In this study, we evaluate artificial neural network (ANN) models that estimate the positions of gamma-ray sources from plastic scintillating fiber (PSF)-based radiation detection systems using different filtering ratios. The PSF-based radiation detection system consists of a single-stranded PSF, two photomultiplier tubes (PMTs) that transform the scintillation signals into electric signals, amplifiers, and a data acquisition system (DAQ). The source used to evaluate the system is Cs-137, with a photopeak of 662 keV and a dose rate of about 5 μSv/h. We construct ANN models with the same structure but different training data. For the training data, we selected a measurement time of 1 minute to secure a sufficient number of data points. Conversely, we chose a measurement time of 10 seconds for extracting time-difference data from the primary data, followed by filtering. During the filtering process, we identified the peak heights of the gaussian-fitted curves obtained from the histogram of the time-difference data, and extracted the data located above the height which is equal to the peak height multiplied by a predetermined percentage. We used percentage values of 0, 20, 40, and 60 for the filtering. The results indicate that the filtering has an effect on the position estimation error, which we define as the absolute value of the difference between the estimated source position and the actual source position. The estimation of the ANN model trained with raw data for the training data shows a total average error of 1.391 m, while the ANN model trained with 20%-filtered data for the training data shows a total average error of 0.263 m. Similarly, the 40%-filtered data result shows a total average error of 0.119 m, and the 60%-filtered data result shows a total average error of 0.0452 m. From the perspective of the total average error, it is clear that the more data are filtered, the more accurate the result is. Further study will be conducted to optimize the filtering ratio for the system and measuring time by evaluating stabilization time for position estimation of the source.