LMI-based online estimation of a time-varying time-delay in continuous glucose measurement devices

We propose an online method to estimate the time-dependent time-delay of continuous glucose measurement devices. The problem is characterized by one delayed signal which is sampled continuously, and a reference signal which is only available for measurement at (few) irregular time samples. The method makes use of a forgetting function to be able to quickly adapt to changes in the time-delay. A simulation example and the application to blood glucose concentration data obtained from type 1 diabetic subjects, where it is of interest to estimate the time-delay of the continuous glucose measurement device, show the usefulness and effectiveness of the proposed method.