With a growing number of available datasets especially from satellite remote sensing, there is a great opportunity to improve our knowledge of the state of the hydrological processes via data assimilation. Observations can be assimilated into numerical models using dynamics and data-driven approaches. The present study aims to assess these assimilation frameworks for integrating different sets of satellite measurements in a hydrological context. To this end, we implement a traditional data assimilation system based on the Square Root Analysis (SQRA) filtering scheme and the newly developed data-driven Kalman-Takens technique to update the water components of a hydrological model with the Gravity Recovery And Climate Experiment (GRACE) terrestrial water storage (TWS), and soil moisture products from the Advanced Microwave Scanning Radiometer - Earth Observing System (AMSR-E) and Soil Moisture and Ocean Salinity (SMOS) in a 5-day temporal scale. While SQRA relies on a physical model for forecasting, the Kalman-Takens only requires a trajectory of the system based on past data. We are particularly interested in testing both methods for assimilating different combination of the satellite data. In most of the cases, simultaneous assimilation of the satellite data by either standard SQRA or Kalman-Takens achieves the largest improvements in the hydrological state, in terms of the agreement with independent in-situ measurements. Furthermore, the Kalman-Takens approach performs comparably well to dynamical method at a fraction of the computational cost.