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In this paper we propose an alternative way to developing a robust and adaptive sequential algorithm for estimating the unknown impulse response of a linear system. Our approach is based on formulating the problem as a maximum penalized likelihood (MPL) problem. We use the Fair penalty function as the generalized log-likelihood and a quadratic function to play a regularization role. The MPL formulation also leads naturally to adaptive schemes for learning the regularization and scale parameters. The robustness of the proposed algorithm to impulsive noise is demonstrated through mathematical analysis and numerical simulations.