In this paper, parameter estimation of a state-space model of noise or noisy speech cepstra is investigated. A blockwise EM algorithm is derived for the estimation of the state and observation noise covariance from noise-only input data. It is supposed to be used during the offline training mode of a speech recognizer. Further a sequential online EM algorithm is developed to adapt the observation noise covariance on noisy speech cepstra at its input. The estimated parameters are then used in model-based speech feature enhancement for noise-robust automatic speech recognition. Experiments on the AURORA4 database lead to improved recognition results with a linear state model compared to the assumption of stationary noise.