Direction estimation in partially unknown noise fields

The problem of direction of arrival estimation in the presence of colored noise with unknown covariance is considered. The unknown noise covariance is assumed to obey a linear parametric model. Using this model, the maximum likelihood directions parameter estimate is derived, and a large sample approximation is formed. It is shown that a priori information on the source signal correlation structure is easily incorporated into this approximate ML (AML) estimator. Furthermore, a closed form expression of the Cramer-Rao bound on the direction parameter is provided. A perturbation analysis with respect to a small error in the assumed noise model is carried out, and an expression of the asymptotic bias due to the model mismatch is given. Computer simulations and an application of the proposed technique to a full-scale passive sonar experiment is provided to illustrate the results.

[1]  L. Scharf,et al.  Statistical Signal Processing: Detection, Estimation, and Time Series Analysis , 1991 .

[2]  Björn E. Ottersten,et al.  Instrumental variable approach to array processing in spatially correlated noise fields , 1994, IEEE Trans. Signal Process..

[3]  Mati Wax.  Detection and localization of multiple sources in noise with unknown covariance , 1992, IEEE Trans. Signal Process..

[4]  Arye Nehorai,et al.  Concentrated Cramer-Rao bound expressions , 1994, IEEE Trans. Inf. Theory.

[5]  Ahmed H. Tewfik.  Direction finding in the presence of colored noise by candidate identification , 1991, IEEE Trans. Signal Process..

[6]  Arogyaswami Paulraj,et al.  A harmonic noise model for direction finding in colored ambient noise , 1995, IEEE Signal Processing Letters.

[7]  Björn E. Ottersten,et al.  Array processing in correlated noise fields based on instrumental variables and subspace fitting , 1995, IEEE Trans. Signal Process..

[8]  Mats Viberg.  Sensitivity of parametric direction finding to colored noise fields and undermodeling , 1993, Signal Process..

[9]  Jian Li,et al.  Computationally efficient angle estimation for signals with known waveforms , 1995, IEEE Trans. Signal Process..

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

[11]  Anthony J. Weiss,et al.  Localization of correlated and uncorrelated signals in colored noise via generalized least squares , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[12]  Thomas Kailath,et al.  Eigenstructure methods for direction of arrival estimation in the presence of unknown noise fields , 1986, IEEE Trans. Acoust. Speech Signal Process..

[13]  Alex B. Gershman,et al.  Experimental results of localization of moving underwater signal by adaptive beamforming , 1995, IEEE Trans. Signal Process..

[14]  Björn E. Ottersten,et al.  Estimation of nominal direction of arrival and angular spread using an array of sensors , 1996, Signal Process..

[15]  Petre Stoica,et al.  On array signal processing in spatially correlated noise fields , 1992 .

[16]  Eric Moulines,et al.  Asymptotic performance analysis of direction-finding algorithms based on fourth-order cumulants , 1995, IEEE Trans. Signal Process..

[17]  Anthony J. Weiss,et al.  Direction finding using noise covariance modeling , 1995, IEEE Trans. Signal Process..

[18]  Fu Li,et al.  Performance degradation of DOA estimators due to unknown noise fields , 1992, IEEE Trans. Signal Process..

[19]  Surendra Prasad,et al.  Signal subspace algorithms for direction of arrival estimation in the presence of a class of unknown noise fields , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[20]  Jitendra K. Tugnait.  Time delay estimation with unknown spatially correlated Gaussian noise , 1993, IEEE Trans. Signal Process..

[21]  Björn E. Ottersten,et al.  Optimal localization of partially known signals in unknown noise fields , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[22]  Johann F. Böhme,et al.  On least squares methods for direction of arrival estimation in the presence of unknown noise fields , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[23]  Surendra Prasad,et al.  An efficient signal subspace algorithm for source localization in noise fields with unknown covariance , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[24]  Björn E. Ottersten,et al.  Detection and estimation in sensor arrays using weighted subspace fitting , 1991, IEEE Trans. Signal Process..

[25]  Jean-Jacques Fuchs.  Estimation of the number of signals in the presence of unknown correlated sensor noise , 1992, IEEE Trans. Signal Process..

[26]  Ralph Otto Schmidt,et al.  A signal subspace approach to multiple emitter location and spectral estimation , 1981 .

[27]  P. Stoica,et al.  Novel eigenanalysis method for direction estimation , 1990 .

[28]  Kon Max Wong,et al.  UN-MUSIC and UN-CLE: an application of generalized correlation analysis to the estimation of the direction of arrival of signals in unknown correlated noise , 1994, IEEE Trans. Signal Process..

[29]  Alexander Graham,et al.  Kronecker Products and Matrix Calculus: With Applications , 1981 .

[30]  Venkatesh Nagesha,et al.  Maximum likelihood estimation for array processing in colored noise , 1996, IEEE Trans. Signal Process..

[31]  Jean-Pierre Le Cadre.  Parametric methods for spatial signal processing in the presence of unknown colored noise fields , 1989, IEEE Trans. Acoust. Speech Signal Process..

[32]  Thomas Kailath,et al.  ESPRIT-estimation of signal parameters via rotational invariance techniques , 1989, IEEE Trans. Acoust. Speech Signal Process..

[33]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[34]  Björn E. Ottersten,et al.  Analysis of a subspace-based spatial frequency estimator , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[35]  James P. Reilly,et al.  Detection of the number of signals in noise with unknown, non-white covariance matrices , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

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