Changes in weather conditions such as temperature and humidity, miscommunication between the control center and circuit breaker transducers and tap changers, and inaccurate manufacturing data may cause parameter errors. Because of incorrect parameters, the state estimator may provide biased state estimates, which may lead to many serious economic and operational results. In order to prevent that, one must identify and correct those parameter errors. This work proposes a local parameter estimator based on the least absolute value (LAV) estimator, which is known to be robust against bad measurements, i.e. measurements with gross error. Considering the increasing number of phasor measurement units (PMUs), as well as their fast refresh rate and high accuracy, the proposed method will employ PMU measurements in local parameter estimation. In general, a PMU measures the current phasor flowing through a branch and the voltage phasor of the sending bus of that branch. However, those two measurements are not sufficient to estimate the parameters of the considered branch. Therefore, multiple measurements taken at different time instants will be used in the parameter estimation process for measurement redundancy, assuming that the line parameters and transformer taps are constant. The proposed method also assumes that the state estimates are available. The LAV estimator is computationally expensive, but it provides unbiased state estimates even in the presence of bad data, provided that enough measurement redundancy is available. This deficiency will be eliminated by performing local parameter estimation.