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Transmissions through multipath channels suffer from Rayleigh fading and intersymbol interference. This can be overcome by sending a (known) training sequence and identifying the channel (active identification). However, in a nonstationary context, the channel model has to be updated by periodically sending the training sequence, thus reducing the transmission rate. We address the problem of blind identification, which does not require such a sequence and allows a higher transmission rate. In order to track nonstationary channels, we have derived an adaptive (Kalman) algorithm which directly estimates the entire set of characteristic parameters. An original adaptive estimation of the noise model has been proposed for this investigation. Monte-Carlo simulations confirm the expected results and demonstrate the performance.