Optimal State Estimation for the Artificial Pancreas

Abstract

The subject of this paper is a novel approach to optimal state estimation of a discrete-time state-space model. Accordingly, the presented algorithm can be seen as an alternative or a substitute to traditional state observers such as the prevailing Kalman filter. Our proposed solution exploits the standard stochastic state-space model and the theoretical back iteration of the state vector with the estimation based on the generalized least squares method. According to the theory of the generalized least squares method, in order to obtain the minimum variance estimate, the weighting matrix had to be equal to the noise variance-covariance matrix inverse, and thereby the proposed algorithm could satisfy the criteria of the best linear unbiased estimator. The target application domain of this state estimator is the type 1 diabetes empirical model, so the paper also marginally concerns the problem of prediction and model predictive control of glycemia, while the fundamental concepts of the artificial pancreas are also discussed. In the end, the comprehensive simulation-based comparative case study focused on glycemia prediction and predictive control was evaluated. The results demonstrated that the proposed state estimator might be a suitable and efficient alternative to the Kalman filter within the eventual implementation of the artificial pancreas.