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Kalman filtering is known as an effective speech enhancement technique. Many Kalman filtering algorithms for single channel speech enhancement were developed in past decades. However, the Kalman filtering algorithm for multichannel speech enhancement is very less. This paper proposes a Kalman filtering algorithm for distributed multichannel speech enhancement in the time domain under colored noise environment. Compared with conventional algorithms for distributed multichannel speech enhancement, the proposed algorithm has lower computational complexity and requires less computational resources. Simulation results show that the proposed algorithm is superior to the conventional algorithms for distributed multichannel speech enhancement in achieving higher noise reduction, less signal distortion and more speech intelligibility. Moreover, the proposed algorithm has a faster speed than several multichannel speech enhancement algorithms.