The Unscented Kalman Filter as a Real-Time Algorithm to Simultaneously Estimate Insulin and Model Parameters

This paper proposes the Unscented Kalman Filter (UKF) as a tool to achieve reliable real-time estimates of plasma insulinemia from noisy sampled glucose measurements. The approach suitably exploits Hovorka's glucose-insulin model and the filter allows to simultaneously estimate also some of the model parameters. Hovorka's model in its original form is a nonlinear ordinary differential equation system; here it is endowed with an additive state noise accounting for the unavoidable uncertainties affecting the glucose-insulin dynamics. The problem is tackled as a state filtering problem for a continuous-discrete state-space model. In our simulation, we evaluated the two representative filters: the Extended Kalman Filter (EKF) and the UKF. Our simulation results indicate that when the initial states for the filters are significantly deviated from the true values, the estimation accuracy of the UKF becomes better than the EKF whilst, when the relatively precise initial filter value is available, the use of the EKF is sufficient.