MAXIMUM-LIKELIHOOD DOA ESTIMATION AND ASYMPTOTIC CRAMER-RAO BOUNDS FOR ADDITIVE UNKNOWN COLORED NOISE

This paper is devoted to the maximum likelihood estimation of multiple sources in the presence of unknown noise, With the spatial noise cova riance modeled as a function of certain unknown parameters, e.g., an a utoregressive (AR) model, a direct and systematic way is developed to find the exact maximum likelihood (ML) estimates of all parameters ass ociated with the direction finding problem, including the direction-of -arrival (DOA) angles Theta, the noise parameters alpha, the signal co variance Phi(s), and the noise power sigma(2). We show that the estima tes of the linear part of the parameter set Phi(s) and sigma(2) can be separated from the nonlinear parts Theta and alpha. Thus, the estimat es of Phi(s), and sigma(2) become explicit functions of Theta and alph a. This results in a significant reduction in the dimensionality of th e nonlinear optimization problem. Asymptotic analysis is performed on the estimates of Theta and alpha, and compact formulas are obtained fo r the Cramer-Rao bounds (CRB's), Finally, a Newton-type algorithm is d esigned to solve the nonlinear optimization problem, and simulations s how that the asymptotic CRB agrees well with the results from Monte Ca rlo trials, even for small numbers of snapshots.