A maximum likelihood method is presented for estimating drift direction and speed of a directional sonobuoy given the deployment location and a time series of acoustic bearings to a sound source at known position. The viability of this method is demonstrated by applying it to two real-world scenarios: (1) during a calibration trial where buoys were independently tracked via satellite, and (2) by applying the technique to sonobuoy recordings of a vocalising Antarctic blue whale that was simultaneously tracked by photogrammetric methods. In both test cases, correcting for sonobuoy drift substantially increased the accuracy of acoustic locations.