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This paper introduces a new realization for maximum likelihood time-delay estimation. The new realization illuminates the relationships between maximum likelihood time delay estimation and other methods. We obtain the result by deriving the likelihood function using a fundamental method that, surprisingly, appears to be new to the field of array processing. This method is a natural complement to the Karhunen-Loeve transform having vector eigenfunctions and scalar eigenvalues, and it generalizes to M measurements, M/spl ges/2. Moreover, it can be applied to other multichannel estimation problems.