In case of physiological systems state and parameter estimation is a crucial question. It is key to describe given patient population with appropriate accuracy. Furthermore, state feedback kind of applications also require some sort of estimation procedure in order to get internal information about the controlled system. Linear parameter varying (LPV) framework is beneficial for controller design as well. However, to realize the necessary scheduling parameters, estimation of both state variables and model parameters is needed. A possible solution is the application of Dual Extended Kalman Filter (DEKF) which is able to estimate these signals. The developed framework can be used to design LPV based controller in our further work. In this study we introduce our developed DEKF solution by using the widely applied Cambridge Type 1 Diabetes Mellitus (TIDM) model for virtual patient generation. We have found that our solution is able to estimate the state variables with good accuracy. The variation of parameters can also be tracked by using the proposed solution.