The dual-frequency signals of GPS can be used to measure the total electron content (TEC). The differential instrumental biases inherent in GPS satellite and receivers are considered as the main sources of error, and they must be removed for an accurate estimation of TEC. We aim at developing an effective method to solve the difficulties involved in the TEC measurement; there are only a few usable ground receivers, especially in lower-latitude areas near the geomagnetic equator where large ionospheric variability exists. For this purpose a new parameter estimation method based on a residual minimization training neural network is applied to determination of the GPS receiver biases. The alternative method is realized by making use of the excellent features of neural networks to approximate a wide range of mapping functions, for which the network training is carried out by minimizing squared residuals of integral equation. To determine receiver biases (unknown parameters), we used additional neural networks, each of which consists of only one neuron without an input channel. It is assumed that satellite biases have already been determined by applying the least squares method to the GEONET data gathered by a large number of receivers. Various cases of observation data for different seasons, different local times, and different geographic locations of the receiver as well as the cases of model data are analyzed, and it is confirmed that the method is very effective for a small number of receivers located in the lower-latitude areas.