The fluctuating target tracking problem through the use of dynamic programming based track-before-detect (DP-TBD) is considered in this paper. The target is modelled by the well-known Swerling family of target amplitude fluctuation models in order to capture the effect of radar cross-section changes that a target would present to radar over time. For each of the target fluctuation models, the complex likelihood ratio (CLLR), which utilizes the target amplitude fluctuation information together with the phase information, is derived and used in the integration process of DP-TBD. Simulation results show a significant gain in detection and tracking performance through accurately modeling the target amplitude fluctuations.