Estimation of process noise variances from the measured output sequence with application to the empirical model of type 1 diabetes

Dodek, Martin; Miklovičová, Eva

doi:10.1016/j.bspc.2023.104773

Cited by 4 publications

(3 citation statements)

References 39 publications

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“…Another problem of applying the recursive least squares method to adapt the parameters of linear models in real time is that the possible effects of exogenous random disturbances affecting the dynamics of glycemia [1] are hard to distinguish from the effects of time-varying system parameters. As a result, the online estimation algorithm will incorrectly adapt the parameters due to the effects of process noise.…”

Section: A State Of the Artmentioning

confidence: 99%

“…However, in contrast to the original offline algorithm [10], here we consider the parameter-varying structure of model (1). To this end, we will introduce the bracket notation •[ ] for particular objects in order to disambiguate their instances in time and make the notation of crucial recursive relations neater throughout the paper.…”

Section: Model Structure and Preliminariesmentioning

confidence: 99%

“…It is known that the actual dynamics of glycemia is of an underlying stochastic nature, since the human body is subject to multiple random exogenous disturbances, which include the level of physical activity and stress factors, while significant roles are also played by the input uncertainties. The aforementioned stochastic effects use to be modelled by the corresponding process noise [1]. Therefore, it can be concluded that statistical and regression methods are suitable for parameter estimation.…”

Section: Introductionmentioning

confidence: 99%

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

Dodek,

Miklovičová

2024

IEEE Access

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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.

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Section: A State Of the Artmentioning

confidence: 99%

Section: Model Structure and Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Dodek,

Miklovičová

2024

IEEE Access

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Predicting the output error of the suboptimal state estimator to improve the performance of the MPC-based artificial pancreas

Dodek

Miklovičová

2023

Control Theory Technol.

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The error of single step-ahead output prediction is the information traditionally used to correct the state estimate while exploiting the new measurement of the system output. However, its dynamics and statistical properties can be further studied and exploited in other ways. It is known that in the case of suboptimal state estimation, this output prediction error forms a correlated sequence, hence it can be effectively predicted in real time. Such a suboptimal scenario is typical in applications where the process noise model is not known or it is uncertain. Therefore, the paper deals with the problems of analytical and empirical modeling, identification, and prediction of the output error of the suboptimal state estimator for the sake of improving the output prediction accuracy and ultimately the performance of the model predictive control. The improvements are validated on an empirical model of type 1 diabetes within an in-silico experiment focused on glycemia prediction and implementation of the MPC-based artificial pancreas.

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Improving the insulin therapy for diabetic patients using optimal impulsive disturbance rejection: Continuous time approach

Dodek,

Miklovičová,

Halás

2024

Biocybernetics and Biomedical Engineering

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Estimation of process noise variances from the measured output sequence with application to the empirical model of type 1 diabetes

Cited by 4 publications

References 39 publications

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

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

Predicting the output error of the suboptimal state estimator to improve the performance of the MPC-based artificial pancreas

Improving the insulin therapy for diabetic patients using optimal impulsive disturbance rejection: Continuous time approach

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