Souleymen Sahnoun

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.

Tensor decomposition exploiting diversity of propagation velocities

The problem of direction of arrival (DoA) estimation of seismic plane waves impinging on an array of sensors is considered from a new deterministic perspective using tensor decomposition techniques. In addition to temporal and spatial sampling, further information is taken into account, based on the different propagation speed of body waves (P and S) through solid media. Performances are evaluated through simulated data in terms of the Cramer-Rao bounds and compared to other reference methods such as ESPRIT and MUSIC, in the presence of additive Gaussian circular noise. The proposed approach is then applied to real seismic data recorded at the Argentiere glacier, occurring at the interface between the ice mass and the underlying bedrock. MUSIC and ESPRIT rely on the estimation of the covariance matrix of received data, thus requiring a large number of time samples. Moreover, information about propagation speed diversity is not taken into account by existing models in array processing. The discovered advantage in terms of the average error in estimating the direction of arrival of body waves is noteworthy, especially for a low number of sensors, and in separating closely located sources. Additionally, an improvement of precision in processing real seismic data is observed. HighlightsA deterministic approach (tensor decomposition) for seismic array processing.Integration of the content of P and S waves for direction of arrival estimation.Evaluation of statistical performances through numerical simulations.Application to real seismic data recorded at Argentiere glacier (Mont Blanc).Comparison with existent narrowband methods such as ESPRIT and MUSIC.

Deterministic blind identification in antenna array processing

The estimation of directions of arrival is formulated as the decomposition of a 3-way array into a sum of rank-one terms. However, a low-rank tensor approximation does not always exist. We propose an optimization technique based on differentiable angular constraints on the factors, ensuring the existence of the low-rank tensor decomposition. The efficiency of the proposed algorithm is demonstrated via numerical simulations, and compared to Cramér-Rao bounds.

Optimal choice of Hankel-block-Hankel matrix shape in 2-D parameter estimation: The rank-one case

In this paper we analyse the performance of 2-D ESPRIT method for estimating parameters of 2-D superimposed damped exponentials. 2-D ESPRIT algorithm is based on low-rank decomposition of a Hankel-block-Hankel matrix that is formed by the 2-D data. Through a first-order perturbation analysis, we derive closed-form expressions for the variances of the complex modes, frequencies and damping factors estimates in the 2-D single-tone case. This analysis allows to define the optimal parameters used in the construction of the Hankel-block-Hankel matrix. A fast algorithm for calculating the SVD of Hankel-block-Hankel matrices is also used to enhance the computational complexity of the 2-D ESPRIT algorithm.

High-Resolution Subspace-Based Methods: Eigenvalue- or Eigenvector-Based Estimation?

In subspace-based methods for mulditimensional harmonic retrieval, the modes can be estimated either from eigenvalues or eigenvectors. The purpose of this study is to find out which way is the best. We compare the state-of-the art methods N-D ESPRIT and IMDF, propose a modification of IMDF based on least-squares criterion, and derive expressions of the first-order perturbations for these methods. The theoretical expressions are confirmed by the computer experiments.