Cooperative Multiple Target Nodes Localization Using TOA in Mixed LOS/NLOS Environments

In this paper, the time-of-arrival based cooperative localization problem under mixed line-of-sight/non-line-of-sight (LOS/NLOS) conditions is addressed. Under the conditions of unknown statistics of NLOS errors and unknown path status, we formulate a non-convex robust weighted least squares (RWLS) problem to locate the multiple stationary target nodes. In this problem, we introduce some “balancing parameters” to alleviate the possible improper upper bounds problem of the existing robust localization methods, and jointly estimate the target node positions and the balancing parameters. With the aid of the semidefinite relaxation technique, the RWLS problem is transformed into a convex mixed semidefinite and second order cone programming problem, which can be solved efficiently. The idea is then extended to the moving target nodes localization problem, where the velocity is assumed to be fixed within a short time period. Both simulated and real experimental data are used to verify the performance of the proposed method. The results show that the proposed method works well for both the sparse and dense NLOS environments, and also confirm the superior performance of the proposed method over the existing methods.