arXiv subjects

Mohammed Nabil El Korso

Publications and source records attributed to Mohammed Nabil El Korso.

26 records · Page 2Linked to original sources

arXiv2017

Relaxed concentrated MLE for robust calibration of radio interferometers

In this paper, we investigate the calibration of radio interferometers in which Jones matrices are considered to model the interaction between the incident electromagnetic field and the antennas of each station. Specifically, perturbation effects are introduced along the signal path, leading to the conversion of the plane wave into an electric voltage by the receptor. In order to design a robust estimator, the noise is assumed to follow a spherically invariant random process (SIRP). The derived algorithm is based on an iterative relaxed concentrated maximum likelihood estimator (MLE), for which closed-form expressions are obtained for most of the unknown parameters.

astro-ph.IM↗

arXiv2016

A Bayesian Lower Bound for Parameter Estimation of Poisson Data Including Multiple Changes (extended)

This paper derives lower bounds for the mean square errors of parameter estimators in the case of Poisson distributed data subjected to multiple abrupt changes. Since both change locations (discrete parameters) and parameters of the Poisson distribution (continuous parameters) are unknown, it is appropriate to consider a mixed Cramer-Rao/Weiss-Weinstein bound for which we derive closed-form expressions and illustrate its tightness by numerical simulations.

cs.IT↗

arXiv2016

A class of Weiss-Weinstein bounds and its relationship with the Bobrovsky-Mayer-Wolf-Zakai bounds

A fairly general class of Bayesian "large-error" lower bounds of the Weiss-Weinstein family, essentially free from regularity conditions on the probability density functions support, and for which a limiting form yields a generalized Bayesian Cramer-Rao bound (BCRB), is introduced. In a large number of cases, the generalized BCRB appears to be the Bobrovsky-Mayer-Wolf-Zakai bound (BMZB). Interestingly enough, a regularized form of the Bobrovsky-Zakai bound (BZB), applicable when the support of the prior is a constrained parameter set, is obtained. Modified Weiss-Weinstein bound and BZB which limiting form is the BMZB are proposed, in expectation of an increased tightness in the threshold region. Some of the proposed results are exemplified with a reference problem in signal processing: the Gaussian observation model with parameterized mean and uniform prior.

cs.IT↗

arXiv2016

Parallel Calibration for Sensor Array Radio Interferometers

In order to meet the theoretically achievable imaging performance, calibration of modern radio interferometers is a mandatory challenge, especially at low frequencies. In this perspective, we propose a novel parallel iterative multi-wavelength calibration algorithm. The proposed algorithm estimates the apparent directions of the calibration sources, the directional and undirectional complex gains of the array elements and their noise powers, with a reasonable computational complexity. Furthermore, the algorithm takes into account the specific variation of the aforementioned parameter values across wavelength. Realistic numerical simulations reveal that the proposed scheme outperforms the mono-wavelength calibration scheme and approaches the derived constrained Cramér-Rao bound even with the presence of non-calibration sources at unknown directions, in a computationally efficient manner.

astro-ph.IM↗

arXiv2016

MIMO Radar Target Localization and Performance Evaluation under SIRP Clutter

Multiple-input multiple-output (MIMO) radar has become a thriving subject of research during the past decades. In the MIMO radar context, it is sometimes more accurate to model the radar clutter as a non-Gaussian process, more specifically, by using the spherically invariant random process (SIRP) model. In this paper, we focus on the estimation and performance analysis of the angular spacing between two targets for the MIMO radar under the SIRP clutter. First, we propose an iterative maximum likelihood as well as an iterative maximum a posteriori estimator, for the target's spacing parameter estimation in the SIRP clutter context. Then we derive and compare various Cramér-Rao-like bounds (CRLBs) for performance assessment. Finally, we address the problem of target resolvability by using the concept of angular resolution limit (ARL), and derive an analytical, closed-form expression of the ARL based on Smith's criterion, between two closely spaced targets in a MIMO radar context under SIRP clutter. For this aim we also obtain the non-matrix, closed-form expressions for each of the CRLBs. Finally, we provide numerical simulations to assess the performance of the proposed algorithms, the validity of the derived ARL expression, and to reveal the ARL's insightful properties.

stat.AP↗

arXiv2016

Maximum Likelihood and Maximum A Posteriori Direction-of-Arrival Estimation in the Presence of SIRP Noise

The maximum likelihood (ML) and maximum a posteriori (MAP) estimation techniques are widely used to address the direction-of-arrival (DOA) estimation problems, an important topic in sensor array processing. Conventionally the ML estimators in the DOA estimation context assume the sensor noise to follow a Gaussian distribution. In real-life application, however, this assumption is sometimes not valid, and it is often more accurate to model the noise as a non-Gaussian process. In this paper we derive an iterative ML as well as an iterative MAP estimation algorithm for the DOA estimation problem under the spherically invariant random process noise assumption, one of the most popular non-Gaussian models, especially in the radar context. Numerical simulation results are provided to assess our proposed algorithms and to show their advantage in terms of performance over the conventional ML algorithm.

stat.AP↗

arXiv2013

Coexistence of Near-Field and Far-Field Sources: the Angular Resolution Limit

Passive source localization is a well known inverse problem in which we convert the observed measurements into information about the direction of arrivals. In this paper we focus on the optimal resolution of such problem. More precisely, we propose in this contribution to derive and analyze the Angular Resolution Limit (ARL) for the scenario of mixed Near-Field (NF) and Far-Field (FF) Sources. This scenario is relevant to some realistic situations. We base our analysis on the Smith's equation which involves the Cramér-Rao Bound (CRB). This equation provides the theoretical ARL which is independent of a specific estimator. Our methodology is the following: first, we derive a closed-form expression of the CRB for the considered problem. Using these expressions, we can rewrite the Smith's equation as a 4-th order polynomial by assuming a small separation of the sources. Finally, we derive in closed-form the analytic ARL under or not the assumption of low noise variance. The obtained expression is compact and can provide useful qualitative informations on the behavior of the ARL.

cs.IT↗

arXiv2013

Angular resolution limit for deterministic correlated sources

This paper is devoted to the analysis of the angular resolution limit (ARL), an important performance measure in the directions-of-arrival estimation theory. The main fruit of our endeavor takes the form of an explicit, analytical expression of this resolution limit, w.r.t. the angular parameters of interest between two closely spaced point sources in the far-field region. As by-products, closed-form expressions of the Cramér-Rao bound have been derived. Finally, with the aid of numerical tools, we confirm the validity of our derivation and provide a detailed discussion on several enlightening properties of the ARL revealed by our expression, with an emphasis on the impact of the signal correlation.

cs.IT↗