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The speech enhancement is one of the effective techniques to solve speech degraded by noise. In this paper a fast speech enhancement method for noisy speech signals is presented, which is based on improved Kalman filtering. The conventional Kalman filter algorithm for speech enhancement needs to calculate the parameters of AR (auto-regressive) model, and perform a lot of matrix operations, which usually is non-adaptive. The speech enhancement algorithm proposed in this paper eliminates the matrix operations and reduces the calculating time by only constantly updating the first value of state vector X(n). We design a coefficient factor for adaptive filtering, to automatically amend the estimation of environmental noise by the observation data. Simulation results show that the fast adaptive algorithm using Kalman filtering is effective for speech enhancement.