State Space Temporal Gaussian Processes for Glucose Measurements

Measuring the blood glucose (BG) concentrations for people with diabetes is essential to achieve a better glycemic control either by medical professionals or by using feedback control algorithms. Continuous Glucose Monitoring (CGM) devices provide indirect measurements of the BG each I-S minutes. However, CGM devices suffer from correlated measurement errors and calibration errors. Detailed models for the errors of CGM devices already exist in the literature. Nonetheless, the identification of these models requires data from multiple CGM devices at once and accurate reference blood glucose measurements obtained clinically. This fact makes these models difficult to be subject-specific during typical treatment since diabetic subjects only use one CGM device with 3-4 finger pricking blood glucose measurements per day. In this paper, a methodology to obtain subject-specific CGM error models using Temporal Gaussian Processes (TGP) in their state space form is introduced. Three different TGPs are proposed and a strategy based on a particle Markov Chain Monte Carlo (MCMC) is used to perform regression and fit parameters for the models. The strategy is tested against data generated from virtual subject using detailed CGM error measurement models which were fitted with more than one CGM device and detailed clinical data from the literature. The results demonstrated the ability for TGP models with the proposed particle MCMC strategy to obtain subject-specific CGM error models using data available during the typical life of diabetic subjects.