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This paper deals with the problem of speech enhancement when a corrupted speech signal with additive colored noise is the only information available for processing. Kalman filtering is known as an effective speech enhancement technique, in which the speech signal is usually modeled as an autoregressive (AR) process and represented in the state-space domain. In the above context, all the Kalman filter-based approaches proposed in the past operate in two steps: first, the noise and the signal parameters are estimated; second, the speech signal is estimated by using Kalman filtering. New sequential estimators are developed for sub-optimal adaptive estimation of the statistics of the unknown a priori driving processes simultaneously with the system state; a recursive least-squares lattice (RLSL) algorithm is used for adaptive estimation of the speech and noise AR parameters. The algorithm provides improved speech estimate at little computational expense.