One of the popular techniques for solving GPS pseudorange nonlinear quadratic equations to obtain the receiver's position and clock bias involves linearizing the equations and solving them by the least-squares (LS) scheme, which is based on the L2 minimization criterion. When outliers are a problem, LS estimation scheme may not be the best approach because the LS estimator minimizes the mean squared error of the observations. This paper discusses the implementation aspects of L1 and L∞ criteria, and their outlier resistance performance for GPS positioning. Three ordinary differential equation formulation schemes and corresponding circuits of neuron-like analogue L1 (least-absolute), L∞ (minimax), and L2 (least-squares) processors will be employed for GPS navigation processing. The circuits of simple neuron-like analogue processors are employed essentially for solving systems of linear equations. Experiments on single epoch and thereafter kinematic positioning will be conducted by computer simulation for investigating the outlier resistance performance for the least-absolute and minimax schemes as compared to the one provided by the least-squares scheme.