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

Abstract

This work describes a novel nonparametric identification method for estimating impulse responses of the general two-input single-output linear system with its target application to the individualization of an empirical model of type 1 diabetes. The proposed algorithm is based on correlation functions and the derived generalization of the Wiener-Hopf equation for systems with two inputs, while taking the stochastic properties of the output measurements into account. Ultimately, this approach to solving the deconvolution problem can be seen as an alternative to widely used prediction error methods. To estimate the impulse response coefficients, the generalized least squares method was used in order to reflect nonuniform variances and nonzero covariances of the stochastic estimate of the cross-correlation functions, hence yielding the minimum variance estimator. Estimate regularization strategies were also involved, while three different types of penalties were applied. The combination of smoothing, stability, and causality regularization was proposed to improve the general validity of the estimate and also to lower its variance. The findings of this identification method are meant to be applied within an eventual predictive control synthesis for the artificial pancreas, so a procedure for transforming the nonparametric model into the transfer function-based parametric model was also described. A discussion on the results of a comprehensive simulation-based experiment concludes the paper.

Keywords

• Correlation function
• generalized least squares method
• minimum variance estimate
• multiple-input single-output systems
• nonparametric model
• regularization