Semi-physical Identification and State Estimation of Energy Intake for Interventions to Manage Gestational Weight Gain

Abstract

Excessive gestational weight gain (i.e., weight gain during pregnancy) is a significant public health concern, and has been the recent focus of novel, control systems-based interventions. This paper develops a control-oriented dynamical systems model based on a first-principles energy balance model from the literature, which is evaluated against participant data from a study targeted to obese and overweight pregnant women. The results indicate significant under-reporting of energy intake among the participant population. A series of approaches based on system identification and state estimation are developed in the paper to better understand and characterize the extent of under-reporting; these range from back-calculating energy intake from a closed-form of the energy balance model, to a constrained semi-physical identification approach that estimates the extent of systematic under-reporting in the presence of noise and possibly missing data. Additionally, we describe an adaptive algorithm based on Kalman filtering to estimate energy intake in real-time. The approaches are illustrated with data from both simulated and actual intervention participants.

Fig. 1

Simulations of the reformulated EB model using self-reported and back-calculated EI from two representative intervention participants. BMI: body mass index; GA: gestational age at baseline.

Fig. 2

Block diagram of the linear regression model.

Fig. 3

A hypothetical case for EI estimation using the semiphysical identification approach. Here, n_EI ~ N(0, 400²), n_GWG ~ N(0, 0.1²); α = 1.1, γ = 400. Error bars represent the 95% confidence interval calculated using bootstrp in MATLAB®.

Fig. 4

The results of estimating the true EI from self-reported EI for two intervention participants using the proposed semi-physical identification approach. Error bars represent the 95% confidence interval.

Fig. 5

The performance of the KF algorithm illustrated using a hypothetical participant. The RMSE stands for Root Mean Square Error.

Fig. 6

Performance of the KF algorithm evaluated using two actual intervention participants.