  We investigate the problem of time-of-arrival (TOA) based localization under
possible non-line-of-sight (NLOS) propagation conditions. To robustify the
squared-range-based location estimator, we follow the maximum correntropy
criterion, essentially the Welsch $M$-estimator with a redescending influence
function which behaves like $\ell_0$-minimization towards the grossly biased
measurements, to derive the formulation. The half-quadratic technique is then
applied to settle the resulting optimization problem in an alternating
maximization (AM) manner. By construction, the major computational challenge at
each AM iteration boils down to handling an easily solvable generalized trust
region subproblem. It is worth noting that the implementation of our
localization method requires nothing but merely the TOA-based range
measurements and sensor positions as prior information. Simulation and
experimental results demonstrate the competence of the presented scheme in
outperforming several state-of-the-art approaches in terms of positioning
accuracy, especially in scenarios where the percentage of NLOS paths is not
large enough.
