Chair: Louis Scharf, University of Colorado (USA)
V. Capdevielle, CEPHAG-ENSIEG (FRANCE)
Ch. Serviere, CEPHAG-ENSIEG (FRANCE)
J. L. Lacoume, CEPHAG-ENSIEG (FRANCE)
Conventional antenna array processing techniques are based on the use of second order statistics but rest on restrictive assumptions. Thus, when a priori information about the propagation or the geometry of the array are hardly available, the model can be generalized to a blind sources separation model. It supposes the statistical independence of the sources and their non- gaussianity. We focus in this paper on the generalization of the sources separation problem to convolutive mixtures of wide-band sources in the frequency domain.
Bill M. Radich, University of Minnesota (USA)
Kevin M. Buckley, University of Minnesota (USA)
We present a Bayesian evidence technique for the parameter estimation/model selection problem within the conditional maximum likelihood (CML) framework. The CML is chosen because of its flexibility: it allows for a wide range of source amplitude models (e.g., no unreasonable or restrictive assumptions, such as Gaussian signals are necessary). In contrast to other CML studies, we eliminate the large number of unknown amplitude parameters by marginalization with a proper (normalizable), yet very broad prior. The resulting marginal is used to derive a new model selection/parameter estimation procedure, based on the Bayesian evidence of each considered model, given the observed data. Monte Carlo simulations for a scenario consisting of two narrowband, far-field sources demonstrate the effectiveness of the proposed method in low SNR, small temporal/spatial sample situations.
P. Stoica, Chalmers University of Technology
M. Viberg, Chalmers University of Technology
M. Wong, McMaster University (CANADA)
Q. Wu, McMaster University (CANADA)
The main goal of this paper is to describe and analyse, in a unifying manner, the spatial and temporal IV-SSF approaches recently proposed for array signal processing in colored noise fields. (The acronym IV-SSF stands for ``Instrumental Variable -- Signal Subspace Fitting). We derive a general, optimally-weighted, IV-SSF direction estimator and show that this estimator encompasses the UNCLE estimator of Wong and Wu, which is a spatial IV-SSF method; and the temporal IV-SSF estimator of Viberg, Stoica and Ottersten. The latter two estimators have seemingly different forms, so their asymptotic equivalence shown in this paper comes as a surprising unifying result.
Panagiotis Tsakalides, University of Southern California (USA)
Chrysostomos L. Nikias, University of Southern California (USA)
There exist real world applications in which impulsive channels tend to produce large amplitude interferences more frequently than Gaussian channels. The stable law has been shown to successfully model noise over certain impulsive channels. In this paper, we propose subspace-based methods for the direction-of-arrival estimation problem in impulsive noise environments. We define the covariation matrix of the array sensor outputs and show that eigendecompostion-based methods, such as the MUSIC algorithm, can be applied to the sample covariation matrix to extract the bearing information from the measurements.
Martin Haardt, Technical University of Munich (GERMANY)
Michael D. Zoltowski, Purdue University
Cherian P. Mathews, Rose-Hulman Institute of Technology(USA)
Josef A. Nossek, Technical University of Munich (GERMANY)
Consider multiple narrowband signals that are incident upon a planar sensor array. 2D Unitary ESPRIT is a new closed-form high resolution algorithm to provide automatically paired source azimuth and elevation angle estimates, along with an efficient way to reconstruct the impinging signals. In the final stage of the algorithm, the real and imaginary parts of the ith eigenvalue of a matrix are one-to-one related to the respective direction cosines of the ith source relative to the two array axes. 2D Unitary ESPRIT offers several advantages over other recently proposed ESPRIT based closed-form 2D angle estimation techniques. First, except for the final eigenvalue decomposition of dimension equal to the number of sources, it is efficiently formulated in terms of real-valued computation throughout. Second, it is amenable to an efficient DFT beamspace implementation. Third, it is also applicable to array configurations that do not exhibit three identical subarrays, as long as the array is centro-symmetric and possesses invariances in two distinct directions. Finally, 2D Unitary ESPRIT easily handles sources having one member of the spatial frequency coordinate pair in common.
Jean-Jacques Fuchs, IRISA Universite de Rennes I (FRANCE)
When applied to array processing, the Pisarenko harmonic retrieval method is limited to linear equispaced arrays. We present an approach that allows to extend it to general arrays. For the ease of exposition, we consider only sparse linear arrays. Though limited in generality, these arrays already permit to localize up to N(N-1)/2 narrow-band sources with N-sensors. We actually show that the Pisarenko approach can be seen as a deconvolution or model-fitting approach that minimizes an l 1 norm and can be implemented as a standard linear program. Further extensions allowing to model and take into account the statistical nature of the data (the estimation errors) are also proposed.
Anthony J. Weiss, Tel-Aviv University (ISRAEL)
A new method for localizing multiple signals in spatially-colored background noise using an arbitrary passive sensor array is presented. The method enables also to exploit prior knowledge that the signals are uncorrelated, in case such information is available, so as to improve the performance and allow localization even if the number of signals exceeds the number of sensors. The estimation is based on the Generalized Least Squares criterion, and is both consistent and efficient. Simulation results confirming the theoretical results are included.
F. Gersemsky, Ruhr University-Bochum (GERMANY)
B. Yang, Ruhr University-Bochum (GERMANY)
A large number of array processing applications such as radar, sonar, etc require the estimation of some parameters given the output of an array of sensors. Many high resolution methods for source parameter estimation are based on the eigen decomposition of the covariance matrix of the sensor output. The PASTd (projection approximation subspace tracking with deflation) algorithm has been recently published for tracking both the signal subspace and its rank at a computational cost of order O(nr), where n is the number of sensors and r the number of sources to be detected. In this paper we address the problem of tracking the physical parameters as direction, distance, etc given the estimated signal subspace. All known parameter estimation methods as MUSIC, MinNorm or WSF are based on a different cost function which is minimized with respect to the desired parameters. Standard minimization methods as gradient or Newton's method fail to converge to the global minimum if the starting value is not close enough to the desired solution. We introduce a new cost function which has to be minimized with respect to the parameters and an algorithm of low computational cost which is able to find the global minimum, starting from any initial value in all our experiments.
Jacob Sheinvald, RAFAEL 83 (ISRAEL)
Mati Wax, RAFAEL 83 (ISRAEL)
A new technique for localization of multiple signals is presented. Unlike existing techniques which require that the whole array be sampled simultaneously and consequently require many receivers, our technique allows to sample arbitrary subarrays sequentially and consequently significantly reduces the required number of receivers. The estimation method we use in conjunction with this sampling scheme is based on approximating the corresponding maximum likelihood estimator by a computationally simpler Generalized Least Squares (GLS) estimator that is proved to be both consistent and efficient.
Russell H. Lambert, University of Southern California (USA)
A new adaptive filtering approach to multichannel source separation is presented. The method is based on an extension of traditional single channel blind equalization. This multichannel extension will be presented theoretically and the results will be demonstrated by simulation using both communications data and speech. The new source separation algorithm is compared to existing adaptive separation algorithms which handle multipath: the Herault-Jutten source separation algorithm, and the time-recursive Weinstein et. al. algorithms. The new method offers dramatic performance improvement over existing methods and the ability to handle different source data types in an optimal fashion.