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In this work, we consider a perpendicular magnetic recording channel where the data is stored perpendicular to the plane of magnetic media. The perpendicular magnetic recording provides significant aerial density gain compared to the conventional longitudinal magnetic recording. This gain comes at the cost of adding a baseline wander noise which degrades the system performance and affects the data integrity. In this paper, we propose a model for the baseline wander noise. The parameters of the proposed model are computed by posing the problem as minimizing the mean square error. We demonstrate that this problem can be appropriately simplified and posed as finding a least squares problem. The proposed model on the baseline wander noise requires the knowledge of information bits to estimate the noise but this information is unavailable at the time of decoding. We propose a novel technique to cancel the baseline wander effect on the Viterbi trellis. This cancelation is done on the fly in the trellis and obviates the need of the bits information yet provides the performance gain close to the genie performance. Simulation results corroborate the analysis of the proposed algorithm and demonstrate that the proposed algorithm provides a significant performance gain.