In remote sensing systems, exact knowledge of the sensor locations is critical for generating focused images. In order to accurately locate misplaced or perturbed sensors from their received signal data, we proposed a robust sensor localization method based on low-rank Euclidean distance matrix (EDM) reconstruction. To this end, an EDM of sensors and objects is defined and partially initialized by computing distances between the inaccurate sensor locations and distances from the sensors to the objects using signal coherence analysis. We then decompose the noisy EDM with missing entries into a low-rank EDM corresponding to true sensor locations and a sparse matrix of distance errors by solving a constrained optimization problem using the alternating direction method of multipliers (ADMM). We verify our method with simulations on a uniform linear array with unknown perturbations up to several wavelengths.