The Least Squares (LS) approach has been widely used for solving GPS Navigation problems. Despite its many superior properties, however, the LS estimate can be sensitive to outliers, and its performance, in terms of accuracy and statistical inferences, may be compromised when the errors are large and heterogeneous. The GPS signal is strongly affected by multipath propagation errors. The LS is not able to cope with the above condition to provide a useful and plausible solution. In this paper, an alternative approach, based on the Least Absolute Deviation (LAD) criterion, for estimating Navigation solutions is carried out. As a robust estimator, the LAD estimator is known to approximately produce maximum-likelihood estimation. In this case, the maximum-likelihood estimator is obtained by minimizing the mean absolute deviation, rather than the mean square deviation, and, accordingly, can perform robust and effective estimations. Unlike the LS method, the LAD method is not as sensitive to outliers and, so, may provide more robust estimates. Therefore, the LAD method provides a useful and plausible Navigation solution. Simulation results show that the method can effectively mitigate GPS multipath errors.