Modeling and Mismodeling in Adaptive Radar Detection – Parameter Bounds Under Misspecified Models

Intervenant : FULVIO GINIFulvioGini

Date : Lundi 08 Juin 2015 à 14h30

Lieu : Amphi Ouabdeslam (ex 1C)

 Abstract

The problem of estimating a deterministic parameters vector from a set of acquired data is ubiquitous in signal processing applications. A fundamental assumption underlying estimation problems is that the true data model and the model assumed to derive an estimation algorithm are the same, that is, the model is correctly specified. However, a certain amount of mismatch is often inevitable in practice. Among others, the model mismatch can be due to a not perfect knowledge of the true data model or to the need to fulfill some operative constraints on the estimation algorithm (processing time, simple hardware implementation, and so on). In the statistical literature, much attention has been devoted to the behavior of the Maximum Likelihood (ML) estimator under mismatched conditions. In particular, it has been shown that the asymptotic distribution of the ML estimator in misspecified models is a Gaussian distribution whose mean value is the vector that minimizes the Kullback-Leibler (KL) divergence between the true and the assumed data distributions and covariance matrix given by the so-called Huber “sandwich” matrix. On the other hand, little consideration has been given to the relative performance bounds.

In this talk, a lower bound on Mean Square Error (MSE) of the estimate of a real deterministic parameter vector under misspecified model is proposed and discussed. In particular, a lower bound on the MSE of the Mismatched Maximum Likelihood (MML) estimator is derived in closed form and its relation with the Huber “sandwich” matrix is investigated. We further provide two illustrative examples, i.e. the estimation of the mean and the variance of a set of one-dimensional Gaussian data. In the second part of the talk, we propose a possible application of the proposed framework in a classical radar signal processing problem: the estimation of the disturbance covariance (scatter) matrix for adaptive detection algorithms. We put this classical radar problem in the more general context of the estimation of the scatter matrix in the Complex Elliptically Symmetric (CES) distribution family. Also, in this case, some numerical examples will be analyzed in order to clarify the theoretical concepts. We end this talk by sketching some open issues and presenting the concluding remarks.

 Biography

Fulvio GINI (Fellow, IEEE)received the Doctor Engineer (cum laude) and the Research Doctor degrees in electronic engineering from the University of Pisa, Italy, in 1990 and 1995 respectively. In 1993 he joined the Department of Ingegneria dell’Informazione of the University of Pisa, where he become Associate Professor in 2000 and he is Full Professor since 2006. From July 1996 through January 1997, he was a visiting researcher at the Department of Electrical Engineering, University of Virginia, Charlottesville. He is an Associate Editor for the IEEE Transactions on Aerospace and Electronic Systems and for the Elsevier Signal Processing journal. He has been AE for the Transactions on Signal Processing (2000–06) and a Member of the EURASIP JASP Editorial Board. He has been the Editor-in-Chief of the Hindawi International Journal on Navigation and Observation (IJNO). He is the Area Editor for the Special issues of the IEEE Signal Processing Magazine. He was co-recipient of the 2001 IEEE AES Society’s Barry Carlton Award for Best Paper. He was recipient of the 2003 IEE Achievement Award for outstanding contribution in signal processing and of the 2003 IEEE AES Society Nathanson Award to the Young Engineer of the Year. He has been a Member of the Signal Processing Theory and Methods (SPTM) Technical Committee (TC) of the IEEE Signal Processing Society and of the Sensor Array and Multichannel (SAM) TC for many years. He is a Member of the Board of Directors (BoD) of the EURASIP Society, the Award Chair (2006-2012) and the EURASIP President for the years 2013-2016. He was the Technical co-Chair of the 2006 EURASIP Signal and Image Processing Conference (EUSIPCO), Florence, Italy, September 2006, of the 2008 Radar Conference, Rome, Italy, May 2008, and of the IEEE CAMSAP 2015 workshop, to be held in Cancun, Mexico in December 2015. He was the General co-Chair of the 2nd Workshop on Cognitive Information Processing (CIP2010), of the IEEE ICASSP 2014, to be held in Florence in May 2014, and of the CoSeRa 2015 workshop on compressive sensing in radar, to be held in Pisa in June 2015. He was the guest co-editor of the special section of the Journal of the IEEE SP Society on Special Topics in Signal Processing on “Adaptive Waveform Design for Agile Sensing and Communication” (2007), guest editor of the special section of the IEEE Signal Processing Magazine on “Knowledge Based Systems for Adaptive Radar Detection, Tracking and Classification” (2006), guest co-editor of the two special issues of the EURASIP Signal Processing journal on “New trends and findings in antenna array processing for radar” (2004) and on "Advances in Sensor Array Processing (in memory of Alex Gershman)" (2013). He is co-editor and author of the book ”Knowledge Based Radar Detection, Tracking and Classification” (2008) and of the book "Waveform Diversity and Design" (2012) . His research interests include modeling and statistical analysis of radar clutter data, non-Gaussian signal detection and estimation, parameter estimation and data extraction from multichannel interferometric SAR data. He authored or co-authored 8 book chapters, about 110 journal papers and more than 140 conference papers.

Dernière modification le dimanche, 24 mai 2015 09:33