A technique to localize an impact source for an elastic spherical shell is proposed. The conventional source localization techniques when the source is located on a dispersive medium, require both the time-of-arrival differences (TOADs) between the transducer signals and the group velocities. In practice, the material properties or the geometry of the medium are not fully informed, therefore the group velocity is not available. Furthermore, they are only applicable if we have a high signal-to-noise ratio (SNR). In this paper, we propose a method that can be applicable in practice, which does not need to know the group velocity, when we have a relatively small SNR. The scanning procedure over the structure to acquire a minimum variance point of the estimated group velocities is suggested. To reduce the noise effect, an exponential function is asymmetrically weighted in smoothed Wigner-Ville distributions (WVDs). Experiments have been conducted to confirm the validity of this method. As a result, the proposed technique is found to be effective for an impact source localization for a spherical shell without prior information on the group velocity, even in a noisy environment.