This study presents a robust method for detecting the location of fault in the wide-area power networks considering the limited number of synchronised phasor measurement units. In this manner, by employing the positive-sequence components in the governing equations at pre- and post-fault occurrence, the fault location (FL) problem is formulated as an optimisation problem. The constructed objective function consists of two terms that are dependent on the voltage and current changes so that each of them can be employed in the optimisation procedure, alone. Various factors, such as cyber attacks and measurement device failures, may lead to induce the bad data to the measurement set, and thus the results will not be valid. Automatic detection and elimination of erroneous measurements, contaminated with gross errors, from the measurement set, will be carried out utilising the least absolute value (LAV) estimator. This is the most important property of the LAV estimator, in which the bad measurements will be screened and suppressed during the iterative optimisation. An algorithm based on LAV estimation is presented to identify the FL. The efficiency of the proposed method is not affected by fault type and resistance. The method is tested on IEEE 14-bus, 57-bus and 118-bus case studies and simulation results indicate the accuracy of the developed technique.