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This paper presents a simple alternative to the traditional handling of autoregressive colored observation noise processes in Kalman filter-based speech enhancement algorithms. The method is entirely centered on a rewriting of the state-space equations describing the problem. The proposed approach decreases the dimension of the state vector and the amount of computations per iteration, and also naturally reduces to the white noise case when a zero-order autoregressive colored noise is chosen. In addition, from the multiple experiments conducted using several Kalman filter-based algorithms, it is found that the quality obtained with the new method, as measured by different speech quality measures, is equivalent and in some cases better. The simulations presented are based on both computer-generated and real-world colored noises, in stationary and nonstationary cases.