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Register a new userBounds for maximum likelihood regular and non-regular DoA estimation in $K$-distributed noise
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Olivier Besson
Publication date
2015
fields
Mathematical Statistics
and research's language is
English
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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.
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In this paper, the problem of determining the number of signal sources impinging on an array of sensors and estimating their directions-of-arrival (DOAs) in the presence of spatially white nonuniform noise is considered. It is known that, in the case of nonuniform noise, the stochastic likelihood function cannot be concentrated with respect to the diagonal elements of noise covariance matrix. Therefore, the stochastic maximum-likelihood (SML) DOA estimation and source enumeration in the presence of nonuniform noise requires multidimensional search with very high computational complexity. Recently, two algorithms for estimating noise covariance matrix in the presence of nonuniform noise have been proposed in the literature. Using these new estimates of noise covariance matrix, an approach for obtaining the SML estimate of signal DOAs is proposed. In addition, new approaches are proposed for SML source enumeration with information criteria in the presence of nonuniform noise. The important feature of the proposed SML approaches for DOA estimation and source enumeration is that they have admissible computational complexity. In addition, some of them are robust against correlation between source signals. The performance of the proposed DOA estimation and source enumeration approaches are investigated using computer simulations.
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