This work proposes a novel approach to reinforce localization security in wireless networks in the presence of malicious nodes that are able to manipulate (spoof) radio measurements. It substitutes the original measurement model by another one containing an auxiliary variance dilation parameter that disguises corrupted radio links into ones with large noise variances. This allows for relaxing the non-convex maximum likelihood estimator (MLE) into a semidefinite programming (SDP) problem by applying convex-concave programming (CCP) procedure. The proposed SDP solution simultaneously outputs target location and attacker detection estimates, eliminating the need for further application of sophisticated detectors. Numerical results corroborate excellent performance of the proposed method in terms of localization accuracy and show that its detection rates are highly competitive with the state of the art.