Newton-type methods in array processing

Despite their good features, Newton-type methods are not usually employed in array processing due to the lack of appropriate formulas for the first- and second-order differentials. One specific property of most array processing models is that each column of the signal matrix depends only on the corresponding element of one or more parameter vectors. In this letter, we exploit this property to derive compact expressions of the gradient, Hessian, and Hessian approximation of common maximum-likelihood (ML) cost functions, using a proper symbolic technique. Specifically, we study the conditional ML, row-correlated ML, and asymptotic ML cost functions.