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The identification of model parameters of a highs density recording channel is usually difficult and complicated. In this paper, we successfully apply the alternating coordinates minimization (ACM) algorithm for estimating parameters of a partial erasure plus transition shift model (PETSM). The resulting algorithm turns out to iteratively solve two least square problems and is guaranteed to converge. Furthermore, the obtained model for a nonlinear partial response channel is more accurate than conventional models such that the maximum likelihood (ML) detector has better bit error rate (BER) performance without increasing its realization complexity. Computer simulations show that the ACM algorithm can accurately estimate the model parameters and the BER for the detector is significantly improved especially when the transition shift parameter is large. [ABSTRACT FROM AUTHOR]