Joint Source Estimation and Localization

The estimation of directions of arrival is formulated as the decomposition of a 3-way array into a sum of rank-one terms, which is possible when the receive array enjoys some geometrical structure. The main advantage is that this decomposition is essentially unique under mild assumptions, if computed exactly. The drawback is that a low-rank approximation does not always exist. Therefore, a coherence constraint is introduced that ensures the existence of the latter best approximate, which allows to localize and estimate closely located or highly correlated sources. Then Cramér-Rao bounds are derived for localization parameters and source signals, assuming the others are nuisance parameters; some inaccuracies found in the literature are pointed out. Performances are eventually compared with unconstrained reference algorithms such as ESPRIT, in the presence of additive complex Gaussian noise, with possibly noncircular distribution.

[1]  Zbynek Koldovský,et al.  Cramér-Rao-Induced Bounds for CANDECOMP/PARAFAC Tensor Decomposition , 2012, IEEE Transactions on Signal Processing.

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

[3]  Rémy Boyer,et al.  Second-order near-field localization with automatic paring operation , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[4]  Björn E. Ottersten,et al.  Multiple invariance ESPRIT , 1992, IEEE Trans. Signal Process..

[5]  A. Geramita,et al.  Higher secant varieties of the Segre varieties , 2005 .

[6]  Jian Li,et al.  SPICE: A Sparse Covariance-Based Estimation Method for Array Processing , 2011, IEEE Transactions on Signal Processing.

[7]  Souleymen Sahnoun,et al.  Deterministic blind identification in antenna array processing , 2014, 2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop (SAM).

[8]  M. Viberg,et al.  Two decades of array signal processing research: the parametric approach , 1996, IEEE Signal Process. Mag..

[9]  Charles Soussen,et al.  Sparse multidimensional modal analysis using a multigrid dictionary refinement , 2012, EURASIP J. Adv. Signal Process..

[10]  Pierre Comon,et al.  Blind Multilinear Identification , 2012, IEEE Transactions on Information Theory.

[11]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[12]  Bjorn Ottersten,et al.  Performance analysis of the total least squares ESPRIT algorithm , 1991, IEEE Trans. Signal Process..

[13]  Rasmus Bro,et al.  A comparison of algorithms for fitting the PARAFAC model , 2006, Comput. Stat. Data Anal..

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

[15]  Jun Liu,et al.  An Eigenvector-Based Approach for Multidimensional Frequency Estimation With Improved Identifiability , 2006, IEEE Transactions on Signal Processing.

[16]  H. Kiers.  Towards a standardized notation and terminology in multiway analysis , 2000 .

[17]  Pierre Comon.  4 - Estimation multivariable complexe , 1986 .

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

[19]  Lieven De Lathauwer,et al.  A Link between the Canonical Decomposition in Multilinear Algebra and Simultaneous Matrix Diagonalization , 2006, SIAM J. Matrix Anal. Appl..

[20]  Kaj Madsen,et al.  Methods for Non-Linear Least Squares Problems , 1999 .

[21]  Rémi Gribonval,et al.  Sparse representations in unions of bases , 2003, IEEE Trans. Inf. Theory.

[22]  Harry L. Van Trees,et al.  Optimum Array Processing , 2002 .

[23]  Michael Elad,et al.  Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[24]  Pierre Comon,et al.  Tensors : A brief introduction , 2014, IEEE Signal Processing Magazine.

[25]  Chris Peterson,et al.  Induction for secant varieties of Segre varieties , 2006, math/0607191.

[26]  Adriaan van den Bos,et al.  A Cramer-Rao lower bound for complex parameters , 1994, IEEE Trans. Signal Process..

[27]  Nikos D. Sidiropoulos,et al.  Cramer-Rao lower bounds for low-rank decomposition of multidimensional arrays , 2001, IEEE Trans. Signal Process..

[28]  Fredrik Athley,et al.  Threshold region performance of maximum likelihood direction of arrival estimators , 2005, IEEE Transactions on Signal Processing.

[29]  Are Hjørungnes,et al.  Complex-Valued Matrix Differentiation: Techniques and Key Results , 2007, IEEE Transactions on Signal Processing.

[30]  G. Golub,et al.  Tracking a few extreme singular values and vectors in signal processing , 1990, Proc. IEEE.

[31]  P. Comon,et al.  Tensor decompositions, alternating least squares and other tales , 2009 .

[32]  Nikos D. Sidiropoulos,et al.  Parallel factor analysis in sensor array processing , 2000, IEEE Trans. Signal Process..

[33]  Marius Pesavento,et al.  Direction finding in partly calibrated sensor arrays composed of multiple subarrays , 2002, IEEE Trans. Signal Process..