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Smart transmission grids are intended to utilize various measurements for enhanced operation. In particular, synchronized phasor measurements have found many applications in this context. This paper presents a linear weighted least-squares (WLS) method for fault location estimation of transmission lines by synchronized voltage measurements. The measurements may be taken from the faulted line terminals or buses far from the faulted line. The circuit equations of the network are used to find the transfer function between the fault location and each voltage measurement. Next, two auxiliary variables are defined to transform the nonlinear fault location estimation problem into a linear WLS problem. A closed-form solution is then obtained for fault location. The use of multiple measurements provides the opportunity of identifying erroneous measurements by a statistical test. The linearity of the problem expedites both estimation and identification procedures. Moreover, the method requires neither to classify the fault type nor to estimate the fault resistance. Furthermore, transmission lines are modeled by distributed parameters so that the method can be applicable to long lines. Electromagnetic transient simulations for 9-bus and 22-bus test systems reveal accurate fault location estimation, regardless of fault type and resistance, as well as successful identification of measurement errors.