The enormous growth of consumer electronic industry is driving the need for achieving ultra-high areal storage densities. Shingled magnetic recording (SMR) is a promising high density storage technique where shingles are created by overlapping tracks for increasing the track per inch (TPI) and achieving higher areal densities. High TPI values, however, introduce sidetrack interference in the equalized output of the center track sensed through the read head. The problem of removing interference from the center track signal can be formulated as estimating pulse shapes of sidetracks assuming sidetracks are decodable. In this paper, we first propose a solution using the correlation method for estimating the pulse shape and the phase-misalignment. The correlation method fails when there is a frequency offset present from sidetracks. Furthermore, we devise a solution based on the least mean square (LMS) algorithm which can provide time varying estimates of the sidetrack pulse shapes and remove the interference from the center track signal. Experimental and simulation results which corroborate the analysis of the proposed algorithm, demonstrate that the proposed algorithm outperforms other techniques and gives the minimum bit error rate (BER). The complexity of the proposed algorithm is low and it can be easily implemented on the hardware.