Joint State-Parameter Inference Enhances Estimation Performance in Model-Based Digital Therapeutics for Type 1 Diabetes

Blood glucose estimation is the cornerstone of model-based decision support (DS) and Automated Insulin Delivery (AID) systems. Control systems that rely on physiologic/compartmental models depend heavily on model parameterization, which is either defined using population values or personalized through the user's data. Often, the model parameters are defined as constants. However, under real-world free-living conditions, fixed parameters can limit the accurate reconstruction and estimation of glucose levels and states. In this paper, we propose and discuss a recursive filtering framework for online joint state estimation and parameter identification in nonlinear, time-varying physiological models for Type 1 Diabetes (T1D). Specifically, we employ a Rao-Blackwellized Stein Variational Gradient Descent (RBSVGD) filter to compute the joint posterior distributions of model states and parameters. The proposed approach is applied to the Hovorka glucose-insulin model and validated using data generated by the the Oregon Health & Science University (OHSU) simulator across 20 virtual patients. We perform a comparative analysis against: (i) a standard Extended Kalman Filter (EKF) with fixed model parameters, and (ii) an Augmented Extended Kalman Filter (AEKF) for joint state-parameter estimation. The results demonstrate that the proposed RBSVGD-based framework outperforms both EKF and AEKF approaches not only in terms of the accuracy of glucose estimation, but also in terms of estimated model parameters.