This paper presents a new method to estimate J motion parameters of loud transiting acoustic sources with a single stationary hydrophone in shallow water environments. The parameters of interest include the time of Closest Point of Approach (CPA) and the ratio of velocity over the CPA range. The method involves only processing the intensity surface of the spectrogram of received broadband acoustic signals. The shapes of striation curves on such surfaces are directly related to motion parameters by the principle of the waveguide invariant theory. Since little environmental information besides the waveguide invariant parameter, beta, is used, the proposed method promises to be more robust than full matched field source localization. Successful application of the method to speed boat localization in a lake experiment is described to illustrate its effectiveness.