Optimal Sensor Placement for 2-D Range-Only Target Localization in Constrained Sensor Geometry

Localization of an emitting or reflecting target is one of the most important issues in a wide range of applications including radar, sonar, wireless communication and sensor networks. Due to significant effect on the positioning accuracy, designing the optimal sensor-target geometry has been considered as an important problem in the localization literature. The existing sensor placement methods mainly solve the problem in the cases without any constraints on the sensors locations. In the realistic scenarios, however, the sensors cannot be placed simply in arbitrary locations due to such constraints as the geographical limitations, communication problems between the sensor pairs and the security issues. In this paper, the optimal sensor-target geometries under sensor location constraints for range-based positioning are determined based on the A-optimality, E-optimality and D-optimality criteria. First, the special case of two-sensor in a circular area is considered as the permissible sensors placement region, and then, the results are extended to more number of sensors in a connected arbitrarily-shaped sensor region. The proposed sensor placement method can be applied to any application that the target is located outside the sensor region.