The conventional matrix inversion method for weighted geometric dilution of precision (WGDOP) calculation has a large amount of operation. This paper employs an artificial neural network approach, namely, the resilient back-propagation (Rprop) method to implement WGDOP. We also present two novel architectures to implement the Rprop-based WGDOP. Simulation results show that the proposed architectures always yield superior estimation accuracy with much reduced computational complexity, compared to conventional implementation methods for WGDOP. The proposed architectures are applicable not only to global positioning system (GPS) but also to wireless sensor networks (WSN) and cellular communication systems regardless of the number of the measurement units. To further reduce the complexity, we propose to combine the serving base station (BS) and the optimal three measurements with minimum WGDOP to reduce the number of subsets in cellular communication systems.