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.