This paper presents new algorithms for estimating the spatio-temporal spectrum of the signals received by a passive array. The algorithms are based on the eigenstructure of the covariance and spectral density matrices of the received signals. They allow partial correlation between the sources and thus are applicable to certain kinds of multipath problems. Simulation results that illustrate the performance of the new algorithms are presented.

Spatio-temporal spectral analysis by eigenstructure methods

The equivalence between the problem of determining the bearing of a radiating source with an array of sensors and the problem of estimating the spectrum of a signal is demonstrated. Modern spectral estimation algorithms are derived within the context of array processing using an algebraic approach. Emphasis is placed on the problem of determining the bearing of a sound source with an array. Special issues encountered in applying these estimates are discussed.

The application of spectral estimation methods to bearing estimation problems

In the classical approach to underwater passive listening, the medium is sampled in a convenient number of "look-directions" from which the signals are estimated in order to build an image of the noise field. In contrast, a modern trend is to consider the noise field as a global entity depending on few parameters to be estimated simultaneously. In a Gaussian context, it is worthwhile to consider the application of likelihood methods in order to derive a detection test for the number of sources and estimators for their locations and spectral levels. This paper aims to compute such estimators when the wavefront shapes are not assumed known a priori. This justifies results previously found using the asymptotical properties of the eigenvalue-eigenvector decomposition of the estimated spectral density matrix of the sensor signals: they have led to a variety of "high resolution" array processing methods. More specifically, a covariance matrix test for equality of the smallest eigenvalues is presented for source detection. For source localization, a "best fit" method and a test of orthogonality between the "smallest" eigenvectors and the "source" vectors are discussed.

Optimality of high resolution array processing using the eigensystem approach

A method of improving the bearing-resolving capabilities of a passive array is discussed. This method is an adaptive beamforming method, having many similarities to the minimum energy approach. The evaluation of energy in each steered beam is preceded by an eigenvalue-eigenvector analysis of the empirical correlation matrix. Modification of the computations according to the eigenvalue structure results in improved resolution of the bearing of acoustic sources. The increase in resolution is related to the time-bandwidth product of the computation of the correlation matrix. However, this increased resolution is obtained at the expense of array gain.

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Improving the resolution of bearing in passive sonar arrays by eigenvalue analysis

The maximum likelihood (ML) estimator of the location of multiple sources and the corresponding Cramer-Rao lower bound on the error covariance matrix are derived. The derivation is carried out for the general case of correlated sources so that multipath propagation is included as a special case. It is shown that the ML processor consists of a bank of beam-formers, each focused to a different source, followed by a variable matrix-filter that is controlled by the assumed location of the sources. In the special case of uncorrelated sources and very low signal-to-noise ratio this processor reduces to an aggregate of ML processors for a single source with each processor matched to a different source. Iterative algorithms for the actual computation of the ML estimator are also presented.

Optimum localization of multiple sources by passive arrays

In the eigenvalue - eigenvector decomposition of the spectral density matrix of the signals received on a passive array, two sets of eigenvectors are found. The first set contains eigenvectors which are asymptotcally orthogonal to the sources direction vectors : from them a high resolution bearing estimator has been deduced. The other set contains eigenvectors which are asymptotically a basis for the sources direction vectors space. It is shown in this paper that from this set and the corresponding eigenvalues, an estimator for the sources spectral densities can be derived. Simulation results are given.

G. Bienvenu

Papers

Source power estimation method associated with high resolution bearing estimator