Data assimilation, which relies on explicit knowledge of dynamical models, is a well‐known approach that addresses models' limitations due to various reasons, such as errors in input and forcing data sets. This approach, however, requires intensive computational efforts, especially for high‐dimensional systems such as distributed hydrological models. Alternatively, data‐driven methods offer comparable solutions when the physics underlying the models are unknown. For the first time in a hydrological context, a nonparametric framework is implemented here to improve model estimates using available observations. This method uses Takens delay coordinate method to reconstruct the dynamics of the system within a Kalman filtering framework, called the Kalman‐Takens filter. A synthetic experiment is undertaken to fully investigate the capability of the proposed method by comparing its performance with that of a standard assimilation framework based on an adaptive unscented Kalman filter (AUKF). Furthermore, using terrestrial water storage (TWS) estimates obtained from the Gravity Recovery And Climate Experiment mission, both filters are applied to a real case scenario to update different water storages over Australia. In situ groundwater and soil moisture measurements within Australia are used to further evaluate the results. The Kalman‐Takens filter successfully improves the estimated water storages at levels comparable to the AUKF results, with an average root‐mean‐square error reduction of 37.30% for groundwater and 12.11% for soil moisture estimates. Additionally, the Kalman‐Takens filter, while reducing estimation complexities, requires a fraction of the computational time, that is, ∼8 times faster compared to the AUKF approach.