We investigate the problem of time-of-arrival (TOA) based localization under possible non-line-of-sight (NLOS) propagation conditions. To robustify squared-range-based location estimator, we follow maximum correntropy criterion, essentially Welsch $M$-estimator with a redescending influence function which behaves like $\ell_0$-minimization towards grossly biased measurements, to derive formulat...