Maximum Likelihood DOA Estimation of Multiple Wideband Sources in the Presence of Nonuniform Sensor Noise
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Research Article Maximum Likelihood DOA Estimation of Multiple Wideband Sources in the Presence of Nonuniform Sensor Noise C. E. Chen, F. Lorenzelli, R. E. Hudson, and K. Yao Los Angeles EE Department, University of California, Los Angeles, CA 90095, USA Correspondence should be addressed to C. E. Chen, [email protected] Received 1 March 2007; Revised 21 July 2007; Accepted 8 October 2007 Recommended by Sinan Gezici We investigate the maximum likelihood (ML) direction-of-arrival (DOA) estimation of multiple wideband sources in the presence of unknown nonuniform sensor noise. New closed-form expression for the direction estimation Cram´er-Rao-Bound (CRB) has been derived. The performance of the conventional wideband uniform ML estimator under nonuniform noise has been studied. In order to mitigate the performance degradation caused by the nonuniformity of the noise, a new deterministic wideband nonuniform ML DOA estimator is derived and two associated processing algorithms are proposed. The first algorithm is based on an iterative procedure which stepwise concentrates the log-likelihood function with respect to the DOAs and the noise nuisance parameters, while the second is a noniterative algorithm that maximizes the derived approximately concentrated loglikelihood function. The performance of the proposed algorithms is tested through extensive computer simulations. Simulation results show the stepwise-concentrated ML algorithm (SC-ML) requires only a few iterations to converge and both the SC-ML and the approximately-concentrated ML algorithm (AC-ML) attain a solution close to the derived CRB at high signal-to-noise ratio. Copyright © 2008 C. E. Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
Direction-of-arrival (DOA) estimation has been one of the central problems in radar, sonar, navigation, geophysics, and acoustic tracking. A wide variety of high-resolution narrowband DOA estimators have been proposed and analyzed in the past few decades [1–4]. The maximum likelihood (ML) estimator, which shows excellent asymptotic performance, plays an important role among these techniques. Many of the proposed ML estimators are derived from the uniform white noise assumption [4–6], in which the noise process of each sensor is assumed to be spatially uncorrelated white Gaussian with identical unknown variance. It is shown that under this assumption the ML estimates of the nuisance parameters (source waveforms/spectra and noise variance) can be expressed as a function of DOAs [7–9], and therefore the number of independent parameters to be estimated is reduced. This procedure is called concentration, which substantially reduces the search space and usually leads to a more efficient implementation. Recently, there has been a great interest in estimating the DOAs for wideband sources, whose energy is spread over a
broad bandwidth. For ex
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