Aiming at the problem of underwater short-range detection of incoming targets, a random positioning method driven by fluid dynamics is proposed. The single-beam pulse laser driven by the navigation hydrodynamic force is used to dynamically scan, and the scanning periodic is recorded by the magnetic sensor. Based on the heavy tail function, the target echo equation is derived, and the magnetic dipole equivalent model of the magnetic detection system is established. The optical magnetic measurement signals are calculated respectively by using the peak detection method and the threshold detection method. The underwater short-range target acquisition model and the azimuth detection accuracy equivalent model are established. The influence mechanism of laser emission power, pulse width, threshold, and noise on measurement accuracy is studied. The results show that the azimuth measurement accuracy and target capture rate increase with the increase of the laser emission power, and decrease with the increase of the pulse width and the receiving circuit noise voltage. The azimuth measurement accuracy reaches the maximum when the detection threshold is 300 mV. The capture rate varies slightly with the increase of the threshold. When the threshold is close to the peak of the echo pulse, the target capture rate decreases rapidly.