Accurate measurements of soil moisture are essential for hydrological, agricultural and environmental sciences. Among many indirect measurement approaches, Frequency-Domain Reflectometry (FDR) soil moisture sensors are popular but are prone to be affected by many factors (e.g., temperature, bulk density, texture, mineralogy) at different installation sites. To avoid the enormous effort required for site-specific FDR calibration, we propose a calibration-free framework, in which a linear calibration model (that links FDR observation and true soil moisture) is incorporated. Based on the classical bias-blind methods using the ensemble Kalman filter (EnKF) and the iterative ensemble smoother (IES), two such bias-aware data assimilation methods are developed to simultaneously identify the unknown hydraulic and the linear calibration parameters based on uncalibrated FDR observations as well as meteorological data. We thoroughly discuss the effects of various factors (i.e., observation noise and number of observations, ensemble size, number of unknown parameters and two potential model errors) on their performances in the synthetic cases and make an application in a real-world case, besides comparing them with their previous versions simultaneously. In particular, the linear calibration model coupled with IES is more favored. From a pragmatic point of view, we demonstrate the usefulness of the proposed approaches in calibrating the FDR data in an online manner with easily-accessible meteorological data.