Spectral acoustic imaging is a widely used approach in the automotive industry for sound source localization. However, because the vibroacoustic mechanisms in rotating machines are non-stationary during run-up or run-down, conventional techniques cannot be directly implemented. This necessitates the development of an acoustic imaging method for source localization to deal with non-stationary engine speeds. Ordertracking is a well-known technique to analyze a machine under large speed variation, which has an ability to extract orders, that are proportional to shaft rotational frequency, investigate critical frequencies and tonal components. In this paper, a novel method, coined Order-Based Beamforming (OBBF) is presented. OBBF performs beamforming on extracted orders to localize the sources at various speeds during a run-up or rundown. The proposed method is evaluated through both simulated and experimental data. The key outcome of this work is to show the automotive industry a way to perform localization at non-stationary operating conditions.