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This paper presents a study on source localization using time difference of arrival (TDOA) measurements from static sensors in the presence of random errors in sensor positions. We develop a constrained weighted least squares (CWLS) source localization method which incorporates the relationship between the source position and an auxiliary variable as a constraint. The CWLS source localization is formulated as an indefinite quadratically constrained quadratic optimization problem, which is a nonconvex problem. By employing the hidden convexity of the original optimization problem, the global optimal source location estimate can be efficiently obtained. Simulations are used to corroborate the good performance of the proposed method.