Optimal trajectory determination of a single moving beacon for efficient localization in a mobile ad-hoc network

An ad hoc network of small robots (sensor nodes) adjusting their positions to establish network connectivity would be able to provide a communication infrastructure in an urban battlefield environment. A sensor node would be capable of moving to a particular position to establish network connectivity, provided it knows its current position, positions of other sensor nodes and the radio propagation characteristics of the sensor area.In this paper, we present a pseudo formation control based trajectory algorithm to determine the optimal trajectory of a moving beacon used in localization of the sensor nodes in real-time. The trajectory and the frequency of transmission of the GPS based position information of the moving beacon influences the accuracy of localization and the power consumed by the beacon to localize. Localization accuracy and reduction in the number of position information messages can be achieved, in real-time, by determining the optimal position from where the beacon should transmit its next position information. This will decrease the time required to localize, and power consumed by the beacon in comparison to random or predetermined trajectories.We first show that optimal position determination is a pseudo formation control problem. Next, we show the pseudo formation control problem formulated as an unconstrained optimization problem under the free space propagation model. We further present the modeling of the beacon incorporating the trajectory algorithm based on the pseudo formation control in a discrete event simulator. Simulation results, comparing the performance of localization with pseudo formation control based trajectory against random waypoint and predetermined trajectories for the beacon are presented. The simulation results show that the localization accuracy is significantly improved along with reduction in the number of position information messages transmitted when the beacon traverses along the pseudo formation control based trajectory.