We have already developed three kinds of time-varying complex AR (TV-CAR) parameter estimation algorithms for analytic speech signal, which are based on minimizing mean square error (MMSE), Huber's robust M-estimation and Instrumental Variable (IV) method. This paper presents novel robust TV-CAR model parameter estimation algorithms on the basis of a Generalized Least Square (GLS) and Extended Least Square (ELS) method, in which the equation error is modeled by complex AR model with white Gaussian input to whiten the equation error. The experiments with natural speech corrupted by white Gaussian demonstrate that the proposed methods achieve robust spectral estimation against additive white Gaussian.