In this proposed approach to unobtrusive human activity classification, a two-stage machine learning-based algorithm was applied to backscattered ultrawideband radar signals. First, a preprocessing step was applied for noise and clutter suppression. Then, feature extraction and a combination of time-frequency (TF) and time-range (TR) domains were used to extract the features of human activities. Then, feature analysis was performed to determine robust features relative to this kind of classification and reduce the dimensionality of the feature vector. Subsequently, different recognition algorithms were applied to group activities as fall or non-fall and categorise their types. Finally, a performance study was used to choose the higher accuracy algorithm. The ensemble bagged tree and fine K-nearest neighbour methods showed the best performance. The results show that the two-stage classification was more accurate than the one-stage. Finally, it was observed that the proposed approach using a combination of TR and TF domains with two-stage recognition outperformed reference approaches mentioned in the literature, with average accuracies of 95.8% for eight-activities classification and 96.9% in distinguishing between fall and non-fall activities with efficient computational complexity.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.