Robust Online Correlation Method for Identification of a Nonparametric Model of Type 1 Diabetes

The paper presents an online version of the identification method for estimating the impulse responses in the case of a two-input single-output linear empirical model of type 1 diabetes that allows us to adapt the model parameters due to the intra-subject time variability in real time. The method builds on and augments our original research by providing important enhancements concerning the online parameter estimation, recursive formulation of essential equations, improved regularization, and new effective approaches to numerically solve the estimation problem. Recursive equations are derived to update the covariance matrix of the sample cross-correlation function, as well as the inverse of this covariance matrix, where the customized Sherman-Morrison formula was considered. To efficiently update the parameter estimate at each sample while avoiding direct calculation of the Hessian matrix inverse, two alternative strategies are proposed to be applied instead. The first is based on the numeric minimization by the conjugate gradient method, whereas the second takes advantage of the Schulz method to approximate the inverse Hessian matrix. As a result, all steps of the identification algorithm were designed so that only basic linear operations are required. Features to robustify the estimate were also involved, as the optimal regularization strategies based on the inverse of the covariance matrix of the actual parameter distribution and the inter-sample parameter drift were applied. In the end of the paper, a series of simulation-based experiments was carried out to assess the effectiveness of the proposed method and to demonstrate all of its aspects and important characteristics. The documented results showed that the method can yield valid estimates of impulse responses and also effectively adapt parameters in real time under the influence of time-varying physiology.