We investigate a wireless network localization scenario in which the need for synchronized nodes is avoided. It consists of a set of fixed anchor nodes transmitting according to a given sequence and a self-localizing receiver node. The setup can accommodate additional nodes with unknown positions participating in the sequence. We propose a localization method which is robust with respect to uncertainty of the anchor positions and other system parameters. Further, we investigate the Cramér-Rao bound for the considered problem and show through numerical simulations that the proposed method attains the bound.