Detection-estimation of more uncorrelated Gaussian sources than sensors using partially augmentable sparse antenna arrays

We introduce a new approach for the detection-estimation problem for "partially augmentable" nonuni-form linear antenna arrays, whose set of intersensor differences is not complete. We propose a positive-definite completion method of the partially specified Mα-variate Toeplitz covariance matrix via direct augmentation, followed by its transformation into a sequence of positive-definite Toeplitz matrices Tμ, each having their (Mα − μ) smallest eigenvalues equalised, and so being an appropriate candidate for the number of sources μ. Likelihood ratio information criteria (AIC, MDL and MAP) are then used to select the best candidate model, simultaneously providing DOA estimates for the indicated number of sources.