This paper considers the estimation of speech parameters and their enhancement using an approach based on the estimation-maximization (EM) algorithm, when only noisy speech data is available. The distribution of the excitation source for the speech signal is assumed as a mixture of two Gaussian probability distribution functions with differing variances. This mixture assumption is experimentally valid for removing the residual excitation signal. The assumption also is found to be effective in enhancing noise-corrupted speech. We adaptively estimate the speech parameters and analyze the characteristics of its excitation source in a sequential manner. In the maximum likelihood estimation scheme we utilize the EM algorithm, and employ a detection and an estimation step for the parameters. For speech enhancement we use Kalman filtering for the parameters obtained from the above estimation procedure. The estimation and maximization procedures are closely coupled. Simulation results using synthetic and real speech vindicate the improved performance of our algorithm in noisy situations, with an increase of about 3 dB in terms of output SNR compared to conventional Gaussian assumption. The proposed algorithm also may be noteworthy in that it needs no voiced/unvoiced decision logic, due to the use of the residual approach.