Localization is one of the current challenges in indoor navigation research. The conventional global positioning system (GPS) is affected by weak signal strengths due to high levels of signal interference and fading in indoor environments. Therefore, new positioning solutions tailored for indoor environments need to be developed. In this paper, we propose a deep learning approach for indoor localization. However, the performance of a deep learning system depends on the quality of the feature representation. This paper introduces two novel feature set extractions based on the continuous wavelet transforms (CWT) of the received signal strength indicators’ (RSSI) data. The two novel CWT feature sets were augmented with additive white Gaussian noise. The first feature set is CWT image-based, and the second is composed of the CWT PSD numerical data that were dimensionally equalized using principal component analysis (PCA). These proposed image and numerical data feature sets were both evaluated using CNN and ANN models with the goal of identifying the room that the human subject was in and estimating the precise location of the human subject in that particular room. Extensive experiments were conducted to generate the proposed augmented CWT feature set and numerical CWT PSD feature set using two analyzing functions, namely, Morlet and Morse. For validation purposes, the performance of the two proposed feature sets were compared with each other and other existing feature set formulations. The accuracy, precision and recall results show that the proposed feature sets performed better than the conventional feature sets used to validate the study. Similarly, the mean localization error generated by the proposed feature set predictions was less than those of the conventional feature sets used in indoor localization. More particularly, the proposed augmented CWT-image feature set outperformed the augmented CWT-PSD numerical feature set. The results also show that the Morse-based feature sets trained with CNN produced the best indoor positioning results compared to all Morlet and ANN-based feature set formulations.