This paper presents an autonomous search technique that enables vehicles to uniformly search for moving targets within a recursive Bayesian estimation (RBE) framework. The detailed process of the grid-based method for the search task is introduced: prediction and update steps of the grid-based filter are thoroughly explained. Entropic information is selected as information measure for the optimal control strategy. The N-step look-ahead planning in terms of future observations is associated with the grid-based approach. Finally, the numerical analysis was conducted to show the performance of the proposed technique for the optimal search.