Phase-field (PF) simulations can predict complex microstructure formations, including eutectic reactions. However, determining appropriate computational parameters for reproducing experimental microstructures remains a challenge. In recent years, data assimilation has been proposed to address this issue by systematically integrating observed data into model predictions, enabling the estimation of the system's states and unknown parameters. In this study, we constructed a novel PF model for Al-Si eutectic alloys in which the stoichiometric compound phase is treated as a non-equilibrium phase and evaluated the capability of data assimilation for determining solid-liquid interfacial properties. In conventional PF models, the free energy of stoichiometric compounds was approximated as parabolic functions. In contrast, the adopted method accounts for the driving forces of stoichiometric reactions and atomic diffusions under non-equilibrium conditions. The alloy composition was set to Al-10 at.%Si, and the Si phase was treated as a stoichiometric compound with a fixed molar fraction of Si = 1. Microstructural evolution under isothermal holding at 841 K, which is 9 K below the eutectic temperature (850 K), was simulated, and the PF model predicted the stable time evolution of the Si phase. We conducted the twin experiments employing the ensemble Kalman filter (EnKF) using the constructed PF model. Twin experiments were conducted using four filtering intervals (0.05 ms, 0.1 ms, 0.25 ms, and 0.5 ms), and three interfacial mobilities of α/liquid, Si/liquid, and α/Si interfaces were simultaneously estimated. As a result, all three interfacial parameters were successfully estimated. Additionally, estimation accuracy was higher at filtering intervals of 0.1 ms and 0.25 ms than at the smallest interval of 0.05 ms. This disagrees with previous studies, in which estimation accuracy has been shown to improve with smaller filtering intervals. It is proposed that an observation experiment for the data assimilation be performed under optimal frame-rate conditions.