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In recent years a new, and very powerful technique for parameter estimation - the eigenstructure, or signal subspace method - has been developed. Eigenstructure algorithms are closely related to Pisarenko's method for estimating the frequencies of sinusoids in white Gaussian noise. In theory they yield asymptotically unbiased estimates of arbitrarily close parameters, independent of the signal-to-noise ratio (SNR). Although signal subspace methods have proven to be powerful tools, they are not without drawbacks. An important weakness of all signal subspace algorithmis their need to know the noise covariance explicitly. The important problem of developing signal subspace based procedures for signals in noise fields with unknown covariance has not been satisfactorily addressed. It is our intent to propose a solution to the problem of direction-of-arrival (DOA) estimation for a broad class of unknown noise fields. We will then briefly discuss other important estimation problems for which modified versions of this procedure can be applied.