A joint time synchronization and localization method without known clock parameters

Time synchronization and localization should be jointly conducted for time-related localization model when the local clock of sensor node has clock drift with respect to the real clock for imperfect hardware. A joint estimation method for the source locations and clock parameters is proposed by using the time difference of arrival (TDOA) measurements. The proposed joint estimation method does not rely on the clock parameters of anchor nodes. To estimate the clock parameters and source locations, the noncooperative linear estimators including unconstrained weighting least square (UWLS) and constrained weighting least square (CWLS) are put forward. The noncooperative and cooperative semidefinite programming (SDP) algorithms are also designed by relaxing the optimization function of maximum likelihood (ML) estimator as convex form. The proposed UWLS, CWLS and SDP algorithms provide the joint estimates for the source locations and clock parameters and avoid the shortcoming of ML estimator which requires an initial solution. The simulations show that the cooperative approaches provide better accuracy performance compared with the noncooperative approaches including the linear UWLS and CWLS estimators since more measurements are involved into the model. The cooperative SDP algorithm provides more robust estimates for the clock parameters and source locations especially when the source node is outside of the convex hull of the anchor nodes.