The health status of an elderly person can be identified by examining the additive effects of aging along with disease linked to it and can lead to ‘unstable incapacity’. This health status is determined by the apparent decline of independence in activities of daily living (ADLs). Detecting ADLs provides possibilities of improving the home life of elderly people as it can be applied to fall detection systems. This paper presents fall detection in elderly people based on radar image classification by examining their daily routine activities, using radar data that were previously collected for 99 volunteers. Machine learning techniques are used classify six human activities, namely walking, sitting, standing, picking up objects, drinking water and fall events. Different machine learning algorithms, such as random forest, K-nearest neighbours, support vector machine, long short-term memory, bi-directional long short-term memory and convolutional neural networks, were used for data classification. To obtain optimum results, we applied data processing techniques, such as principal component analysis and data augmentation, to the available radar images. The aim of this paper is to improve upon the results achieved using a publicly available dataset to further improve upon research of fall detection systems. It was found out that the best results were obtained using the CNN algorithm with principal component analysis and data augmentation together to obtain a result of 95.30% accuracy. The results also demonstrated that principal component analysis was most beneficial when the training data were expanded by augmentation of the available data. The results of our proposed approach, in comparison to the state of the art, have shown the highest accuracy.