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conditions: Estimation and performance analysis
Mohammed Nabil El Korso
To cite this version:
Mohammed Nabil El Korso. Contributions to array processing in non standard conditions: Estimation and performance analysis. Signal and Image processing. Université Paris Nanterre, 2018. �hal-02472407�
Habilitation à diriger des recherches Université Paris Nanterre
Spécialité : Traitement du signal
Présentée par Mohammed Nabil El Korso
Contributions à l'estimation et à l'analyse de performance en
traitement d'antennes dans des conditions non standards
pContributions to array processing in non standard conditions: Estimation and performance analysis
Soutenue le 27/09/2018 devant le jury composé de :
DR. Laure Blanc-Féraud CNRS-Laboratoire I3S Présidente
Pr. Cedric Richard Université de Nice Examinateur
Pr. Olivier Michel Université de Grenoble Examinateur
Pr. Guillaume Ginolhac Université Savoie Mont-Blanc Examinateur
Pr. David Brie Université de Nancy Rapporteur
Pr. Yannick Berthoumieu Université de Bordeaux Rapporteur Pr. Philippe Forster Université Paris Nanterre Garant
Laboratoire Energétique Mécanique Electromagnétisme EA-4416 50, rue de Sèvres, 92410 Ville d'Avray
Contents
I Curriculum Vitæ 1 0.1 Contact information . . . 2 0.2 Education . . . 2 0.3 Professional background . . . 2 0.4 Teachning activity . . . 3 0.5 Research activity . . . 4 0.5.1 Scienti c interests . . . 4 0.5.2 Applications . . . 4 0.6 Publication record . . . 4 0.6.1 Book chapters . . . 4 0.6.2 International journals . . . 5 0.6.3 International conferences . . . 6 0.6.4 National conferences . . . 90.7 Ph.D. and postdoctoral students advising . . . 9
0.7.1 Ph.D. students . . . 9
0.7.2 Post-doc . . . 11
0.7.3 Research trainees . . . 11
0.8 Community life and awards . . . 11
0.9 Projects . . . 14
0.10 Educational and academic responsibilities . . . 15
0.11 Miscellaneous . . . 16
II Research statement 17 1 Introduction 18 1.1 Summary of my Ph.D. thesis . . . 18
1.2 Overview of my current research activity . . . 19
2 Robust scatter matrix estimation and subspace estimation with application to radar 25 2.1 E cient estimation of covariance/scatter matrices with convex structure under CES distribution . . . 26
2.1.1 Background and problem setup . . . 27
2.1.1.1 CES distribution . . . 27
2.1.1.2 M-estimators . . . 27
2.1.1.3 Fisher information matrix . . . 29
2.1.1.4 Problem setup . . . 29
2.1.2 SESAME : StructurEd ScAtter Matrix Estimator . . . 29 iii
2.1.2.3 Application of SESAME to some CES distributions . . . 30
2.1.3 Asymptotic analysis . . . 31
2.1.4 Iterative SESAME . . . 32
2.1.5 Applications and numerical results . . . 33
2.1.5.1 SESAME with linear parameterization . . . 33
2.1.5.2 Simulation for Toeplitz structure with t-distributed data . . . 34
2.2 Minimum mean square distance estimation of subspaces in presence of non Gaus-sian sources . . . 37
2.2.1 Background theory . . . 38
2.2.1.1 Minimum mean square distance estimator . . . 38
2.2.1.2 Compound Gaussian distribution . . . 38
2.2.1.3 Complex generalized Bingham Langevin distribution . . . 39
2.2.2 The proposed MMSD estimator . . . 39
2.2.2.1 Model and problem statement . . . 39
2.2.2.2 Algorithm derivation . . . 40
2.2.3 Numerical simulations . . . 43
2.3 Robust parameterized mean estimation without secondary data . . . 47
2.3.1 Model setup . . . 47
2.3.1.1 Observation model . . . 47
2.3.1.2 Observation statistics . . . 48
2.3.1.3 Unknown parameter vector and likelihood function . . . 49
2.3.2 Iterative marginal maximum likelihood estimator . . . 49
2.3.3 Iterative maximum likelihood estimator & its Bayesian variant . . . 51
2.3.4 Discussions . . . 53
2.3.5 Performance analysis . . . 54
2.3.6 Numerical simulations . . . 55
3 Robust and scalable parametric calibration with application to radio astro-nomical arrays 59 3.1 Sparse and parallel multi-wavelength calibration algorithm . . . 61
3.1.1 Model setup . . . 61
3.1.2 Model eects of the wavelength on antenna gains, source direction shifts and source powers . . . 63
3.1.3 Joint parameter estimation problem . . . 63
3.1.4 Proposed parallel multi-wavelength calibration algorithm . . . 64
3.1.4.1 Overview of the proposed parallel multi-wavelength calibration algorithm . . . 64
3.1.4.2 Direction independent antenna gain estimation . . . 65
3.1.4.3 Direction dependent parameter and noise power estimation . . . 67
3.1.5 Simulations . . . 68
3.2 Robust calibration of radio interferometers in non-Gaussian environment . . . 75
3.2.1 Data model . . . 75
3.2.1.1 Case of non-structured Jones matrices . . . 75
3.2.1.2 Speci c case of the 3DC calibration regime . . . 76
3.2.2 Robust calibration estimator . . . 77
3.2.2.1 Estimation in the case of non-structured Jones matrices . . . 78 iv
3.2.2.2 Structured Jones matrices . . . 79
3.2.2.3 Extension to the multi-frequency case . . . 82
3.2.3 Numerical simulations . . . 84
4 Performance analysis with applications to array processing 87 4.1 Misspeci ed Cramér-Rao bound and its Slepian-Bangs-type formulas for CES dis-tributions . . . 89
4.1.1 Problem setup . . . 90
4.1.2 Slepian-Bangs formulas under misspeci ed CES models . . . 93
4.1.3 Relationship to previous results . . . 96
4.2 Performance analysis in the presence of unknown continuous and discrete param-eters: Application to change-points estimation . . . 99
4.2.1 Problem statement . . . 99
4.2.2 Proposed bound . . . 101
4.2.2.1 Background on the covariance inequality . . . 101
4.2.2.2 The hybrid Cramér-RaoWeiss-Weinstein bound . . . 101
4.2.2.3 Practical computation of the Hybrid Cramér-RaoWeiss-Weinstein bound . . . 104
4.2.3 Expressions of the Hybrid Cramér-RaoWeiss-Weinstein bound for the change-point problem . . . 105
4.2.4 Numerical results . . . 105
4.2.4.1 ML-MAP estimator . . . 105
4.2.4.2 Changes in the mean of a Gaussian distribution . . . 105
4.2.4.3 Changes in the variance of a Gaussian distribution . . . 107
4.2.4.4 Changes in the mean rate of a Poisson distribution . . . 107
5 Conclusion & perspectives 109 6 Appendices 115 6.1 Some technical considerations w.r.t. the SESAME scheme . . . 115
6.1.1 Practical implementation for holding the PSD constraint . . . 115
6.1.2 Detail of calculus of Table 1 . . . 116
6.1.3 Proof of equation (2.21) . . . 117
6.2 Complex Generalized Bingham Langevin distribution sampling . . . 118
6.2.1 The vector Bingham Langevin distribution . . . 118
6.2.2 The vector complex vector generalized Bingham Langevin distribution . . 118
6.2.3 The matrix complex generalized Bingham Langevin distribution . . . 119
6.3 Notations and derivation of the block coordinate descent algorithm in the context of radio interferometers calibration . . . 120
6.4 SB-formula for misspeci ed models: Proofs and relationship to previous results . 121 6.4.1 Some considerations on the expectation of (4.15) and (4.16) . . . 121
6.4.2 Proof of the SB formulas for the Scenario 1 . . . 122
6.4.3 Proof of the SB formulas for the Scenario 2 . . . 123
6.4.4 The SB formula under correctly speci ed CES models . . . 125
6.4.5 The SB formulas for scatter matrix estimation under misspeci cation of the density generator . . . 126
6.4.6 The SB formulas for misspeci ed Gaussian models . . . 127
6.4.6.1 The generalized Slepian formulas . . . 127
6.4.6.2 The generalized Bangs formulas . . . 127 v
6.5.1 General case . . . 128
6.5.1.1 Block V11 . . . 128
6.5.1.2 Blocks V22and C22 . . . 129
6.5.1.3 Block V12 . . . 130
6.5.2 Case of Gaussian and Poisson distributions . . . 131
6.5.2.1 Gaussian case . . . 131
6.5.2.2 Poisson case . . . 132
Part I
Curriculum Vitæ
0.1 Contact information
Name: EL KORSO, Mohammed Nabil Birthday: 19/05/1983, Oran, Algeria
Status: Assistant Professor at IUT de Ville d'Avray-Paris Nanterre University, LEME EA4416 (laboratoire énergétique mécanique électromagnétisme).
Webpage: https://sites.google.com/site/nabkorso/ Address: 50 Rue de Sèvres, 92410 Ville-d'Avray, Tel.: +33140974139
E-mail: [email protected]
0.2 Education
• 2008-2011: Ph.D. in Electrical Engineering (Signal Processing)
Location: Paris-Saclay University/L2S (laboratory of signals and systems), Gif sur Yvette, France
Subject: Performance analysis in array signal processing. Lower bounds on the mean squared error and statistical resolution limit
Advisors: DR. Sylvie Marcos, Dr. Rémy Boyer and Dr. Alexandre Renaux
Committee: Prof. Jean-Yves Tourneret (reviewer), Prof. Jean-Marc Brossier (reviewer), Prof. Pascal Larzabal, DR. Gérard Favier, Prof. Karim Abed Meraim.
• 2007-2008: M.S. in Automatic, Signal and Image Processing (ATSI) Location: Paris-Saclay University/Supélec, France
Grade: Summa Cum Laude
Topic: Statistical signal processing and its application to array signal processing. • 2004-2007: Engineering degree in Electrical Engineering
Location: National Polytechnic School, Algiers, Algeria Grade: Summa Cum Laude
Topic: Mobile communications, automatics, computer science, signal processing. • 2001-2004: Preparation to Engineering School
Location: National School Preparatory to Engineering Studies, Algiers, Algeria Grade: Summa Cum Laude
Topic: Mathematics and Physics.
0.3 Professional background
• 2013-present : Assistant Professor (Maître de conférences) Location : Paris Nanterre University, France
Teaching : IUT de Ville d'Avray, Electrical Engineering department (GEII)
Research : LEME EA4416 laboratory (Laboratoire Energétique Mécanique Electromag-nétisme).
0.4. TEACHNING ACTIVITY 3
• 2012-2013: Temporary assistant professor & research assistant (Full time ATER) Location : École Normale Supérieure de Paris-Saclay, France
Teaching : École Normale Supérieure de Paris-Saclay, Electrical Engineering department Research : SATIE laboratory (laboratoire des systèmes et applications des technologies de l'information et de l'énergie)
Topic: Estimation performance for the Bayesian hierarchical linear model • 2011-2012: Post-doc position at the Communication Systems Group
Location: Technische Universitat Darmstadt, Germany.
Topic: Robust array signal processing and performance analysis. • 2008: Research Trainee
Location: Paris-Saclay University/Supélec, France Advisors: DR. Sylvie Marcos and Dr. Rèmy Boyer Topic: Passive source localization.
• 2007: Final Master Project
Location: Institut Fresnel, Ecole Centrale Marseille, France Advisors: Prof. Adel Belouchrani and Prof. Salah Bourennane Topic: Parametric estimation of the instantaneous frequency.
0.4 Teachning activity
• 2013-present: IUT de Ville d'Avray/Paris Nanterre University, France Position: Assistant Professor
Lectures: Analog electronics, C programming, VHDL programming, Micro-controllers pro-gramming and Signal processing
Level: Mostly, DUT rst and second years (B.Sc level) and Master of science M1
Year Nb. of hours
2013-2014 167h (due to the primo-entrant décharge)
2014-2015 286h
2015-2016 342h
2016-2017 304h
2017-2018 240h
2018-2019 (expected) 96h (due to the CRCT )
Example: 2015-2016 Level Nb. of hours
Etude et réalisation en système numérique d'information GEII-1 28h
Informatique C GEII-1 50h
Système numérique d'information GEII-1 91h
Electronique numérique GEII-2 30h
Statistiques GEII-2 32h
Outils logiciel 3 GEII-2 34h
Traitement du signal M1 24h
Traitement du signal avancé M1 33h
• 2012-2013: École Normale Supérieure de Paris-Saclay, France Position: Temporary assistant professor (Full time ATER) Lectures: Mathematics, signal processing and automatic control Level: Licence, 192hrs/year.
• 2008-2011: IUT de Cachan, France
Position: Temporary assistant teacher (Moniteur)
Lectures: Analog electronics and Micro-controllers programming Level: DUT rst year, 64hrs/year.
0.5 Research activity
0.5.1 Scienti c interests
• Detection/estimation theory
• Robust/distributed/adaptive signal processing • Asymptotic/non-asymptotic performance analysis
0.5.2 Applications
• Direction of arrivals estimation, source localization and spectral analysis • Radio astronomy calibration
• MIMO Radar/SAR/STAP
• High resolution sensor array processing • Change point detection/localization
0.6 Publication record
My publications can be downloaded at https://sites.google.com/site/nabkorso/. The underlined names correspond to Ph.D. students or post-docs that I co-supervised/under my supervision. The underlined and italic names correspond to Ph.D. students that I co-supervised momentarily (i.e., without an o cial percentage of supervision).
0.6.1 Book chapters
[L2] V. Ollier, M. N. El Korso, et al. French SKA White Book - The French community towards the Square Kilometre Array, Published by the SKA-France Coordination in collaboration with AS SKA-LOFAR, Chapter 4 "Technological developments", 2017.
[L1] M. Haardt, M. Pesavento, F. Roemer, and M. N. El Korso, "Subspace Methods and Exploitation of Special Array Structures", Electronic Reference in Signal Processing: Array and Statistical Signal Processing (M. Viberg, ed.), vol. 3, pp. 651-717, Academic Press Library in Signal Processing, Elsevier Ltd., 2014, Chapter 2.15.
0.6. PUBLICATION RECORD 5
0.6.2 International journals
[SJ6] H. Gazzah, J.-P. Delmas and M. N. El Korso, "Impact of the power pro le on the localization of near- eld sources and array optimization", submitted to Elsevier Signal Processing Journal.
[SJ5] L. Bacharach, M. N. El Korso, A. Renaux and J-Y. Tourneret, "A Hybrid Lower Bound for Parameter Estimation of Signals Comprising Multiple Change-Points", submitted to IEEE Transactions on Signal Processing.
[SJ4] B. Mériaux, C. Ren, M. N. El Korso, A. Breloy and P. Forster, "On the E ciency of Structured Covariance Matrix Estimation for CES Distribution", submitted to IEEE Transac-tions on Signal Processing.
[SJ3] X. Zhang, M. N. El Korso and M. Pesavento, "Iterative Marginal Maximum Likelihood DOD and DOA Estimation for MIMO Radar in the Presence of SIRP Clutter", submitted to Elsevier Signal Processing Journal.
[SJ2] R. Ben Abdallah, A. Breloy, M. N. El Korso and D. Lautru, "Bayesian robust subspace estimation in presence of compound Gaussian sources", submitted to IEEE Transactions on Signal Processing.
[SJ1] V. Ollier, M. N. El Korso, R. Boyer and P. Larzabal, "Robust distributed calibration of radio interferometers with direction dependent distortions", submitted to Elsevier Signal Pro-cessing Journal.
[J19] T. Boukaba, M. N. El Korso, A. M. Zoubir and D. Berkani, "Bootstrap Based Sequential Detection in Non-Gaussian Correlated Clutter", Progress In Electromagnetics Research C, Vol. 81, 125-140, 2018.
[J18] M. Brossard, M. N. El Korso, M. Pesavento, R. Boyer, P. Larzabal and S. Wijnholds, "Parallel Multi-Wavelength Calibration Algorithm for Radio Astronomical Arrays", Elsevier Signal Processing Journal, Volume 145, April 2018, Pages 258-271.
[J17] A. Mennad, S. Fortunati, M. N. El Korso, A. Younsi, A. M. Zoubir and A. Renaux, "Slepian-Bangs-type formulas and the related Misspeci ed Cramer-Rao Bounds for Complex Elliptically Symmetric distributions", Elsevier Signal Processing Journal, Volume 142, January 2018, Pages 320-329
[J16] V. Ollier, M. N. El Korso, R. Boyer, P. Larzabal and M. Pesavento, "Robust Cali-bration of Radio Interferometers in Non-Gaussian Environment", IEEE Transactions on Signal Processing, Volume: 65, Issue: 21, Nov. 2017, pp. 5649-5660
[J15] E. Chaumette, A. Renaux, and M. N. El Korso, "A class of Weiss-Weinstein bounds and its relationship with the Bobrovsky-Mayer-Wolf-Zakai bounds", IEEE Transactions on In-formation Theory, Volume: 63, Issue: 4, Apr. 2017, pp. 2226-2240
[J14] L. Bacharach, A. Renaux, M. N. El Korso, and E. Chaumette, "Weiss-Weinstein bound on multiple change-points estimation", IEEE Transactions on Signal Processing, Volume: 65, Issue: 10, May 2017, pp. 2686-2700
[J13] X. Zhang, M. N. El Korso and M. Pesavento, "MIMO radar target localization and performance evaluation under SIRP clutter", Signal Processing Journal, Elsevier, Volume 130, January 2017, Pages 217-232.
[J12] A. Mennad, A. Younsi, M. N. El Korso, and A. M. Zoubir, "Adaptive Detection of Range-Spread Target in Compound-Gaussian Clutter Without Secondary Data", Digital Signal Processing, Elsevier, Volume 60, January 2017, Pages 90-98.
[J11] J.-P. Delmas, M. N. El Korso, H. Gazzah and M. Castella, CRB analysis of planar antenna array for optimizing near- eld source localization, Signal Processing Journal, Elsevier, Volume 127, Octobre 2016, Pages 117-134.
[J10] M. N. El Korso, R. Boyer, P. Larzabal and B.-H. Fleury, "Estimation Performance for the Bayesian Hierarchical Linear Model", IEEE Signal Processing Letters, Volume 23, April 2016, Pages 488-492.
[J9] T. Bao, M. N. El Korso and H. H. Ouslimani, "Cramér-Rao Bound and Statistical Resolu-tion Limit InvestigaResolu-tion for Near- eld Source LocalizaResolu-tion", Digital Signal Processing, Elsevier, Volume 48, January 2016, pp. 137-147.
[J8] C. Ren, M. N. El Korso, J. Galy, E. Chaumette, P. Larzabal and A. Renaux, "On the Accuracy and Resolvability of Vector Parameter Estimates", IEEE Transactions on Signal Processing, Volume: 62, Issue: 14, Jul. 2014, pp. 3682-3694.
[J7] M. N. El Korso, A. Renaux, R. Boyer and S. Marcos, "Deterministic Performance Bounds on the Mean Square Error for Near Field Source Localization", IEEE Transactions on Signal Processing, Volume: 61, Issue: 4, Feb. 2013, pp. 871-877.
[J6] M. N. El Korso, R. Boyer, A. Renaux and S. Marcos, "Statistical resolution limit for source localization with clutter interference in a MIMO radar context", IEEE Transactions on Signal Processing, Volume: 60, Issue: 2, February 2012, Page s 987-992.
[J5] M. N. El Korso, R. Boyer, A. Renaux and S. Marcos, On the Asymptotic Resolvability Of Two Point Sources in Known Subspace Interference Using a GLRT-Based Framework", Elsevier Signal Processing, Volume: 92, Issue: 10, Oct. 2012, pp. 2471-248.
[J4] M. N. El Korso, R. Boyer, A. Renaux and S. Marcos, "Statistical Analysis of Achievable Resolution Limit in the Near Field Source Localization Context", Elsevier Signal Processing, Volume 92, Issue 2, February 2012, Pages 547-552.
[J3] M. N. El Korso, R. Boyer, A. Renaux and S. Marcos, "Statistical resolution limit for the multidimensional harmonic retrieval model: Hypothesis test and Cramér-Rao bound ap-proaches", EURASIP Journal on Advances in Signal Processing, special issue on Advances in Angle-of-Arrival and Multidimensional Signal Processing for Localization and Communications, Jun. 2011, pp. 1-14.
[J2] M. N. El Korso, R. Boyer, A. Renaux and S. Marcos, "Statistical resolution limit of the uniform linear cocentered orthogonal loop and dipole array IEEE Transactions on Signal Processing, Volume: 59, Issue: 1, Jan. 2011, pp. 425-431.
[J1] M. N. El Korso, R. Boyer, A. Renaux and S. Marcos, "Conditional and unconditional Cramer-Rao bounds for near- eld source localization", IEEE Transactions on Signal Processing, Volume: 58, Issue: 5, May 2010, pp. 2901-2907.
0.6.3 International conferences
[ICS4] R. Ben Abdellah, A. Breloy, M. N. El Korso and D. Lautru, "Bayesian Low-Rank Sig-nal Subspace Estimation for Compound Gaussian Sources", submitted to EUSIPCO'18, Rome, Italy.
[ICS3] A. Breloy, M. N. El Korso, A. Panahi and H. Krim, "Robust Subspace Clustering for Radar Detection", submitted to EUSIPCO'18, Rome, Italy.
[ICS2] L. Bacharach, A. Renaux and M. N. El Korso, "Prior In uence on Weiss-Weinstein Bounds for Multiple Change-Point Estimation", submitted to EUSIPCO'18, Rome, Italy. [ICS1] V. Ollier, M. N. El Korso, A. Ferrari, R. Boyer and P. Larzabal, "Bayesian Calibration Using Dierent Prior Distributions: An Iterative Maximum a Posteriori Approach for Radio Interferometers", submitted to EUSIPCO'18, Rome, Italy.
[IC34] B. Mériaux, C. Ren, M. N. El Korso, A. Breloy and P. Forster, "E cient estimation of scatter matrix with convex structure under T-distribution", accepted ICASSP'18, Calgary, Canada.
0.6. PUBLICATION RECORD 7
[IC33] V. Ollier, M. N. El Korso, A. Ferrari, R. Boyer and P. Larzabal, "Robust calibration of radio interferometers in multi-frequency scenario", accepted ICASSP'18, Calgary, Canada [IC32] B. Mériaux, C. Ren, M. N. El Korso, A. Breloy and P. Forster, "Robust-COMET for Covariance Estimation in Convex Structures: Algorithm and Statistical Properties", in proc. of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Pro-cessing, CAMSAP-2017, curacao dutch antilles.
[IC31] R. Ben Abdallah, A. Breloy, M. N. El Korso, D. Lautru and H. Ouslimani, "Minimum Mean Square Distance Estimation of Subspaces in presence of Gaussian sources with application to STAP detection", 7th International Conference on New Computational Methods for Inverse Problems, Paris, 2017.
[IC30] T. Bao, A. Breloy, M. N. El Korso, K. Abed-Meraim and H. H. Ouslimani, "Per-formance analysis of direction-of-arrival and polarization estimation using a non-uniform linear COLD array",in Proc. of Detection, Architecture and Technology Workshop DAT-2017, Algiers, Algeria.
[IC29] L. Bacharach, M. N. El Korso, A. Renaux and J.-Y. Tourneret, "A Bayesian Lower Bound for Parameter Estimation of Poisson Data Including Multiple Changes", in Proc. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2017), New Or-leans, USA, March 2017.
[IC28] M. Brossard, M. N. El Korso, M. Pesavento, R. Boyer and P. Larzabal, "Calibration of Radio Interferometers Using a Sparse DOA Estimation Framework", (invited) in Proc. of EUSIPCO 2016, Budapest, Hungary.
[IC27] V. Ollier, M. N. El Korso, R. Boyer, P. Larzabal and M. Pesavento, "Relaxed con-centrated MLE for robust calibration of radio interferometers", (invited) in Proc. of EUSIPCO 2016, Budapest, Hungary.
[IC26] V. Ollier, R. Boyer, M. N. El Korso and P. Larzabal, "Bayesian Lower Bounds for Dense or Sparse (Outlier) Noise in the RMT Framework", (invited) in Proc. of IEEE International Sensor Array and Multichannel Signal Processing Workshop, SAM-2016, Rio, Brazil.
[IC25] L. Bacharach, M. N. El Korso and A. Renaux, "Weiss-Weinstein bound for an abrupt unknown frequency change", (invited) in Proc. of IEEE Workshop on Statistical Signal Process-ing, SSP-16, Palma de Mallorca, June 26-29, 2016.
[IC24] V. Ollier, M. N. El Korso, R. Boyer, P. Larzabal and M. Pesavento, "Joint ML cal-ibration and DOA estimation with separated arrays", in Proc. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2016), Shaingai, China, March 2016. [IC23] X. Zhang, M. N. El Korso and M. Pesavento, "Maximum likelihood and maximum a posteriori direction-of-arrival estimation in the presence of SIRP noise", in Proc. IEEE Interna-tional Conference on Acoustics, Speech and Signal Processing (ICASSP 2016), Shaingai, China, March 2016.
[IC22] P. Zarka et al., "NenUFAR: Instrument description and science case", IEEE International Conference on Antenna Theory and Techniques (ICATT), Kharkiv, Ukraine, 2015.
[IC21] L. Bacharach, A. Renaux, M. N. El Korso, and E. Chaumette, "Weiss-Weinstein Bound for Change-Point Estimation", in proc. of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP-2015, Cancun, Mexico.
[IC20] A. Rubiano, J. L. Ramirez, M. N. El Korso, L. Gallimard, N. Jouandeau and O. Polit, "Elbow Flexion And Extension Identi cation Using Surface Electromyography Signals, in Proc. EUSIPCO 2015, Nice, France, August 2015.
[IC19] C. Ren, M. N. El Korso, J. Galy, E. Chaumette, P. Larzabal and A. Renaux, "Perfor-mance bounds under misspeci cation model for MIMO Radar application, in Proc. EUSIPCO 2015, Nice, France, August 2015.
[IC18] A. Rubiano, J. L. Ramirez, M. N. El Korso, L. Gallimard, N. Jouandeau and O. Polit, "Best Feature Selection and Classication For Elbow Flexion And Extension Movements", The International Workshop on New Computational Methods for Inverse Problems, IOP publishing in the series Journal of Physics : Conference Series 2015, Cachan, France.
[IC17] J. L. Ramirez, A. Rubiano, N. Jouandeau, M. N. El Korso, L. Gallimard and O. Polit, "Hybrid kinematic model applied to the under-actuated robotic hand prosthesis ProMain-I and experimental evaluation", in Proc. ICORR, Singapore, August 2015.
[IC16] M. N. El Korso, A. Renaux and P. Forster, "CRLB under K-distributed observation with parameterized mean, in Proc. of IEEE International Sensor Array and Multichannel Signal Processing Workshop, SAM-2014, A Coruna, Spain.
[IC15] X. Zhang, M. N. El Korso, and M. Pesavento, "MIMO Radar Performance Analysis under K-distributed Clutter, in Proc. of IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP-2014, Florence, Italy.
[IC14] M. N. El Korso, R. Boyer and S. Marcos, "A root- nding technique for direction of arrival estimation", in Proc. of Detection, Architecture and Technology Workshop DAT-2014, Algiers, Algeria.
[IC13] R. Boyer, M. N. El Korso, A. Renaux and S. Marcos, "Coexistence of near- eld and far- eld sources : The angular resolution limit", 3rd International Workshop on New Computational Methods for Inverse Problems, 2013, Cachan, France.
[IC12] X. Zhang, M. N. El Korso, and M. Pesavento, "Angular resolution limit for determin-istic correlated sources, in Proc. of IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP-2013, Montreal, Canada.
[IC11] M. N. El Korso, F. Pascal and M. Pesavento, "On the resolvability of closely spaced targets using a MIMO radar", invited paper, IEEE Asilomar Conference on Signals, Systems & Computers, Paci c Grove, California, 2012.
[IC10] X. Zhang, M. N. El Korso, and M. Pesavento, "Statistical Resolution Limit for Two Closely Spaced Stochastic Far Field Sources", the European Signal Processing conference (EU-SIPCO 2012), Bucharest, Romania, August 2012.
[IC9] M. N. El Korso and M. Pesavento, "Performance analysis for near eld source localiza-tion", in Proc. of IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM-12, Hoboken, NJ.
[IC8] M. N. El Korso, R. Boyer, A. Renaux and S. Marcos, "Statistical Resolution Limit: Application to Passive Polarized Source Localization", in Proc. of Detection, Architecture and Technology Workshop DAT-2011, Algiers, Algeria.
[IC7] M. N. El Korso, R. Boyer, A. Renaux and S. Marcos, "Statistical resolution limit for source localization in a MIMO context", in Proc. of IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP-11, Prague, Czech Republic.
[IC6] D. T. Vu, M. N. El Korso, R. Boyer, A. Renaux and S. Marcos, "Angular Resolution Limit for Vector Sensor Arrays : Detection and Information Theory Approaches", in Proc. of IEEE Workshop on Statistical Signal Processing, SSP-11, Nice, France.
[IC5] M. N. El Korso, R. Boyer, A. Renaux and S. Marcos, "A GLRT-based framework for the multidimensional statistical resolution limit", in Proc. of IEEE Workshop on Statistical Signal Processing, SSP-11, Nice, France.
[IC4] M. N. El Korso, B. Boyer and S. Marcos, "Sequential Source Localization Using the Pro-jected Companion Matrix Approach", in Proc. of IEEE Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP-09, Aruba, Dutch Antilles.
[IC3] M. N. El Korso, R. Boyer, A. Renaux and S. Marcos, "Statistical resolution limits for multiple parameters of interest and for multiple signals", in Proc. of IEEE International
0.7. PH.D. AND POSTDOCTORAL STUDENTS ADVISING 9
Conference on Acoustics, Speech, and Signal Processing, ICASSP-10, Dallas, TX, USA.
[IC2] M. N. El Korso, G. Bouleux, B. Boyer and S. Marcos, "Sequential estimation of the range and the bearing using the zero-forcing MUSIC approach", in Proc. of the 17th European Signal Processing Conference, EUSIPCO-09, Glasgow, Scotland.
[IC1] M. N. El Korso, R. Boyer, A. Renaux and S. Marcos, "Non-matrix closed form ex-pressions of the Cramér-Rao bounds for near- eld localization parameters", in Proc. of IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP-09, Taipei, Tai-wan.
0.6.4 National conferences
[NC11] A. Taylor, A. Breloy, M. N. El Korso, "Détection d'anomalie de composantes princi-pales pour des cibles mobiles étendues en SAR", GRETSI 2017.
[NC10] V. Ollier, M. N. El Korso, R. Boyer, P. Larzabal and M. Pesavento, "Algorithme de calibration robuste dans un contexte de radio interférométrie", GRETSI 2017.
[NC9] R. Ben Abdallah, A. Breloy, M. N. El Korso, D. Lautru and H. Ouslimani, "Estima-tion de sous-espaces en présence de sources gaussiennes avec applica"Estima-tion à la détec"Estima-tion STAP", GRETSI 2017.
[NC8] L. Bacharach, G. Bibiche, A. Renaux and M. N. El Korso, "Bornes bayésiennes pour la localisation d'un point de rupture : Application à des processus exponentiels", GRETSI 2017. [NC7] V. Ollier, R. Boyer, M. N. El Korso and P. Larzabal, "Borne Bayésienne pour les systèmes large-échelle : cas d'un bruit à queue lourde", GRETSI 2017.
[NC6] C. Ren, M. N. El Korso, J. Galy, E. Chaumette, P. Larzabal and A. Renaux, "Une nou-velle approche de résolution limite dans le cadre d'estimation paramétrique multidimensionnelle, in Proc. GRETSI 2015, Lyon, France, September 2015.
[NC5] M. N. El Korso, P. Forster, F. Pascal and P. Larzabal, "Résolution limite dans un contexte de localisation active de sources", GRETSI 2013, Brest, France.
[NC4] D. T. Vu, M. N. El Korso, R. Boyer, A. Renaux and S. Marcos, "Résolution limite angulaire Appoches basées sur la théorie de l'information et sur la théorie de la détection, GRETSI-11, Bordeaux, France.
[NC3] M. N. El Korso, A. Renaux, R. Boyer and S. Marcos, "Bornes inférieures de l'erreur quadratique moyenne pour la localisation de sources en champ proche", GRETSI-11, Bordeaux, France.
[NC2] M. N. El Korso, G. Bouleux, B. Boyer and S. Marcos, " Estimation séquentielle des paramètres de localisation en champ proche à l'aide de l'approche Zero-Forcing", in Proc. of Colloque GRETSI-09, Dijon, France.
[NC1] M. N. El Korso, R. Boyer, A. Renaux and S. Marcos, "Expressions non-matricielles des bornes de Cramér-Rao pour la localisation de source en champ proche", in Proc. of Colloque GRETSI-09, Dijon, France.
0.7 Ph.D. and postdoctoral students advising
0.7.1 Ph.D. students
• Xin Zhang Technische Universitat Darmstadt, Germany, Sep. 2012- Aug. 2016
Subject: MIMO radar DOD/DOA estimation and performance analysis in the presence of SIRP clutter
Publications: [J13,JS3,IC21,IC13,IC10,IC8] Details: 50% (with Prof. M. Pesavento 50%)
Remark: The Ph.D. thesis of X. Zhang was done in Germany, where Ph.D. thesis duration is larger than 36 months unlike in our French education system.
Actual position: R&D ADAS Engineer at Launch Tech Co., Ltd, Shenzhen, China. • Astrid Rubiano Fonseca Paris Nanterre University-LEME, France, Sept. 2013- Dec. 2016
Subject: Smart control of a soft robotic hand prosthesis Publications: [IC18,IC16,IC15]
Details: 30% (with Prof. O. Polit 35% and Prof. L. Gallimard 35%)
Remark: The Ph.D. thesis of A. R. Fonseca was mainly focused on mechanical issues with a practical goals (design of a soft robotic hand prosthesis which can be viewed in the follow-ing youtube link https://www.youtube.com/watch?v=ypBFVAvRsZE&feature=youtu.be). My main objective was to supervise A. R. Fonseca in the study of best feature selection strategy and a robust classi cation for elbow exion and extension movements [IC20,CI18]. It is worth mentioning that A. R. Fonseca has a lot of publications in mechanical Journal for which I decided not to be an co-author since my contribution was modest in those papers.
Actual position: Assistant professor, Universidad Militar Nueva Granada, Colombia. • Virginie Ollier ENS Paris-Saclay-SATIE/L2S, France, Sept. 2015-(expected defense) Jul.
2018
Subject: Contribution to robust calibration of the next generation of radio interferometers Publications: [J16,JS1,IC33,IC25,IC24,IC22,NC8,NC5,ICS1]
Details: 50% (with Prof. P. Larzabal 20% and Dr. R. Boyer 30%).
• Lucien Bacharach Paris-Saclay University-L2S, France, Oct. 2015-(expected defense) Sept. 2018
Subject: Contribution to lower bounds on the MSE for change-point estimation Publications: [JS5,J14,IC27,IC23,IC19,ICS2,NC6].
Details: 50% (with Dr. A. Renaux 50%).
• Rayen BenAbdellah Paris Nanterre University-LEME, France, Sept. 2016-(expected de-fense) Sept. 2019
Subject: Adaptive scheme for urban and forest target detection using synthetic aperture radar
Publications: [IC31,NC9,ICS4,SJ2].
Details: 40% (with Prof. D. Lautru 20% and Dr. A. Breloy 40%).
• Bruno Mériaux CentraleSupélec-SONDRA, France, Oct. 2017-(expected defense) Sept. 2020
Subject: Contribution to robust adaptive signal processing in MIMO systems without secondary data
Publications: [IC30,IC34,SJ4]
0.8. COMMUNITY LIFE AND AWARDS 11
0.7.2 Post-doc
• Tao Bao Paris Nanterre University-LEME, France, Oct. 2013- Sep. 2014
Subject: Performances investigation in the context of near- eld source localization Details: 100%
Publications: [J9,CI30]
Actual position: Assistant professor at the Northwestern Polytechnical University, China.
0.7.3 Research trainees
• Xin Zhang Technische Universitat Darmstadt, Germany, Sept. 2011-May 2012 Subject: MIMO radar performance analysis under K-distributed clutter Publication: [IC8]
Details: 50% (with Prof. M. Pesavento 50%).
• Martin Brossard Technische Universitat Darmstadt, Germany, Sept. 2015-Aug. 2016 Subject: Distributed multi-frequency calibration for sensor array radio interferometers Publications: [IC28,J18]
Details: 50% (with Prof. M. Pesavento 50%).
• Virginie Ollier ENS Paris-Saclay-SATIE, France, Apr.-Sept. 2015
Subject: Joint maximum likelihood calibration and DOA estimation with separated arrays. Publication: [IC22].
Details: 100%.
Remark: Virginie's ICASSP paper IEEE ICASSP was selected as the one of the three highest review scores in IEEE ICASSP SAM. Furthermore, Virginie obtained the intership award 2015 from école centrale de Marseille.
• Lucien Bacharach Paris-Saclay University/L2S, France, Apr.-Sept. 2015 Subject: Weiss-Weinstein bound for an abrupt unknown frequency change. Publication: [IC19].
Details: 50% (with Dr. A. Renaux 50%).
• Bruno Mériaux CentraleSupélec-SONDRA, France, Apr.-Sept. 2017 Subject: Robust covariance matrix estimation in convex structures Publications: [IC30]
Details: 25% (with Prof. P. Forster 10%, Dr. C. Ren 35% and Dr. A. Breloy 30%).
0.8 Community life and awards
• The prize/bonus of the national French excellence in scienti c research (PEDR) since 2017.
• 6 months of CRCT (Congé pour Recherches ou Conversions Thématiques) from January 2019 to June 2019.
• Award of the allocation ministérielle MSER (from the French ministry of education and research) as Ph.D. student (2008-2011).
• Expert of the French National Research Agency (ANR 2017 and ANR 2018). • Member of the board "Special Area Team - Signal Processing for Multisensor Systems
(SAT-SPMuS)" EURASIP, since Jan. 2018.
• Member of the board "Special Area Team - Theoretical and Methodological Trends in Signal Processing (SAT-TMTSP)" EURASIP, since Aug. 2015.
• A liated member of the IEEE Big Data SIG (Special Interest Group) since Jan. 2016. • A liated member of the Sensor Array and Multichannel Technical Committee in the IEEE
Signal Processing Society (IEEE SPS SAM TC), since Mars 2013.
• Outstanding reviewer (top 10th percentile of reviewers) : Elsevier - Signal Processing 2016 & Elsevier - Digital Signal Processing 2016
• Tutorial and plenary talks
Tutorial at the international conference DAT-2017, Algeria, Fev. 2017, entitled: "Lower bounds on the MSE : From Theory to Practice".
Plenary talk in the RADAR-EMP 2015 conference, at Military Polytechnic School, Algiers, May, 7th 2015, entitled: "MIMO Radar: Performance Analysis Investiga-tion".
Invited presentation at the rst SKA-France meeting for signal processsing, Sept., 8th, 2016 at ENS Paris-Saclay, France. SKA-France (Square Kilometre Array) is a national coordination of industrial, technical and scienti c activities preparatory to the SKA project in France, set in place jointly by the Institute for Earth Sci-ences and Astronomy (CNRS/INSU), Paris Observatory, Côte d'Azur Observatory, Bordeaux University and Orléans University. (Slides are available at https://ska-france.oca.eu/fr/evenements/atelier-scienti ques/14-ateliers-scienti ques).
• Scienti c committee/technical program committee
The 5th International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing (CoSeRa'18), University of Siegen, Northrhine Westfalia , Germany, 10-13 September 2018.
The 26th European Signal Processing Conference (EUSIPCO'18), Rome, Italy, 3 -7 September 2018.
The 25th European Signal Processing Conference (EUSIPCO'17), Kos, Greece, 28 August - 2 September 2017.
The 7th international conference Detection Systems: Architectures and Technologies DAT'17, Algiers, Algeria, Fev. 2017.
The Second international conference on image and signal processing, January 02-03, 2017, Zurich, Switzerland
0.8. COMMUNITY LIFE AND AWARDS 13
The 24th European Signal Processing Conference (EUSIPCO'16), Budapest, Hun-gary, 29 August - 02 September 2016.
The 4th International Workshop on Compressed Sensing Theory and its Applica-tions to Radar, Sonar and Remote Sensing (CoSeRa'16), Aachen, Germany, 19-22 September 2016.
The 2nd Conference on Computing Systems and Applications 13-14 December 2016, Algiers, Algeria.
The IEACon'16, 2016 IEEE Industrial Electronics and Applications Conference, Kota Kinabalu, Malaysia, November 20-22, 2016.
The International Conference on Single Processing & Data Mining (ICSPDM'15), Roma, Italy, 05-07, November 2015.
The 3rd International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing (CoSeRa'15), Pisa, Italy, 16-19 Juin 2015. The 15th IEEE International Symposium on Signal Processing and Information
Tech-nology 2015 (IEEE ISSPIT'15), December 2015, Abu Dhabi, UAE.
The International conference on research in signal processing and communication (SPC'13) Oct 31, 2015, Trivandrum, India.
The 6th international conference Detection Systems: Architectures and Technologies DAT'14, Algiers, Algeria, Fev. 2014.
• (Co)-Organizer of the following special sessions
EUSIPCO 2018 (European Signal Processing Conference) Roma, Italy (Sept. 2018). Entitled: "Emerging Data Structure Paradigms for Subspace Estimation". Co-organization with Prof. H. Krim and Dr. A. Breloy.
GRETSI 2017 (Groupe d'Etudes du Traitement du Signal et des Images) Juan-Les-Pins, France (Sept. 2017). Entitled: "Traitement d'antenne". Chair of the an ordi-nary session.
EUSIPCO 2016 (European Signal Processing Conference) Budapest, Hungry (Sept. 2016). Entitled: "Trends and new challenges in calibration of phased array in radio-astronomy". Co-organization with Prof. P. Larzabal and Dr. R. Boyer.
EUSIPCO 2016 (European Signal Processing Conference) Budapest, Hungry (Sept. 2016). Entitled: "Trends in robust statistics: Theory and applications in signal and image processing". Co-organization with Prof. A. Zoubir and Prof. G. Ginolhac. IEEE SAM-2014 (Sensor Array and Multichannel Conference) Coruna, Spain (Juin
2014). Entitled: "Dealing with Non-Standard Conditions in Array Processing and Spectral Analysis". Co-organization with Prof. P. Forster and Dr. A. Renaux. IEEE Asilomar-2012, Monterey, California (Nov. 2012). Entitled: "Threshold limits
in array processing : Performance analysis and methods". • Co-organization of scienti c thematic days GDR-ISIS
Entitled: "Array processing: non Gaussian, non circular and non stationary signals", Dec. 2016 at Telecom ParisTech, France (with Prof. J.-P. Delmas and Prof. P. Chevalier).
Entitled: "Robustness and large dimension in array processing", Dec. 2015 at Telecom ParisTech, France (with Prof. G. Ginolhac and Dr. A. Renaux).
• Guest Stays
Germany : invitation from Prof. Marius Pesavento, TU-Darmstadt Germany, 28/10/2013-04/11/2013, 24/02/2015-03/03/2015 and 19/02/2016-27/02/2016. Main topic: Par-allel multi-wavelength calibration algorithm for radio astronomical arrays [J18,IC28]. USA : invitation from Prof. Hamid Krim, NC State University Raleigh, 18/10/2016-30/10/2016. Main topic: Robust subspace clustering for radar detection [ICS3, and a paper is under redaction]. We also co-organized a special session at EUSIPCO'18 entitled: Emerging Data Structure Paradigms for Subspace Estimation.
0.9 Projects
• On-going
ON FIRE project: calibratiON of Future radio InteRferometErs Role: Principal investigator
Type: GDR-ISIS young researcher (Groupe de recherche Information, Signal, Images et ViSion)
Details: Oct. 2016-Sept. 2018, 7.000 euros.
MARGARITA project: Modern Adaptive Radar: Great Advances in Robust and In-ference Techniques and Application
Role: Local investigator and coordinator of the LEME laboratory
Type: ANR-ASTRID (the French National Research Agency for Speci c Support for Innovation and Defense Research)
Details: Jan. 2018-Dec. 2020, 78.352 euros.
MAGELLAN project: MAchine learninG methods for the vEry Large Arrays in radio astroNomy,
Role: Scienti c o cer of the work-package 2.2
Type: ANR (the French National Research Agency). WebPage: https://magellan.oca.eu/magellan/index.html Details: Oct. 2015-Sept. 2018, 87.000 euros.
• Past
ANACONDA project: AdvaNced parAmetric methods with application to array Cali-bratiON in raDio-Astronomy
Role: Participant
Type: Paris-Saclay I-Code Grant
Details: Jan. 2014-Dec. 2016, 12.000 euros (+7000 euros as an complement)
0.10. EDUCATIONAL AND ACADEMIC RESPONSIBILITIES 15
ProMain project: Development and smart control of a soft robotic hand prosthesis Role: Participant and responsible of the signal processing issues
Type: Paris Lumiére project (Paris Nanterre University and Paris 8 University) Details: Jan. 2014-Dec. 2016, 33.000 euros.
MASTODONS-Display: Distributed processing for very large arrays in radioastron-omy
Role: Participant
Type: MI CNRS : Mission pour l'Interdisciplinarité du CNRS
Details: 2013-2014, 30.000 euros, link https://www-n.oca.eu/aferrari/display/wiki/. NEWCOM]: Network of Excellence in Wireless COMmunications
Role: Participant (work-package 1.1: Performance limits of wireless communications) Type: NEWCOM] (FP7-ICT-318306)
Details: Nov. 2012-Dec. 2015
0.10 Educational and academic responsibilities
• Elected member of the CCD (Comité Consultatif des sections CNU 61/63) of Paris Nanterre University since Feb. 2015. Role of the CCD: MCF pro le's redaction, constitu-tion of MCF elecconstitu-tion committees, recruitment of ATER, etc.
• Elected member of the LEME laboratory board (Paris Nanterre University) since Apr. 2014.
• Head of the ES-group (Equipe Signal) since Jan. 2018.
• Invited member of the UFR's board (UFR SITEC of Paris Nanterre University) since Sept. 2014.
• Correspondant GDR-ISIS (information, signal, image, vision) for the LEME-EA4416 laboratory of Paris Nanterre University since Avril 2015.
• In charge of the EESC Master of Science (Responsable M1-EESC ) of Paris Nan-terre University since Sept 2014. EESC stands for Embedded Electronics and Communi-cations Systems (15 lectures and approximatively 22 students/year). My missions are
Students recruitment
Setting up of the timetable (room management, teachers, temporary sta, ...) Management of internship and apprenticeship research
Organization of the defenses and preparation of the jury Budget management (around 75k euros/year)
• Responsible of the students recruitment procedure for IUT GEII Ville d'Avray, ap-proximatively 100 students/year (total number of applicant around 1300/year).
• Member of the improvement council board of the Master of Science EESC (Em-bedded Electronics and Communications Systems) of Paris Nanterre University since Sept 2016.
0.11 Miscellaneous
• Member of 7 Ph.D. defenses committee (Ph.D. defenses of A. Boudjellal Sept. 2015 at Uni-versity of Orléans-France, X. Zhang Aug. 2016 at TU-Darmstadt-Germany, S. Chiarucci Dec. 2016 at University of Florence-Italy and A. Mennad Dec. 2017 at EMP-Algiers A. Bitar Jun. 2018 at SONDRA-France, V. Ollier Jul. 2018 at SATIE-France, L. Bacharcah Sep. 2018 at L2S-France).
• Member of 5 assistant professor/PRAG hiring committee since 2015 (3 for Paris Nanterre University (MCF-61, MCF-63 and PRAG-Maths), 2 for Centrale-Supelec (2 LRU equiva-lent to MCF-61)) .
• Responsible of the work-package integration of calibration techniques developed at ENS Paris-Saclay in the SKA-France (my team is composed of 2 assistant professors, 1 adjoint astronomer, 1 astronomer and 1 Ph.D. student).
• Reviewer for
International Journals: ≈ 7/year (IEEE Transactions on Signal Processing, Elsevier Signal Processing, Signal Processing Letters, IEEE Transactions on Information The-ory, Digital Signal Processing).
Part II
Research statement
Introduction
In this chapter, I present brie y the main contributions that I obtained during the past ve years, i.e., since I held the position of Assistant Professor at IUT de Ville d'Avray. This work concerns the study of some recent and ubiquitous problems related to array signal processing in non standard conditions: mismatched models, presence of outliers, non-Gaussian noise, low signal to noise ratio, low number of samples, etc. Before developing the aforementioned issues, I rst, present in the next subsection a summary of my Ph.D. thesis in order to highlight the dierence and evolution from my Ph.D. subject/work to my current research.
1.1 Summary of my Ph.D. thesis
During my Ph.D. thesis I focused on the study of performance analysis in array signal process-ing by derivprocess-ing lower bounds on the mean square error as well the statistical resolution limit. Speci cally,
• The rst part of my Ph.D. had been dedicated to the calculus of the Cramér-Rao bound (CRB) for dierent data models under Gaussian noise assumption adapted for the asymp-totic area (i.e., for a high signal to noise ratio and/or with in nite number of observations.). More precisely, I derived and analyzed the so-called conditional and unconditional CRBs for a single time-varying near- eld source. In each case, I obtained non-matrix closed-form expressions. This calculus has two advantages: i) due to the fact that one has to inverse the Fisher information matrix (FIM), the computational cost for a large number of snapshots (in the case of the conditional CRB) and/or for a large number of sensors (in the case of the unconditional CRB), of a matrix-based CRB can be high while the proposed approach is low and ii) some useful information had been deduced from the behavior of the bound. In particular, an explicit relationship between the conditional and the unconditional CRBs was provided.
In the same vein, in order to characterize the optimal performances in the non-asymptotic region, I derived the Seidman, the Hammersley-Chapman-Robbins, the McAulay-Hofstetter bounds and the so-called Todros-Tabrikian bound.
• In the second part of my Ph.D., I focused on the concept of the statistical resolution limit (i.e., the minimum distance between two closely spaced signals embedded in an additive noise that allows a correct resolvability/parameter estimation.) More precisely, I de ned
1.2. OVERVIEW OF MY CURRENT RESEARCH ACTIVITY 19
and derived the statistical resolution limit using the CRB and the hypothesis test ap-proaches for the mono-dimensional case, i.e., one parameter of interest per source/signal. Then, I extended this concept to the multidimensional case, i.e., multiple parameters of interest per source/signal. Applications that I considered in this context go from the po-larized sources (sensed using the so-called COLD array; co-centered orthogonal loop and dipole array) to the study of the resolvability for source localization with known clutter interference in a MIMO radar context.
These studies allowed me to obtain interesting results and a comfortable level of accomplishment with 4 IEEE Transactions on Signal Processing Journal, 2 Elsevier Signal Processing Journal and 1 EURASIP JSAP during my Ph.D. thesis [J1-J7]. Nevertheless, I felt the need to move forward and to explore new leads in the area of array signal processing. In this spirit, I decided to work on some recent and ubiquitous problems and emerging subjects related to array signal processing in non standard conditions, namely, mismatched models, presence of outliers, non-Gaussian noise, low signal to noise ratio, low number of samples, etc.
1.2 Overview of my current research activity
Since September 1st, 2013, I am holding an assistant professor position at IUT de Ville d'Avray, and I am a liated to the Laboratoire Energétique Mécanique Electromagnétisme (LEME EA-4416). At the time of my recruitment, I was the sole researcher from CNU-61 in the LEME. While this can be seen as a disadvantage, I took it as an advantage by freely proposing new subjects, external collaborations, partners to my laboratory and by giving a signal processing touch to the LEME. This lead us to recruit, in our laboratory, permanent and a liated researchers as well Ph.D. students in the area of signal processing. Nowadays, I am the head of the Equipe Signal group of the LEME laboratory. Regarding, my research activity, while maintaining a parallel research activity for new problems related to performance analysis (mostly in non-Gaussian scenario), I guided my research interest towards robust and/or scalable parametric estimation procedure with applications in the eld of array signal processing.
First, I summarizes my research activity in the estimation context:
• Since January 2014, I am a member of the ANR MAGELLAN (Machine learning methods for the very large arrays in radio astronomy), and more speci cally, I am in charge of the task 2.2 related to the advanced calibration methods for the next radio interferometers generation. In this context, I am working, with my colleagues from Lagrange-University of Nice and SATIE-ENS Paris-Saclay, in proposing new robust and fast self-calibration algorithms. The radio interferometers context, imposes us to i) work with correlations a.k.a. visibilities (and not directly with the sensed measurements them self as it is usually the case in most array processing applications), ii) solve the unknown antenna gains and phases as well as the unknown atmospheric and ionospheric disturbances, iii) to handle a large number of elements and a large eld of view and nally, iv) robustify the calibration process since radio interferometer observations are often aected by the presence of out-liers which are due to several causes, e.g., weak non-calibrator sources or man made radio frequency interferences. This makes calibration a daunting parameter estimation task for which the existing methods are ineective.
in the Ph.D. thesis of V. Ollier (ANR MAGELLAN Project), the ARPE internship of M. Brossard (Grant from ENS Paris-Sacaly jointly with TU-Darmstadt as host university), the ANACONDA project (an I-code grant) and the ON-FIRE project (GDR-ISIS Jeunes Chercheurs grant for which I am the principal investigator) [L2,JS1,J18,J16,IC33,IC28,IC27]. These projects have been giving me the opportunity to collaborate with many researchers, to cite few; Prof. P. Larzabal, Prof. A. Ferrari, Prof. M. Pesavento, Prof. S. Wijnholds, Dr. R. Boyer, Dr. A. Breloy, Dr. R. Flamary, Dr. F. Iutzeler.
• An other important research track was initiated during my guest visits in Germany with a collaboration with Prof. M. Pesavento from Technische Universitat Darmstadt: designing novel estimation procedure in the context of parameterized mean and variance under com-pound Gaussian (CG) distributed clutter without secondary data (i.e., without assuming the existing of target-free signals). This rises, for example, in the recent high resolution radars for which the central limit theorem is not valid any more and thus the radar clutter cannot be correctly modeled as a Gaussian process. In this context, we recently devised in [JS3,J13,IC23,IC15] the conditional (i.e., the relaxed iterative maximum likelihood es-timator), the joint (i.e., the iterative maximum a posteriori estimator) and the marginal (i.e., the exact iterative maximum likelihood estimator) maximum-likelihood-based itera-tive estimator for parameterized mean (for direction-of-departure and direction-of-arrival estimation in the MIMO radar context as an application). The proposed estimators employ a stepwise numerical concentration approach w.r.t. the objective function related to the conditional, joint and marginal likelihoods of the observation data. Our estimators leads to superior performance w.r.t. the existing state-of-the art. Interconnections, pros and cons of these three proposed estimators are discussed in [JS3,J13].
The aforementioned studies have been considered in the Ph.D. thesis of X. Zhang.
• In the same vein, a fructus discussions with my colleagues of SATIE laboratory (Prof. P. Forster), SONDRA-CentraleSupelec (Dr. C. Ren) and LEME-Paris Nanterre University (Dr. A. Breloy) lead us to consider the problem of estimating covariance matrices in con-vex structure. More precisely, in [JS4,IC34,IC32], we are considering the estimation of structured covariance matrices of a complex elliptically symmetric (CES) distributed ob-servations (the complex elliptically symmetric distributions are a generalization of the CG distribution). We take into account the speci c structure of the covariance matrix (e.g., Toeplitz structure appears in array processing with uniform linear array) and the non gaus-sianity of the data in order to improve substantially the estimation accuracy. Speci cally, we are tackling this problem by proposing a novel estimator, named StructurEd ScAt-ter Matrix Estimator (SESAME), which is based on the EXtended Invariance Principle (EXIP). In addition, we are conducting theoretical analysis on the unbiasedness and the asymptotic e ciency of the proposed SESAME. Finally, we are proposing an iterative pro-cedure of the proposed SESAME, called Iterative-SESAME (I-SESAME), reaching faster the CRB.
This study is currently addressed in the Ph.D. thesis of B. Mériaux.
• One of my current interest is the problem of low dimensional signal subspace estimation in a Bayesian context [SJ2,ICS4,IC31]. This has been initiated with my colleague of Paris Nanterre University, Dr. A. Breloy and the with the help of Pr. D. Lautru, with whom, we obtained a scholarship (allocation ministérielle MSER) for R. Ben Abdellah as Ph.D.
1.2. OVERVIEW OF MY CURRENT RESEARCH ACTIVITY 21
candidate. The essence of this work is to devise new estimators using the so-called minimum mean square distance (MMSD), which minimizes the expected natural distance between the true range space of interest and its estimate taking into account the presence of a subspace basis priori distribution. Such approach has shown its interest for signal subspace estimation for small sample support and/or low signal to noise ratio contexts. Following this framework, we are deriving the MMSD of the signal subspace estimators in the context of CG sources embedded in white Gaussian noise, which is an useful model for various array processing applications. As a byproduct, we also introduce a generalized version of the complex Bingham Langevin distribution in order to model the prior on the subspace unitary basis.
As mentionned above, this work is under consideration in the Ph.D. thesis of R. Ben Abdellah.
• Miscellaneous: For sake of brevity some of my recent works are not detailed in this manuscript. As an example, the reader is referred to [J19,J12] for topics related to au-toregressive based methods for the generalized likelihood ratio test. Speci cally, in [J12], we focus on the adaptive detection of range-spread target in CG clutter without secondary data, whereas in [J19], we set up a sequential detection test in non-Gaussian correlated clutter using bootstrap framework.
This works have been done in collaboration with Prof. A. Zoubir from Technische Univer-sitat Darmstadt, Germany.
Second, as mentioned above, I maintains parallel research activities related to new problems in the context of array processing performance analysis. Nevertheless, it is worth mentioning that these topics dier from my previous Ph.D. works that had been essentially concentrated around the calculus of the CRB and the statistical resolution limit under Gaussian noise for dierent array processing applications. Speci cally, my recent works related to the performance analysis context, can be categorized as follows
• Our recent paper [J17] is a result of a collaboration with Prof. A. Zoubir and his Ph.D. student, A. Mennad. In this latter, we derived Slepian-Bangs-type formulas for CES dis-tributed data vectors in the presence of model misspeci cation. The basic Slepian-Bangs (SB) formula has been introduced in the array processing literature as a convenient and compact representation of the FIM for parameter estimation under (parametric) Gaussian data model. In [J17], we provided a new generalization of the classical SB formula to para-metric estimation problems involving i) non-Gaussian, heavy-tailed and CES distributed data in ii) the presence of model misspeci cation. Moreover, we showed that our proposed formulas encompass the special cases of the SB formula for CES distributions under perfect model speci cation, the SB formulas in the presence of misspeci ed Gaussian models, and the SB formula for the estimation of the scatter matrix of a set of CES distributed data under misspeci cation of the density generator.
The aforementioned study has been considered in the Ph.D. thesis of A. Mennad.
• In the Ph.D. work of L. Bacharach, and with collaboration with Dr. A. Renaux, Prof. E. Chaumette and Prof. J.-Y. Tourneret, we are focusing on the performance analysis of change-point estimation. It is worth mentioning that change-point estimation has received
much attention as it plays a signi cant role in several signal and array processing applica-tions. Nevertheless, the study of the optimal estimation performances in such context is a di cult task since the unknown parameter vector of interest may contain both continuous (observations distribution's parameters) and discrete (change-point locations) parameters. Our idea is to handle this by deriving a lower bound on the mean square error. More precisely, a Hybrid Cramér-Rao-Weiss-Weinstein bound (HCRWWB) and its associated closed-form expressions, whatever the considered distribution of the data, is proposed. Furthermore, contrary to several works about performance analysis in the change-point literature, our study is adapted to multiple changes but also to unknown observations dis-tribution's parameters [JS5,J14]. In addition, a semide nite programming formulation of the minimization procedure is given in order to compute the tightest proposed HCRWWB in an e cient way. This latter consists of nding the unique minimum volume covering the set constituted by hyper-ellipsoid elements which are generated using the derived candidate HCRWWB matrices w.r.t. the so-called Loewner partial ordering.
The aforementioned work is currently being studied in the Ph.D. thesis of L. Bacharch (funded by an allocation ministérielle MSER).
• Miscellaneous: Again, for sake of concisely some of my recent works are not detailed in this manuscript. The reader can refer to [J15,J8,IC19] for more details. As an example, and brie y speaking, on the one hand, in [J15,J8] and in collaboration with Prof. E. Chaumette, we addressed, respectively i) the problem of fundamental limitations on resolution in de-terministic parameters estimation by introducing a new rigourous de nition of resolvability based on a probabilistic framework and incorporating a requirement for accuracy unlike most existing de nitions; and ii) we proposed a new class of Weiss-Weinstein bounds (es-sentially free from regularity conditions on the probability density functions support) and we discussed its relationship with the Bobrovsky-Mayer-Wolf-Zakai bounds in [J15]. On the other hand, in [JS6,J11] with collaboration with Prof. J.-P. Delmas, we focused on the geometry design of planar antenna array in the context of near- eld source local-ization with and without the presence of a variable power pro le. Speci cally, we studied the class of square and cross-based centro-symmetric arrays and highlight some of their attractive features. In particular, we identi ed key geometric parameters that control the near- eld array performance. Opportunistically, these geometric parameters were used in order to design non-uniform square and cross-based centro-symmetric arrays that achieve better near- eld localization accuracy. Such design is handled by minimizing the relative peak sidelobe level ratio derived from the conventional array beampattern. This latter, is a max-min problem under constraints, which can be transformed into a nite sequence of convex linear matrix inequality problems solved using the Matlab GloptiPoly utility. After this brief introduction, in the following, I details some of my current activities. It is worth mentioning that the following research activities description has been partially presented and/or extracted from my publications which are listed in section.0.6. Consequently, some slight changes in notations from chapter to chapter may exist.
Notations: In the following, vectors (respectively matrices) are denoted by boldface lowercase letters (respectively uppercase letters). The notation d
=indicates has the same distribution as". Convergence in distribution and in probability are, respectively, denoted by d
→ and →P. For a matrix A, |A| and Tr (A) denote the determinant and the trace of A. AT (respectively AH) stands for the transpose (respectively conjugate transpose) matrix. The vec-operator vec(A)
1.2. OVERVIEW OF MY CURRENT RESEARCH ACTIVITY 23
stacks all columns of A into a vector. The operators ⊗, and ◦ refer, respectively, to Kronecker, element-wise and Khatri-Rao (column-wise Kronecker) matrix product. Ep{.} and EX/Y {.} denote respectively, the expectation under the pdf p and the conditional expectation. E {.} will be used when there is no ambiguity.
Chapter 2
Robust scatter matrix estimation and
subspace estimation with application to
radar
In most of the array processing literature, the additive noise or clutter (in the radar applications) is simply assumed to be a Gaussian stochastic process. Such assumption is generally a good approximation in many cases and has its theoretical basis in the central limit theorem. However, in certain speci c scenarios, the radar clutter cannot be correctly described by the Gaussian model anymore. As an example, experimental measurements reveal that the ground clutter data heavily deviate from the Gaussian model [1]. This is also true, e.g., for the sea clutter in a high-resolution and low-grazing-angle radar context, where the scatter number is random and the clutter shows nonstationarity [2]. To account for such problems, where the noise and/or the clutter is a non-Gaussian process, numerous clutter models have been developed. Among them, • The so-called complex elliptically symmetric (CES) distributions (cf. Section. 2.1.1.1). Its main advantage lies in its generality to encompass a wide variety of non-Gaussian distributions (Generalized Gaussian, compound Gaussian, t-distribution, W -distribution and K-distribution, etc.) which turns out to model accurately impulsive noise, spiky radar clutter measurements or other heavy-tailed observations [3,4].
• An other alternative is the compound-Gaussian (CG) distribution (referred as the spheri-cally invariant random process (SIRP) in the radar community [4]). The CG is a subclass of the CES and is a good alternative; while parametric estimator based on the CG mod-eling are less complex than those based on CES modmod-eling, the CG own the feasibility to describe dierent scales of the clutter roughness, as well as to encompass some important heavy-tailed distribution as K-distribution, t-distribution, Laplace, Cauchy and Weibull distribution, etc (cf. Section. 2.3.1.2). The CG is a two-scale, complex process with ran-dom power, structured as the product of two independent components: a complex Gaussian process with zero mean and unknown covariance matrix, and the square root of a positive scalar random process. As an example, in the radar context, the former describes the local scattering and is usually referred to as speckle, while the latter, modeling the local power changing, is called texture.
• Finally, data following the zero mean complex angular elliptical (CAE) distribution is an other useful alternative which corresponds to the probability density function (pdf) of a normalized zero mean CES distributed random variable. This distribution has the
advantage of being density generator free, but at the cost of a loss of information and thus loss of optimal estimation accuracy. The CAE modeling is not discussed in this Chapter due to space limitation. Nevertheless, the reader is referred to our paper [5] in which we focused on structured covariance matrix estimation in a robust statistical framework using the CAE modeling.
In the following, I present some of our recent works related to the scatter, covariance and signal subspace robust estimation as well robust source localization without the use of secondary data. This Chapter is based on the following articles
[SJ4,SJ3,SJ2,J13,ICS4,IC34,IC32,IC31,IC23,IC16,IC15].
2.1 E cient estimation of covariance/scatter matrices with
con-vex structure under CES distribution
Covariance Matrix (CM) estimation turns out to be a crucial step in most existing algorithms used in various domains such as adaptive signal processing, nancial engineering, communication systems [6, 7]. By de nition, a CM is Hermitian (symmetric for real random variables) and belongs to the set of Positive Semi-De nite (PSD) matrices. However, in many applications, the CM naturally holds a speci c structure such as Toeplitz or Kronecker product [811]. Taking into account this structure in the estimation problem usually implies a smaller parameter of interest vector to be estimated, and thus leads theoretically to a better estimation accuracy. The structured estimation problem has been investigated for diverse types of structures. For instance, the Toeplitz structure appears in array processing with Uniform Linear Array (ULA) or in time series analysis [8]. In MIMO communications or spatio-temporal noise processes in MEG/EEG data, the CM exhibits a Kronecker structure, where the factor matrices could be themselves structured [9,10]. In some applications, the CM lies in a small-dimension subspace [12,13].
In the afore-mentioned works, the CM estimation is unequivocally improved, when the prior structure is considered. However, they usually assume complex Gaussian distributed samples. Then, the structured CM estimation is realized either by projecting onto a subset describing the structure of the Sample Covariance Matrix (SCM), which is the unstructured Maximum Likelihood (ML) estimator for the CM [14, 15] or by deriving the ML with constraints. In some practical applications, performance is degraded, because the assumption of Gaussian distribution is inappropriate and the previous algorithms are not robust to outliers. In order to overcome this issue, a wide class of distribution free methods based on the unstructured Tyler's estimate has been proposed [5, 1618]. Those methods begin by normalizing the zero mean observations to get rid of the texture. Speci cally, in [5], we proposed a robust extension of the COvariance Matching Estimation Technique (RCOMET). In [16, 17], estimators have been proposed which minimize a constrained version of Tyler's cost function using iterative Majorization-Minimization algorithms. In [18], a COnvexly ConstrAined (COCA) CM estimator is presented, based on the generalized Method of Moments (MoM) for the Tyler's estimate subject to convex constraints. However, normalizing the observation causes a loss of information, notably the scaling factor, which is the reason why we chose to work directly with a larger class of distributions, namely, the CES distribution [19].
In this section, we introduce a StructurEd ScAtter Matrix Estimator (SESAME) for any given CES distribution, whose scatter matrix (which is proportional to the covariance matrix) owns a convex structure. This method is carried out in two steps. In the same vein as COMET but generalized to CES distributions, SESAME combines the unstructured ML estimation of the scatter matrix and the EXtended Invariance Principle (EXIP) [20]. A theoretical analysis of
![Figure 3.2: LOFAR's Initial Test Station antenna locations [155].](https://thumb-eu.123doks.com/thumbv2/123doknet/14708855.748486/77.892.87.763.113.864/figure-lofar-s-initial-test-station-antenna-locations.webp)
