A TPSN-RBS joint time synchronization algorithm based on weighted least square method is proposed

aiming at synchronization errors and its calculative errors existing between massive multiple hops sensor network nodes. The optimal solution for the time offset and frequency offset of logical clock of node is obtained by weighted least square method

using messages that can be heard. The Cramér-Rao lower bound is used for performance analysis

and compared with the TPSN algorithm

the simulation results show that

the synchronization precision between nodes is improved

and in large-scale wireless sensor networks with dense nodes

assure lower communication traffic

at the sometime cumulative errors are reduced.