Robust joint localization and time synchronization in wireless sensor networks with bounded anchor uncertainties

A unified framework to jointly solve the problems of localization and synchronization at the same time is presented in this paper. The joint approach is attractive because it can solve both localization and synchronization using the same set of message exchanges, which is extremely important for energy saving in wireless sensor networks. The inaccuracy of anchor locations and timings is taken into account to provide accurate joint localization and synchronization. The anchor uncertainties are assumed to be bounded, but knowledge of the statistics of anchor uncertainties is not required. The problem is formulated into a linear model with uncertainties on both sides of the equation. A robust joint estimator is then proposed based on minimizing the worst-case mean square error and the solution is obtained by solving a semidefinite programming problem. Simulation results show that the proposed estimator outperforms the traditional least squares estimator at the cost of higher computational complexity.