This paper deals with Kalman filter-based enhancement of a speech signal contaminated by a white noise, using a single microphone system. Such a problem can be stated as a realization issue in the framework of identification. For such a purpose we propose to identify the state space model by using subspace non-iterative algorithms based on orthogonal projections. Unlike Estimate-Maximize (EM)-based algorithms, this approach provides, in a single iteration from noisy observations, the matrices related to state space model and the covariance matrices that are necessary to perform Kalman filtering. In addition no voice activity detector is required unlike existing methods. Both methods proposed here are compared with classical approaches