Placement and distributed deployment of sensor teams for triangulation based localization

We address the problem of placing a sensor network so as to minimize the uncertainty in estimating the position of targets. The novelty of our formulation is in the sensing model: we focus on stereo sensors where the measurements from two sensors must be combined for an estimation. We study two versions of this problem. In the first version, which we call the placement problem, we are given a workspace and an error threshold. The objective is to place a minimum number of cameras so that no matter where the target is located in the workspace, the uncertainty in localizing it is less than the threshold. For this problem, we present an approximation algorithm and prove that the deviation of its performence from the optimal value is bounded by a constant. In the second version, called the deployment problem, we study the problem of relocating a mobile sensor team to minimize the uncertainty in localizing possibly moving targets. We present a distributed, discrete-time algorithm which explicity addresses communication and motion constraints and show how to compute the optimal move within the time-step for a given target/sensor-pair assignment. The utility of the algorithm is demonstrated with simulations.