In this study, a three-layered bidirectional Long Short-term Memory (Bi-LSTM) with residual attention, named as RONet, is proposed to achieve localization using range measurements. Accordingly, we acquired our own datasets and tested RONet using realistic conditions. It is shown that the RONet can estimate the position of the mobile robot in real time using the Nvidia Jetson AGX Xavier based only on range measurements. We also analyzed the sequence length of LSTM as a type of hyperparameters. We found that optimal sequence length is eight for more than eight anchors and twelve for fewer anchors compared to sequences with different lengths, given that construction of the network with the optimal sequence length estimates the position precisely and accounts for uncertainties. As verified experimentally, RONet yields more precise performance and results in increased robustness against outliers compared to a conventional range-only approach based on a particle filtering and the other conventional deep-learning-based approaches. We set three cases, reduced the number of anchors, and verified that the RONet was a robust solution. We also confirmed that it is the best solution that yields the smallest Root-Mean-Square-Error (RMSE) values, equal to 4.466 cm, 3.210 cm, and 3.090 cm, in the cases where three, five, and eight anchors were deployed, respectively.