  This article considers the problem of source localization (SL) using possibly
unreliable time-of-arrival (TOA) based range measurements. Adopting the
strategy of statistical robustification, we formulate TOA SL as minimization of
a versatile loss that possesses resistance against the occurrence of outliers.
We then present an alternating direction method of multipliers (ADMM) to tackle
the nonconvex optimization problem in a computationally attractive iterative
manner. Moreover, we prove that the solution obtained by the proposed ADMM will
correspond to a Karush-Kuhn-Tucker point of the formulation when the algorithm
converges, and discuss reasonable assumptions about the robust loss function
under which the approach can be theoretically guaranteed to be convergent.
Numerical investigations demonstrate the superiority of our method over many
existing TOA SL schemes in terms of positioning accuracy and computational
simplicity. In particular, the proposed ADMM achieves estimation results with
mean square error performance closer to the Cram\'{e}r-Rao lower bound than its
competitors in our simulations of impulsive noise environments.
