Addressing the problems facing the elderly, whether living independently or in managed care facilities, is considered one of the most important applications for action recognition research. However, existing systems are not ready for automation, or for effective use in continuous operation. Therefore, we have developed theoretical and practical foundations for a new real-time action recognition system. This system is based on Hidden Markov Model (HMM) along with colorizing depth maps. The use of depth cameras provides privacy protection. Colorizing depth images in the hue color space enables compressing and visualizing depth data, and detecting persons. The specific detector used for person detection is You Look Only Once (YOLOv5). Appearance and motion features are extracted from depth map sequences and are represented with a Histogram of Oriented Gradients (HOG). These HOG feature vectors are transformed as the observation sequences and then fed into the HMM. Finally, the Viterbi Algorithm is applied to recognize the sequential actions. This system has been tested on real-world data featuring three participants in a care center. We tried out three combinations of HMM with classification algorithms and found that a fusion with Support Vector Machine (SVM) had the best average results, achieving an accuracy rate (84.04%).