In this paper, a novel trilateration positioning technique is proposed that jointly addresses the conventional range-based trilateration localization and measurements outliers detection and processing. The proposed scheme contains three components: (a) detecting outliers, (b) minimizing outliers impact; (c) minimizing conventional noise impact. The method is based on a linear regression model in which the noise and outliers vector effect is considered simultaneously. The cost function includes an ℓ₁-norm minimization component to detect outliers. Once detected, the contaminated ranges are either removed from measurements or corrected. The proposed scheme has been simulated and compared with the recently proposed Linearized LS (L-LS), range-based LS (R-LS), and Squared-Kange Least Squares (SR-LS) approach. The results shows that the proposed approach is able to detect 97% of single introduced outliers and leads to less position error variance compared to the state-of-the-art approaches.