Geometric dilution of precision (GDOP) represents the geometric effect on the relationship between measurement error and positioning determination error. If the measurement variances are equal in each other, GDOP could be the most appropriate selection criterion of location measurement units. The object of this paper is to obtain the optimal position estimates from the available measurement. The conventional matrix inversion method for GDOP calculation has a large amount of operation, which would be a burden for real time application. This paper employs an artificial neural network approach, namely, the resilient back-propagation (Rprop) method to implement GDOP. This paper also presents two novel architectures to implement the Rprop-based GDOP for the 2D location estimation. Simulation results show that the proposed architectures always yield superior estimation accuracy with much reduced computational complexity, compared to conventional implementation methods for GDOP. The proposed architectures are applicable to cellular communication systems regardless of the number of the measurement units.