Underwater Target Positioning with a Single Acoustic Sensor

The availability of reliable underwater positioning systems to localize one or more vehicles simultaneously based on information received on-board a support ship or an autonomous surface vessel is key to the operation of some classes of AUVs. Furthermore, there is considerable interest in reducing the number of sensors involved in acoustic navigation/positioning systems to reduce the costs involved and the time consumed in the deployment, callibration, and recovery phases. Motivated by these considerations, in this paper we address the problem of single underwater target positioning based on measurements of the ranges between the target and a moving sensor at the sea surface, obtained via acoustic ranging devices. In particular, and speaking in loose terms, we are interested in determining the optimal geometric trajectory of the surface sensor that will, in a well defined sense, maximize the range-related information available for underwater target positioning. To this effect, an appropriate Fisher Information Matrix is defined and its determinant is maximized to yield the sensor trajectory that maximizes the accuracy of the target position estimate that can possibly be obtained with any unbiased estimator. It is shown that the optimal trajectory depends on the relative velocity of the sensor, the sampling time between measurements, and the number of measurements acquired for the FIM computation. Simulation examples illustrate the key results derived.