Estimation of Message Source and Destination from Link Intercepts

We consider the problem of estimating the endpoints (source and destination) of a transmission in a network based on partial measurement of the transmission path. Sensors placed at various points within the network provide the basis for endpoint estimation by indicating that a specific transmission has been intercepted at their assigned locations. During a training phase, test transmissions are made between various pairs of endpoints in the network and the sensors they activate are noted. From these possibly noisy measurements, we develop necessary constraints that any feasible network topology must satisfy. Randomized rounding of the solution to a semidefinite programming relaxation generated from the constraints is used to produce samples of network topologies defined over the feasible set. When a subset of the deployed sensors are activated, corresponding to the occurrence of a transmission with unknown endpoints, a monte carlo approximation of the posterior distribution of source/destination pairs given the activated sensors is computed by averaging over the topology samples and used in maximum a posterior estimation of the endpoints. We illustrate the method using simulations of power-law random