In order to improve positioning precision of unknown nodes in space shadow-related environment

due to the complexity of underwater acoustic environment

a semidefinite relaxation（ SDR） localization algorithm for underwater acoustic sensor networks is proposed under received signal strength（ RSS） ranging mode. Combined with transmission loss characteristics of the underwater acoustic channel

the optimization function and the solution model for the problem are established. At the same time

in order to avoid the maximum likelihood convergence problem occur in resolving

the nonconvex optimization problem is transformed into convex problem by relaxation constraint

and unknown nodes location is solved by SDR algorithm in convex optimization theory. In the cases of both irrelevant and relevant spatial shadow

the proposed algorithm is compared with the maximum likelihood localization algorithm and the least squares algorithm respectively. The simulation analysis show that the proposed algorithm has high estimation precision in irrelevant and relevant shadow environments.