Estimation of orientation fields is an essential module in a fingerprint recognition system. Conventional gradient based approaches are popular but very sensitive to noise. In this paper, we propose a new implementation that is more resistant to noise. Our basic idea is to conduct redundant estimation over four overlapping neighborhoods for each target block. Following this idea, we devise a weighted averaging scheme operated on the base blocks directly. Thus, each block (including the target one) in the overlapping neighborhoods has different impact on estimation of the dominant orientation fields. Our preliminary experiment results suggest that the proposed weighted averaging algorithm is more robust against noise in comparison with other gradient based methods.