This paper deals with a Kalman filter-based enhancement of a speech signal contaminated by a colored noise, when using a single microphone system. In classical methods the issue of estimating the quantities necessary to perform Kalman filtering is either not addressed or based on the Durbin-Levinson algorithm or the extended modified Yule Walker equations. But, these solutions may lead to unsatisfying results. Therefore we present an alternative approach which is an extension of the method we have recently proposed for the white noise case. This extension combines Gibson's approach for speech enhancement and subspace non-iterative algorithms for state space model identification. Thus speech enhancement is stated as a realisation issue in the framework of identification. This approach has the advantage of providing, from noisy observations, the matrices related to state space model and the noise covariances that are necessary to perform Kalman filtering.