Detection and estimation in sensor arrays using weighted subspace fitting

The problem of signal parameter estimation of narrowband emitter signals impinging on an array of sensors is addressed. A multidimensional estimation procedure that applies to arbitrary array structures and signal correlation is proposed. The method is based on the recently introduced weighted subspace fitting (WSF) criterion and includes schemes for both detecting the number of sources and estimating the signal parameters. A Gauss-Newton-type method is presented for solving the multidimensional WSF and maximum-likelihood optimization problems. The global and local properties of the search procedure are investigated through computer simulations. Most methods require knowledge of the number of coherent/noncoherent signals present. A scheme for consistently estimating this is proposed based on an asymptotic analysis of the WSF cost function. The performance of the detection scheme is also investigated through simulations. >

[1]  J. H. Wilkinson The algebraic eigenvalue problem , 1966 .

[2]  Z. Bai,et al.  On detection of the number of signals in presence of white noise , 1985 .

[3]  Bjorn Ottersten,et al.  Asymptotic Results For Multidimensional Sensor Array Processing/sup 1/ , 1988, Twenty-Second Asilomar Conference on Signals, Systems and Computers.

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

[5]  Bjorn Ottersten,et al.  Analysis of subspace fitting based methods for sensor array processing , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[6]  James A. Cadzow,et al.  A high resolution direction-of-arrival algorithm for narrow-band coherent and incoherent sources , 1988, IEEE Trans. Acoust. Speech Signal Process..

[7]  R. Kumaresan,et al.  Estimating the Angles of Arrival of Multiple Plane Waves , 1983, IEEE Transactions on Aerospace and Electronic Systems.

[8]  Axel Ruhe,et al.  Algorithms for separable nonlinear least squares problems , 1980 .

[9]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[10]  J. F. Böhme,et al.  Estimation of spectral parameters of correlated signals in wavefields , 1986 .

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

[12]  Ilan Ziskind,et al.  Detection of the number of coherent signals by the MDL principle , 1989, IEEE Trans. Acoust. Speech Signal Process..

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

[14]  Thomas Kailath,et al.  Detection of signals by information theoretic criteria , 1985, IEEE Trans. Acoust. Speech Signal Process..

[15]  Yoram Bresler,et al.  On the number of signals resolvable by a uniform linear array , 1986, IEEE Trans. Acoust. Speech Signal Process..

[16]  Bo Wahlberg,et al.  Stochastic maximum likelihood estimation in sensor arrays by weighted subspace fitting , 1989, Twenty-Third Asilomar Conference on Signals, Systems and Computers, 1989..

[17]  L. Kaufman A variable projection method for solving separable nonlinear least squares problems , 1974 .

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

[19]  G. Stewart Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems , 1973 .

[20]  J. P. Burg,et al.  Maximum entropy spectral analysis. , 1967 .

[21]  Petre Stoica,et al.  MUSIC, maximum likelihood, and Cramer-Rao bound , 1989, IEEE Transactions on Acoustics, Speech, and Signal Processing.

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

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

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

[25]  D. R. Farrier,et al.  Asymptotic results for eigenvector methods , 1985 .

[26]  Fred C. Schweppe,et al.  Sensor-array data processing for multiple-signal sources , 1968, IEEE Trans. Inf. Theory.

[27]  W. Stout Almost sure convergence , 1974 .

[28]  Philip E. Gill,et al.  Practical optimization , 1981 .

[29]  Johann F. Böhme,et al.  Estimation of source parameters by maximum likelihood and nonlinear regression , 1984, ICASSP.

[30]  Thomas Kailath,et al.  ESPIRT-estimation of signal parameters via rotational invariance techniques , 1989 .

[31]  Mostafa Kaveh,et al.  The statistical performance of the MUSIC and the minimum-norm algorithms in resolving plane waves in noise , 1986, IEEE Trans. Acoust. Speech Signal Process..

[32]  Ilan Ziskind,et al.  On unique localization of multiple sources by passive sensor arrays , 1989, IEEE Trans. Acoust. Speech Signal Process..

[33]  T. W. Anderson ASYMPTOTIC THEORY FOR PRINCIPAL COMPONENT ANALYSIS , 1963 .

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

[35]  R. O. Schmidt,et al.  Multiple emitter location and signal Parameter estimation , 1986 .

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