Two families of methods are widely used in data assimilation: the four-dimensional variational (4D-Var) approach, and the ensemble Kalman filter (EnKF) approach. The two families have been developed largely through parallel research efforts. Each method has its advantages and disadvantages. It is of interest to develop hybrid data assimilation algorithms that can combine the relative strengths of the two approaches. This paper proposes a subspace approach to investigate the theoretical equivalence between the suboptimal 4D-Var method (where only a small number of optimization iterations are performed) and the practical EnKF method (where only a small number of ensemble members are used) in a linear setting. The analysis motivates a new hybrid algorithm: the optimization directions obtained from a short window 4D-Var run are used to construct the EnKF initial ensemble. The proposed hybrid method is computationally less expensive than a full 4D-Var, as only short assimilation windows are considered. The hybrid method has the potential to perform better than the regular EnKF due to its look-ahead property. Numerical results show that the proposed hybrid ensemble filter method performs better than the regular EnKF method for the test problem considered.