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We present a new tracking algorithm to perform timing recovery for low-SNR partial response data storage channels. This approach, designated "dual segmented Kalman filters based symbol timing recovery (DSK-STR)", is based on the conventional phase-locked loop (PLL) based timing recovery scheme. However, DSK-STR uses two intertwined PLLs and the gains of these PLLs are updated at each symbol instant according to a modified Kalman filter algorithm. The performance of DSK-STR is investigated via Monte-Carlo simulations and it is seen that DSK-STR offers a 3.5 dB signal-to-noise ratio (SNR) gain over the conventional PLL-based timing recovery scheme for a target loss of lock rate of 1×10-5 in longitudinal magnetic recording channels.