Passive localisation and discrimination of moving targets with a Deterministic Maximum Likelihood (DML) method is investigated by simulations. In the simulated surveillance scenario, the DML method is applied to data from a Flank Array Sonar (FAS), to track two targets moving along crossing trajectories. The simulated data, consisting of narrow-band 1 kHz target signals and superimposed noise, are generated by the RAYLAB sound propagation code in an environment modelling the waters outside Bornholm in the Baltic Sea. For reference, conventional beamforming, and adaptive beamforming with a Minimum Variance Distortionless Response (MVDR) method, are applied on the same data. The resolution performance of the DML method is found to be better than that of the reference methods, when the target signals are weak and/or the target bearings are close.