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Physical activity recognition is an important research area in pervasive computing because of its importance for e-healthcare, security, and human-machine interaction. Among various approaches, passive radio frequency sensing is a well-tried radar principle that has potential to provide the unique solution for non-invasive activity detection and recognition. However, this technology is still far from mature. This paper presents a novel hidden Markov model-based log-likelihood matrix for characterizing the Doppler shifts to break the fixed sliding window limitation in traditional feature extraction approaches. We prove the effectiveness of the proposed feature extraction method by K-means & K-medoids clustering algorithms with experimental Doppler data gathered from a passive radar system. The results show that the time adaptive log-likelihood matrix outperforms the traditional singular value decomposition …