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When a single sequence of noisy observations is available, the autoregressive (AR)-model based methods using Kalman-filter make it possible to enhance speech. However, the estimation of the AR parameters is required, but is still a challenging problem as the signal is corrupted by an additive noise. In this paper, we propose to both estimate the signal and the AR parameters by developing a recursive instrumental variable-based approach. Avoiding a non linear approach such as the EKF, this method involves two conditionally linked Kalman filters running in parallel. Once a new observation is available, the first filter uses the latest estimated AR parameters to estimate the signal, while the second filter uses the estimated signal to update the AR parameters. A comparative study between existing speech enhancement methods is completed.