State Estimation Under Correlated Partial Measurement Losses: Implications for Weight Control Interventions

Abstract

The growing prevalence of obesity and related health problems warrants immediate need for effective weight control interventions. Quantitative energy balance models serve as powerful tools to assist in these interventions, as a result of their ability to accurately predict individual weight change based on reliable measurements of energy intake and energy expenditure. However, the data collected in most existing weight interventions is self-monitored; these measurements often have significant noise or experience losses resulting from participant non-adherence, which in turn, limits accurate model estimation. To address this issue, we develop a Kalman filter-based estimation algorithm for a practical scenario where on-line state estimation for weight, or energy intake/expenditure is still possible despite correlated partial data losses. To account for non-linearities in the models, an algorithm based on extended Kalman filtering is also developed for sequential state estimation in the presence of missing data. Simulation studies are presented to illustrate the performance of the algorithms and the potential benefits of these techniques in real-life interventions.

Keywords: Estimation; Extended Kalman filter; Filtering; Intermittent measurements; Interventions; Kalman filter; Multiple missing measurements; Obesity.

Figures

Fig. 1

Performance of the KF algorithm illustrated using a hypothetical female participant with correlated partial measurement losses during an intervention.

Fig. 2

Simulation results with low arrival rates are shown to be divergent and unstable.

Fig. 3

Performance of the EKF-based algorithm illustrated using a hypothetical participant in an intervention for gestational weight control.