Self-calibration method for TOA based localization systems with generic synchronization requirement

In this paper, we propose and investigate a self-calibration method which estimates the locations and clock offsets of the anchors based on TOA measurements. The agent locations are not surveyed and hence they can be realized by a single moving agent, which makes the calibration procedure simple and cost effective. Instead of considering a specific clock synchronization scenario, which was the case with previous related works, we systematically classify different clock synchronization cases that may arise in practice and provide a generalized formulation of the self-calibration problem that covers all the synchronization classes. The maximum likelihood (ML) solution of the calibration problem, which jointly estimates all the unknown parameters, is shown to be a non-convex optimization problem. We propose to relax the ML estimator to a semi-definite programming (SDP) problem by applying semi-definite relaxation. To improve the accuracy of the SDP solution, we further refine it with the ML estimator. Simulation results confirm that the proposed method is capable of accurately calibrating TOA based localization systems.