Messaoud Thameri

Exact conditional and unconditional Cramér–Rao bounds for near field localization

Abstract This paper considers the Cramer–Rao lower Bound (CRB) for the source localization problem in the near field. More specifically, we use the exact expression of the delay parameter for the CRB derivation and show how this ‘exact CRB’ can be significantly different from the one given in the literature based on an approximate time delay expression (usually considered in the Fresnel region). In addition, we consider the exact expression of the received power profile (i.e., variable gain case) which, to the best of our knowledge, has been ignored in the literature. Finally, we exploit the CRB expression to introduce the new concept of Near Field Localization Region (NFLR) for a target localization performance associated to the application at hand. We illustrate the usefulness of the proposed CRB derivation as well as the NFLR concept through numerical simulations in different scenarios.

Low complexity adaptive algorithms for Principal and Minor Component Analysis

This article introduces new low cost algorithms for the adaptive estimation and tracking of principal and minor components. The proposed algorithms are based on the well-known OPAST method which is adapted and extended in order to achieve the desired MCA or PCA (Minor or Principal Component Analysis). For the PCA case, we propose efficient solutions using Givens rotations to estimate the principal components out of the weight matrix given by OPAST method. These solutions are then extended to the MCA case by using a transformed data covariance matrix in such a way the desired minor components are obtained from the PCA of the new (transformed) matrix. Finally, as a byproduct of our PCA algorithm, we propose a fast adaptive algorithm for data whitening that is shown to overcome the recently proposed RLS-based whitening method.

Minor subspace tracking using MNS technique

This paper introduces new minor (noise) subspace tracking (MST) algorithms based on the minimum noise subspace (MNS) technique. The latter has been introduced as a computationally efficient subspace method for blind system identification. We exploit here the principle of the MNS, to derive the most efficient algorithms for MST. The proposed method joins the advantages of low complexity and fast convergence rate. Moreover, this method is highly parallelizable and hence its computational cost can be easily reduced to a very low level when parallel architectures are available. Different implementations are proposed for different contexts and they are compared via numerical simulations.

Performance improvement of direction finding algorithms in non-homogeneous environment through data fusion

This paper proposes a new effective approach to improve the performance of DOA (Direction Of Arrival) algorithms when bursts affect the array data. The proposed approach is based on the combining of data fusion techniques and the results of theoretical performance analysis of conventional DOA algorithms. For this purpose, the received array data is first split in M time-segments. Then, the DOAs are estimated from each data segment using a conventional DOA algorithm. The obtained estimates are fused using the federated fusion algorithm according to their statistical accuracy obtained from the well-documented performance analysis of the considered algorithm. As proof of concept of the proposed approach, numerical experiments have been conducted by considering the MUSIC algorithm. The obtained results show that the new algorithm outperforms the conventional one in terms of accuracy in a non-homogeneous environment. Therefore, it exhibits enhanced robustness capability. Moreover, it reduces the memory cost and computational complexity which makes it suitable for real time applications. To our knowledge, it is the first time that theoretical performance analysis results are exploited for the derivation of new subspace-DOA methods.

Derivation of an analytical expression of the Gaussian model Statistical Resolution Limit

Statistical Resolution Limit (SRL), defined as the minimal separation to resolve two closely spaced signals, is one of the important tools to evaluate a given system performance. Based on S.T. Smiths formulation of the SRL, this paper provides a methodology to compute an approximate analytical expression of the resolution limit in the Gaussian model case. As an application, we consider the particular case of two sources located in the near field and consider the resolution limit in terms of minimum angular separation. Discussion and numerical illustrations are then given to get more insights on the proposed derivation and to validate our theoretical results.

Fast principal component analysis and data whitening algorithms

In this paper, we propose an adaptive implementation of a fast-convergent algorithm for principal component extraction. Our approach consists of first estimating a basis of the principal subspace through the use of OPAST algorithm. The obtained basis is then fed to a second process where at each iteration one or several Givens transformations are applied to estimate the principal components. Later on, the proposed PCA algorithm is used to derive a fast data whitening solution that overcomes the existing ones of similar complexity order. Simulation results support the high performance of our algorithms in terms of accuracy and speed of convergence.

On the Statistical Resolution Limit (SRL) for Time-Reversal based MIMO radar

In the single-input multiple-output radar, the system transmits scaled (coherent) versions of a single waveform. The multiple-input multiple-output (MIMO) radar uses multiple antennas to simultaneously transmit several non-coherent waveforms and exploits multiple antennas to receive the reflected signals (echoes). This diversity in term of waveform coding allows to transmit orthogonal waveforms which enables the MIMO radar superiority in several fundamental aspects, including: improved parameter identifiability and estimation and much enhanced flexibility for transmit beam-pattern design. The context of this work is the co-located MIMO radar where the transmit and the receive arrays are close in space. In this paper, we provide a theoretical performance analysis to compare two configurations of MIMO radar: conventional configuration and Time Reversal (TR) configuration in term of Statistical Resolution Limit (SRL). This study provides new insights on the performance gain of the TR scheme which is discussed and illustrated by appropriate simulation results depending on the receive noise level.

A new multi-sensor fusion algorithm based on the Information Filter framework

his paper presents a new efficient track-to-track fusion (T2TF) algorithm based on the Information Filter (IF) framework which takes into account phenomena encountered in practical applications. In fact, it combines a modified version of the IF framework and a self-tuning fusion procedure based on likelihood functions to address issues such as the correlation of the estimates, the transmission shortcomings and the measurement origin uncertainty. The proposed method is evaluated through simulations and the obtained results show that the proposed algorithm performs as well the optimal centralized fusion schema in an idealized environment while it exhibits better robustness capabilities than existing decentralized algorithms when observation origin uncertainty is considered. Moreover, its reduced complexity cost is suitable for real time applications.

New algorithms for adaptive BSS

Blind Source Separation (BSS) is a vast field of research where a large number of BSS algorithms have already been proposed. However, derivation of adaptive BSS solutions with good trade-off between the computational cost and the convergence rate is still a challenging problem. In this work we consider low-cost adaptive BSS methods using statistical independence criteria. We introduce new algorithms using fast data whitening followed by source separation via Givens rotations. These algorithms are compared to other existing techniques and shown to present faster convergence rate and better separation performance.