Abstract:

The asynchronous problem between source node and sensor anchors seriously reduces the positioning accuracy in time-of-arrival(TOA) based localization. To solve this problem, a novel algorithm for jointly estimating the clock bias and the position of a source node is developed in this paper. By introducing an intermediate variable, the proposed method first converts the nonlinear TOA equations into pseudo-linear ones, on the basis of which a cost function is constructed. Then, utilizing the relationship between the unknowns and the intermediate variable as the constraint condition, a constrained weighted least squares problem is formulated. Finally, by solving the problem with the technique of Lagrange multipliers, the closed-form solution is obtained. Theoretical analysis and simulation results indicate that our algorithm can reach the Cramér-Rao Lower Bound(CRLB) and perform better than the existing methods.

Key words: time of arrival, joint synchronization and localization, constrained weighted least squares, Cramér-Rao lower bound