Multiple underwater target positioning with optimally placed acoustic surface sensor networks

Abstract

In an increasing number of scientific and commercial mission scenarios at sea, it is required to simultaneously localize a group of underwater targets. The latter may include moored systems, autonomous vehicles, and even human divers. For reasons that have to do with the unavailability of Global Positioning System underwater, cost reduction, and simplicity of operation, there is currently a surge of interest in the development of range-based multiple target localization systems that rely on the computation of the distances between the targets and a number of sensor nodes deployed at the ocean surface, equipped with acoustic range measuring devices. In the case of a single target, there is a wealth of literature on the problem of optimal acoustic sensor placement to maximize the information available for target localization using trilateration methods. In the case of multiple targets, however, the literature is scarce. Motivated by these considerations, we address the problem of optimal sensor placement for multiple underwater target positioning. In this setup, we are naturally led to a multiple objective optimization problem, the solution of which allows for the analysis of the trade-offs involved in the localization of the targets simultaneously. To this end, we resort to tools from estimation theory and multi-objective optimization. For each target, the function to be minimized (by proper choice of the sensor configuration) is related to the determinant of the corresponding Fisher information matrix, which yields information on the minimum possible covariance of the error with which the position of the target can be estimated using any non-biased estimator. To deal with the fact that more than one target is involved, we exploit the concept of multiple objective Pareto-optimal solutions to characterize the best possible accuracy with which each of the targets can be positioned, given constraints on the desired positioning accuracy of the other targets. Simulation examples illustrate how, for a three-sensor network and two targets, it is possible to define an optimal sensor configuration that yields large positioning accuracy for both targets simultaneously, using convex optimization tools. When more than two targets are involved, however, more than three sensors are required to exploit an adequate trade-off of the accuracy with which each target can be positioned by resorting to non-convex and Pareto-optimization tools. We show how in this case the optimal sensor configurations depend on the Pareto weights assigned to each of the targets, as well as on the number of sensors, the number of targets, and the uncertainty with which the positions of the targets are known a priori.

A Review on Optimal Placement of Sensors for Cooperative Localization of AUVs

“…In the cases where 3D localization of the targets was considered, it was assumed that both sensors and targets can be located anywhere in 3D [27,55]. However, only few researchers have assumed the real scenario as discussed above [38,56].…”

“…Therefore, the value of measurement noise depends upon the range between target and the sensor and is to be modelled accordingly in order to achieve realistic results. However, in most of the previous research, measurement noise is assumed as zero mean Gaussian noise with constant covariance [48,56,57]. Clearly, realistic modelling of measurement noise is a challenging task in this field which can be explored in the future.…”

A Robust, Non-Cooperative Localization Algorithm in the Presence of Outlier Measurements in Ocean Sensor Networks

“…Past years have witnessed development of research on localization in OSNs. Considerable efforts have been investigated in recent years [12,13,14,15,16,17,18,19,20,21,22,23,24,25]. To mention a few, an optimal sensor placement strategy that depended on the required task at hand was proposed in [13].…”

“…This strategy could run in the presence of Gaussian noise in the range-based scheme. Then, the authors further proposed a multiple underwater target positioning method in [18] with the strategy exploited. The localization problem in [18] was transformed into an optimization problem.…”

“…Then, the authors further proposed a multiple underwater target positioning method in [18] with the strategy exploited. The localization problem in [18] was transformed into an optimization problem. Two-phase localization was presented, where convex optimization tools were utilized for single target localization, and Pareto optimization tools were used when it came to multiple target localizations.…”