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Bounds for maximum likelihood regular and non-regular DoA estimation in K-distributed noise

Abramovich, Yuri and Besson, Olivier and Johnson, Ben Bounds for maximum likelihood regular and non-regular DoA estimation in K-distributed noise. (2015) IEEE Transactions on Signal Processing, 63 (21). 5746 - 5757. ISSN 1053-587X

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Official URL: http://dx.doi.org/10.1109/TSP.2015.2460218

Abstract

We consider the problem of estimating the direction of arrival of a signal embedded in $K$-distributed noise, when secondary data which contains noise only are assumed to be available. Based upon a recent formula of the Fisher information matrix (FIM) for complex elliptically distributed data, we provide a simple expression of the FIM with the two data sets framework. In the specific case of $K$-distributed noise, we show that, under certain conditions, the FIM for the deterministic part of the model can be unbounded, while the FIM for the covariance part of the model is always bounded. In the general case of elliptical distributions, we provide a sufficient condition for unboundedness of the FIM. Accurate approximations of the FIM for $K$-distributed noise are also derived when it is bounded. Additionally, the maximum likelihood estimator of the signal DoA and an approximated version are derived, assuming known covariance matrix: the latter is then estimated from secondary data using a conventional regularization technique. When the FIM is unbounded, an analysis of the estimators reveals a rate of convergence much faster than the usual $T^{-1}$. Simulations illustrate the different behaviors of the estimators, depending on the FIM being bounded or not.

Item Type:Article
Additional Information:Thanks to IEEE Xplore editor. The definitive version is available at http://ieeexplore.ieee.org The original PDF of the article can be found at IEEE Transactions on Signal Processing website : http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&arnumber=7165645&filter%3DAND%28p_IS_Number%3A7273734%29
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > University of South Australia (AUSTRALIA)
Other partners > WR Systems (USA)
Laboratory name:
Département d'Electronique, Optronique et Signal - DEOS (Toulouse, France) - Signal, Communication, Antenne et Navigation - SCAN
Funders:
DGA/MRIS
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Deposited By: Olivier Besson
Deposited On:14 Oct 2015 12:06

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