State Estimation in Type 2 Diabetes Using the Continuous-Discrete Unscented Kalman Filter

Using a nonlinear model for the glucose-insulin dynamics in type 2 diabetes, formulated in continuous-time as a stochastic differential equation, we seek to estimate the system states and parameters based only on discrete-time self-monitored blood glucose measurements of fasting glucose and the known exogenous insulin dose. This is done by means of continuous-discrete unscented Kalman filtering. The results are compared to an implementation of a continuous-discrete extended Kalman filter. Simulations show that it is possible to estimate all states with good accuracy using the CD-UKF, while it is also possible to estimate one unknown parameter at the same time. Further simulations show that increasing the sample rate makes it possible to estimate more parameters, given that the meal intake of the patient is known perfectly.