Accurately predicting graft failure following kidney transplantation is essential for identifying high-risk patients and tailoring treatment strategies. This thesis aims to forecast kidney graft failure by estimating and predicting the glomerular filtration rate (GFR) using real data related to pre-transplant and post-operative patients status, provided to us by Hannover Medical School. To achieve this, we implement three Bayesian filtering techniques: the Extended Kalman Filter (EKF), the Unscented Kalman Filter (UKF), and the Particle Filter (PF), on a discrete-time state-space stochastic Duffing oscillator model. We also conduct regression analysis between available GFR measurements and the filters' estimated and predicted values, followed by an error analysis using root mean square error. Our results demonstrate that Particle Filter, utilizing 10,000 particles, consistently produced accurate estimates compared to other filters in most patients. Furthermore, we observe that data interpolation yields more accurate results.