In this paper, back-propagation (BP) neural networks (NN) are applied to the GPS satellite Geometric Dilution of Precision (GDOP) approximation. The methods using BPNN are general enough to be applicable regardless of the number of satellite signals being processed by the receiver. BPNN is employed to learn the functional relationships firstly, between the entries of a measurement matrix and the eigenvalues and thus generate GDOP, and secondly, between the entries of a measurement matrix and the GDOP, both without inverting a matrix. Consequently, two sets of entries and two sets of output variables, respectively, are used that in total yield four types of mapping architectures. Simulation results from these four architectures are presented. The performance and computational benefit of neural network-based GDOP approximation are explored.