This paper proposes a technique for estimating speech parameters in noisy environment. The technique uses a spectral model represented by generalized cepstrum and estimates the generalized cepstral coefficients from the speech which has been degraded by additive background noise. Parameter estimation is based on maximum a posteriori (MAP) estimation procedure. An iterative approach which has been formulated for all-pole modeling is applied to the generalized cepstral modeling. Generalized cepstral coefficients are obtained by an iterative procedure that consists of the unbiased estimation of log spectrum and noncausal Wiener filtering. Since the generalized cepstral model includes the all-pole model as a special case, the technique can be viewed as a generalization of the all-pole modeling based on MAP estimation. The proposed technique is applied to the enhancement of speech and several experimental results are also shown.