of coherent signals , 1985, IEEE Trans. Acoust. Speech Signal Process..

[5]  Joe Brewer,et al.  Kronecker products and matrix calculus in system theory , 1978 .

[6]  Ilan Ziskind,et al.  Maximum likelihood localization of multiple sources by alternating projection , 1988, IEEE Trans. Acoust. Speech Signal Process..

[7]  Arye Nehorai,et al.  Maximum likelihood estimation of exponential signals in noise using a Newton algorithm , 1988, Fourth Annual ASSP Workshop on Spectrum Estimation and Modeling.

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

[9]  Ken Sharman,et al.  Maximum likelihood parameter estimation by simulated annealing , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[10]  Jorge J. Moré,et al.  The Levenberg-Marquardt algo-rithm: Implementation and theory , 1977 .

[11]  Petre Stoica,et al.  Maximum likelihood methods for direction-of-arrival estimation , 1990, IEEE Trans. Acoust. Speech Signal Process..

[12]  A. G. Jaffer,et al.  Maximum likelihood direction finding of stochastic sources: a separable solution , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

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

[14]  Björn E. Ottersten,et al.  Sensor array processing based on subspace fitting , 1991, IEEE Trans. Signal Process..

[15]  Ehud Weinstein,et al.  Parameter estimation of superimposed signals using the EM algorithm , 1988, IEEE Trans. Acoust. Speech Signal Process..

[16]  R. Mardani,et al.  A suboptimal, low cost maximum likelihood algorithm , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[17]  Yoram Bresler,et al.  Exact maximum likelihood parameter estimation of superimposed exponential signals in noise , 1986, IEEE Trans. Acoust. Speech Signal Process..

[18]  Ramdas Kumaresan,et al.  An algorithm for pole-zero modeling and spectral analysis , 1986, IEEE Trans. Acoust. Speech Signal Process..

[19]  J. Bohme,et al.  Accuracy of maximum-likelihood estimates for array processing , 1987, ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[20]  Ken Sharman,et al.  Genetic algorithms for maximum likelihood parameter estimation , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[21]  Petre Stoica,et al.  Performance study of conditional and unconditional direction-of-arrival estimation , 1990, IEEE Trans. Acoust. Speech Signal Process..