In this study, we propose a method for localizing an unknown moving emitter by measuring a sequence of the frequency-of-arrival using a single moving observation platform. Furthermore, we introduce the position and velocity errors of the moving observation platform into the theoretical localization error equation to analyze the effect of these errors on the localization accuracy without Monte-Carlo simulations. The proposed theoretical error equation can propagate toward the time direction; therefore, the theoretical localization error can be evaluated at an arbitral time. We demonstrate that the localization error value obtained by the proposed equation and the RMSE evaluated by the Monte-Carlo simulation sufficiently coincide with one another.