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This paper deals with the joint signal and parameter estimation for linear state-space models. An efficient solution to this problem can be obtained by using a recursive instrumental variable technique based on two dual Kalman filters. In that case, the driving process and the observation noise in the state-space representation for each filter must be white with known variances. These conditions, however, are too strong to be always satisfied in real cases. To relax them, we propose a new approach based on two dual Hinfin filters. Once a new observation of the disturbed signal is available, the first Hinfin algorithm uses the latest estimated parameters to estimate the signal, while the second Hinfin algorithm uses the estimated signal to update the parameters. In addition, as the Hinfin filter behavior depends on the choice of various weights, we present a way to recursively tune them. This approach is then studied in the following cases: (1) consistent estimation of the AR parameters from noisy observations and (2) speech enhancement, where no a priori model of the additive noise is required for the proposed approach. In each case, a comparative study with existing methods is carried out to analyze the relevance of our solution.