Location And Spectrum Estimation By Approximate Maximum Likelihood

We investigate the estimation of signal parameters as source locations from sensor array measurements in the presence of partly unknown noise fields and also the estimation of spectral parameters of the signals and of noise. This problem has drawn much interest, and many parameter estimation methods for array data have been discussed in the literature. We concentrate on approximate maximum likelihood estimation in the frequency domain assuming stationary array measurements. We review several concepts in which different asymptotic distributional properties of Fourier transformed array data are applied. We investigate narrowband as well as wideband data. Asymptotic distributional results of the estimates are presented. Numerical procedures, approximations and estimates from different model fits having, in some cases, the same asymptotic behavior as maximum likelihood estimates are discussed. Finally, we summarize the results from numerical experiments that show the behavior of different estimates in the single frequency case for a small number of data snapshots.

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